Method, device and equipment for analyzing performance of particle damper of steel rail

Abstract

The invention provides a method, a device and equipment for analyzing the performance of a particle damper of a steel rail, which can be applied to the technical field of vibration reduction simulation. The performance analysis method for the particle damper of the steel rail comprises the steps that a steel rail particle finite element model is obtained, and a multi-order steel rail modal damping ratio is measured; applying multi-order modal excitation frequencies to the steel rail particle finite element model to obtain steel rail structure energy consumption and shell displacement excitation corresponding to each order of modal excitation frequency; applying a plurality of shell displacement excitations to the particle damper contact model, and determining particle structure energy consumption of the particle damper corresponding to each order of modal excitation frequency; based on an energy accumulation method, according to the particle structure energy consumption, the steel rail structure energy consumption and the measured steel rail modal damping ratio, the additional damping ratio, corresponding to the modal excitation frequency of each order, of the particle damper is obtained; and based on the multiple additional damping ratios and the measured multi-order steel rail modal damping ratio, analyzing the particle damper in the steel rail to obtain a target performance analysis result.

Description

Technical Field

[0001] The present disclosure relates to the technical field of vibration damping simulation, and more particularly to a method, device, and equipment for performance analysis of a particle damper for a rail. Background Art

[0002] As a vibration damping device with good vibration damping effect, particle dampers are widely used in various fields, such as aerospace, vehicle assembly, rail vibration damping, etc. Before installing the particle damper at the corresponding position of the rail, the performance of the particle damper in the rail can be obtained based on the characteristics of the particle damper and the parameters of the rail, so as to optimize the particle damper.

[0003] In the process of implementing the above inventive concept, the inventors found that: due to the structural characteristics and force characteristics of the particle damper, it is difficult to accurately evaluate the performance of the particle damper in the rail by using the existing technology, so it is difficult to optimize the particle damper. At the same time, due to the long calculation period and large resource consumption of the existing technology, the efficiency of performance evaluation is poor, the cost is high, and the uncertainty is high, so it is difficult to be applied to industrial production. Summary of the Invention

[0004] In view of the above problems, the present disclosure provides a method, device, and equipment for performance analysis of a particle damper for a rail.

[0005] According to a first aspect of the present disclosure, there is provided a method for performance analysis of a particle damper for a rail, including: obtaining a finite element model of a rail particle and measuring multi-order rail modal damping ratios, where the finite element model of the rail particle is a model obtained by simulating a rail installed with a particle damper; applying multi-order modal excitation frequencies to the finite element model of the rail particle to obtain the rail structure energy consumption of the rail and the housing displacement excitation of the particle damper corresponding to each order of the multi-order modal excitation frequencies; applying a plurality of housing displacement excitations to the particle damper contact model, and determining the particle structure energy consumption of the particle damper corresponding to each order of the modal excitation frequencies by the discrete element method, where the particle damper contact model is constructed based on the structural parameters of the particle damper and the modal excitation frequencies; based on the cumulative energy method, obtaining the additional damping ratio of the particle damper corresponding to each order of the modal excitation frequencies according to the particle structure energy consumption, the rail structure energy consumption, and the measured rail modal damping ratios corresponding to each order of the modal excitation frequencies; and analyzing the particle damper in the rail based on a plurality of additional damping ratios and the measured multi-order rail modal damping ratios to obtain a target performance analysis result, where the target performance analysis result includes a multi-order rail response analysis result.

[0006] According to an embodiment of the present disclosure, by applying multi-order modal excitation frequencies to the finite element model of the rail particles, the rail structure energy dissipation of the rail corresponding to each of the multi-order modal excitation frequencies and the housing displacement excitation of the particle damper are obtained, including: applying multi-order modal excitation frequencies to the finite element model of the rail particles to obtain the rail modal cumulative energy dissipation values and the housing displacement excitations corresponding to each of the modal excitation frequencies; using the finite element method to extract and process multiple rail modal cumulative energy dissipation values to obtain the rail modal cumulative energy dissipation time history curves corresponding to each of the modal excitation frequencies, wherein the rail modal cumulative energy dissipation time history curve represents the modal cumulative energy dissipation value continuously output by the rail installed with the particle damper within a predetermined period; according to the rail modal cumulative energy dissipation time history curves corresponding to each of the modal excitation frequencies, the rail structure energy dissipation corresponding to each of the modal excitation frequencies is obtained.

[0007] According to an embodiment of the present disclosure, the particle damper contact model includes a housing model and a particle model located inside the housing model;

[0008] Applying multiple housing displacement excitations to the particle damper contact model, and determining the particle structure energy dissipation of the particle damper corresponding to each of the modal excitation frequencies by the discrete element method, including: for any one of the multi-order modal excitation frequencies, applying the housing displacement excitation corresponding to the any one of the modal excitation frequencies to the housing model to obtain the excitation resultant force and the particle force received by the housing model, wherein the excitation resultant force represents the driving force received by the housing model due to the housing displacement excitation, and the particle force represents the force received by the housing model from the particle model; obtaining the external resultant force received by the housing model according to the excitation resultant force and the particle force; performing integral processing on the external resultant force and the housing model displacement information to obtain the external work of the housing model corresponding to any one of the modal excitation frequencies, wherein the housing model displacement information represents the displacement generated by the housing model driven by the housing displacement excitation; according to the external work corresponding to each of the modal excitation frequencies and the change in mechanical energy of the particle model corresponding to each of the modal excitation frequencies, the particle structure energy dissipation of the particle damper corresponding to each of the modal excitation frequencies is obtained.

[0009] According to an embodiment of the present disclosure, applying the housing displacement excitation corresponding to any one of the modal excitation frequencies to the housing model to obtain the excitation resultant force and the particle force received by the housing model, including: applying the housing displacement excitation corresponding to any one of the modal excitation frequencies to the housing model to obtain the housing model displacement information; obtaining the housing acceleration response information of the housing model by performing derivative processing on the housing model displacement information; obtaining the excitation resultant force received by the housing model according to the housing acceleration response information and the mass information of the housing model; obtaining the particle force received by the housing model according to the particle structure parameter information and the particle displacement parameter information of the particle model.

[0010] According to an embodiment of the present disclosure, the particle model includes I particles, where I is a positive integer greater than 1; according to the particle structure parameter information and particle displacement parameter information of the particle model, the particle force received by the housing model is obtained, including: for the i-th particle among the I particles, according to the particle structure parameter information and particle displacement parameter information, the normal resultant force and tangential resultant force between the I - 1 particles other than the i-th particle and the i-th particle among the I particles are obtained, where 1 ≤ i ≤ I; according to the normal resultant force and tangential resultant force between the I - 1 particles and the i-th particle, the particle control equation and motion state equation of the i-th particle are constructed; based on the particle control equation and motion state equation of the i-th particle, according to the normal resultant force and tangential resultant force between the I - 1 particles and the i-th particle, the force exerted by the i-th particle on the housing model is obtained; according to the sum of the forces exerted by the I particles on the housing model, the particle force received by the housing model is obtained.

[0011] According to an embodiment of the present disclosure, the mechanical energy change amount includes the kinetic energy change amount and potential energy change amount of the particle model; according to the external force work corresponding to each order of modal excitation frequency and the mechanical energy change amount of the particle model corresponding to each order of modal excitation frequency, the particle structure energy dissipation of the particle damper contact model corresponding to each order of modal excitation frequency is obtained, including: using the discrete element method, according to the particle structure parameter information, particle mass information, and particle motion velocity information corresponding to each order of modal excitation frequency of the particle model, the kinetic energy change amount corresponding to each order of modal excitation frequency is calculated; using the discrete element method, according to the particle structure parameter information, gravitational acceleration, and particle motion position corresponding to each order of modal excitation frequency, the potential energy change amount corresponding to each order of modal excitation frequency is calculated; according to the external force work corresponding to each order of modal excitation frequency and the difference between the kinetic energy change amount and potential energy change amount corresponding to each order of modal excitation frequency, the particle structure energy dissipation of the particle damper contact model is obtained.

[0012] According to an embodiment of the present disclosure, based on multiple additional damping ratios and measuring the multi-order rail modal damping ratios, the particle damper in the rail is analyzed to obtain the target performance analysis result, including: adding the additional damping ratio corresponding to each order of modal excitation frequency to the measured multi-order rail modal damping ratios to obtain the multi-order target rail modal damping ratios; based on the predetermined rail state information, according to the multi-order target rail modal damping ratios, the multi-order rail response analysis results corresponding to the multi-order target rail modal damping ratios are evaluated.

[0013] According to an embodiment of the present disclosure, obtaining a finite element model of a rail particle and measuring multi-order rail modal damping ratios includes: obtaining an equivalent damping block corresponding to a particle damper, where the mass parameter of the equivalent damping block is equal to the mass parameter of the particle damper; installing the equivalent damping block in the rail according to the predetermined installation position information of the particle damper to obtain a rail installed with the equivalent damping block; performing a modal test on the rail installed with the equivalent damping block to obtain the measured rail modal information, where the measured modal information includes measured multi-order rail modal frequencies, measured multi-order rail modal vibration modes, and measured multi-order rail modal damping ratios; and obtaining a finite element model of a rail particle based on the measured modal information, the rail parameters of the rail, and the structural parameters of the equivalent damping block.

[0014] According to an embodiment of the present disclosure, obtaining a finite element model of a rail particle based on the measured rail modal information, the rail parameters of the rail, and the structural parameters of the equivalent damping block includes: constructing an initial model of a rail particle according to the rail parameters of the rail and the structural parameters of the equivalent damping block; performing a modal test on the initial model of a rail particle to obtain intermediate modal information, where the intermediate modal information includes intermediate multi-order rail modal damping ratios; and adjusting the initial model of a rail particle based on the measured multi-order rail modal damping ratios and the intermediate multi-order rail modal damping ratios to obtain a finite element model of a rail particle.

[0015] A second aspect of the present disclosure provides an apparatus for analyzing the performance of a particle damper of a rail, including: an acquisition module configured to acquire a finite element model of a rail particle and measured multi-order rail modal damping ratios, where the finite element model of a rail particle is a model obtained by simulating a rail installed with a particle damper; a first obtaining module configured to obtain the rail structural energy consumption of the rail and the housing displacement excitation of the particle damper corresponding to each order of modal excitation frequency in the multi-order modal excitation frequencies by applying multi-order modal excitation frequencies to the finite element model of a rail particle; a determination module configured to apply a plurality of housing displacement excitations to a particle damper contact model and determine the particle structural energy consumption of the particle damper corresponding to each order of modal excitation frequency by means of the discrete element method, where the particle damper contact model is constructed according to the structural parameters of the particle damper and the modal excitation frequency; a second obtaining module configured to obtain the additional damping ratio of the particle damper corresponding to each order of modal excitation frequency based on the cumulative energy method, according to the particle structural energy consumption, the rail structural energy consumption, and the measured rail modal damping ratio corresponding to each order of modal excitation frequency; and an analysis module configured to analyze the particle damper in the rail based on a plurality of additional damping ratios and the measured multi-order rail modal damping ratios to obtain a target performance analysis result, where the target performance analysis result includes a multi-order rail response analysis result.

[0016] A third aspect of the present disclosure provides an electronic device, including: one or more processors; a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors are caused to execute the above method.

[0017] A fourth aspect of the present disclosure further provides a computer-readable storage medium having executable instructions stored thereon, which when executed by a processor cause the processor to execute the above method.

[0018] A fifth aspect of the present disclosure further provides a computer program product including a computer program, which when executed by a processor implements the above method.

[0019] According to the method, device and equipment for performance analysis of a particle damper of a steel rail of the present disclosure, by first obtaining a finite element model of the steel rail particles and measuring the multi-order modal damping ratio of the steel rail, and then applying multi-order modal excitation frequencies to the finite element model of the steel rail particles, the rail structure energy consumption of the steel rail corresponding to each order of modal excitation frequency and the housing displacement excitation of the particle damper are obtained. Thus, the obtained multiple housing displacement excitations are applied to the constructed particle damper contact model to determine the particle structure energy consumption of the particle damper corresponding to each order of modal excitation frequency by using the discrete element method. Then, based on the cumulative energy method, according to the particle structure energy consumption, rail structure energy consumption corresponding to each order of modal excitation frequency and the measured rail modal damping ratio obtained above, the additional damping ratio of the particle damper corresponding to each order of modal excitation frequency is calculated. The multiple additional damping ratios are added to the measured multi-order rail modal damping ratio to obtain a linear damping ratio that can be equivalent to the steel rail including the particle damper, so as to analyze the particle damper in the steel rail and obtain the target performance analysis result. It realizes that by based on the energy method, damping ratio calculation, model acquisition and simulation verification, when the particle damper on the steel rail receives impact excitation, information such as the collision and friction between particles inside the particle damper, the force of the particles on the housing, and the external force received by the housing caused by the vibration is analyzed, comprehensively and accurately describes the vibration reduction mechanism and vibration reduction performance of the particle damper in the steel rail, obtains the accurate additional damping ratio of the particle damper, and at the same time analogizes the relationship between the additional damping ratio provided by the particle damper and the dissipated energy, so as to add it to the measured multi-order rail modal damping ratio (linear damping ratio) of the original steel rail to obtain a linear damping ratio of the entire structure that can be equivalent to the steel rail including the particle damper, which is convenient for performance analysis and obtains a target performance analysis result with excellent effect and high accuracy.

[0020] According to an embodiment of the present disclosure, further, the method of the present disclosure has strong adaptability and can adapt to different types of excitation conditions and particulate materials. Furthermore, it can effectively handle vibration problems in a variety of frequency ranges, especially the performance analysis of particulate dampers under dynamic loads such as random excitation. Through equivalent linearization processing, a complex nonlinear system can be simplified into a linear model, thereby reducing computational complexity, improving the processing efficiency of performance analysis and the robustness of the model, reducing processing costs and resource consumption rates, and quickly evaluating the effects of different design parameters (such as particulate filling rate, particle size, etc.) on the damping and vibration reduction effects, so as to facilitate the optimal design of the structure of the particulate damper, so that the particulate damper can exert excellent vibration reduction effects on the rail and can be widely applied to industrial production and other aspects. Description of the Drawings

[0021] Through the following description of the embodiments of the present disclosure with reference to the drawings, the above content and other objects, features, and advantages of the present disclosure will become clearer. In the drawings:

[0022] Figure 1 The application scenario diagram of the method for performance analysis of the particulate damper of the rail according to an embodiment of the present disclosure is shown;

[0023] Figure 2 The flowchart of the method for performance analysis of the particulate damper of the rail according to an embodiment of the present disclosure is shown;

[0024] Figure 3 The schematic diagram of the cumulative energy dissipation time history curve of the rail mode according to an embodiment of the present disclosure is shown;

[0025] Figure 4 The schematic diagram of the particulate force of the particulate in the particulate damper on the housing according to an embodiment of the present disclosure is shown;

[0026] Figure 5 The schematic diagram of the housing model displacement of the particulate damper according to an embodiment of the present disclosure is shown;

[0027] Figure 6 The schematic diagram of the total kinetic energy and total potential energy of the particulate in the particulate damper according to an embodiment of the present disclosure is shown;

[0028] Figure 7 The structural block diagram of the device for performance analysis of the particulate damper of the rail according to an embodiment of the present disclosure is shown;

[0029] Figure 8 The block diagram of the electronic device of the method for performance analysis of the particulate damper of the rail according to an embodiment of the present disclosure is shown. Detailed Embodiments

[0030] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present disclosure. In the following detailed description, for the sake of explanation, numerous specific details are set forth in order to provide a comprehensive understanding of the embodiments of the present disclosure. However, it is obvious that one or more embodiments can also be implemented without these specific details. In addition, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessarily obscuring the concepts of the present disclosure.

[0031] The terms used herein are merely for describing specific embodiments and are not intended to limit the present disclosure. The terms "including", "comprising", etc. used herein indicate the presence of the described features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0032] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein should be interpreted as having a meaning consistent with the context of this specification and should not be interpreted in an idealized or overly rigid manner.

[0033] In the case of using expressions such as "at least one of A, B, and C, etc.", generally, it should be interpreted according to the meaning commonly understood by those skilled in the art (for example, "a system having at least one of A, B, and C" should include, but not be limited to, a system having only A, only B, only C, having A and B, having A and C, having B and C, and / or having A, B, and C, etc.).

[0034] In the technical solutions of the present disclosure, the user information involved (including but not limited to user personal information, user image information, user device information, such as location information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) are all information and data that have been authorized by the user or fully authorized by all parties. Moreover, the processing of relevant data, such as collection, storage, use, processing, transmission, provision, disclosure, and application, etc., all comply with relevant laws, regulations, and standards, adopt necessary confidentiality measures, do not violate public order and good customs, and provide corresponding operation entrances for users to choose to authorize or refuse.

[0035] Due to the advantages of a relatively wide applicable temperature range and adaptability to harsh environments, particle dampers are widely used in various fields, such as aerospace, vehicle assembly, rail vibration reduction, etc. Before installing the particle damper on the rail, it is necessary to conduct performance tests on the rail structure containing the particle damper, so as to optimize and adjust parameters such as the structure and installation position of the particle damper in combination with the obtained performance analysis results, so that the particle damper can achieve a relatively prominent vibration reduction effect and reduce the vibration received by the rail.

[0036] The existing method for performing performance tests on the rail structure containing particle dampers relies on the coupled simulation of the discrete element method and the finite element method. However, due to the complex structure and force of the particle damper, the calculation period of this method is long and the resource consumption is high, making it difficult to accurately analyze the performance, and thus unable to optimize the design of the particle damper. During the research and development process, the researchers found that due to the structural and force characteristics of the particle damper, it is difficult to accurately evaluate the performance of the particle damper in the rail using existing technologies, making it difficult to optimize the particle damper. At the same time, due to the long calculation period and large resource consumption of existing technologies, the efficiency of performance evaluation is poor, the cost is high, and the uncertainty is high, making it difficult to be applicable to industrial production technical problems.

[0037] In view of this, the embodiments of the present disclosure provide a method for analyzing the performance of a particle damper of a rail, including: obtaining a finite element model of rail particles and measuring the multi-order modal damping ratio of the rail, where the finite element model of rail particles is a model obtained by simulating the rail installed with a particle damper; applying multi-order modal excitation frequencies to the finite element model of rail particles to obtain the rail structure energy consumption of the rail and the housing displacement excitation of the particle damper corresponding to each order of modal excitation frequency in the multi-order modal excitation frequencies; applying multiple housing displacement excitations to the particle damper contact model, and determining the particle structure energy consumption of the particle damper corresponding to each order of modal excitation frequency through the discrete element method, where the particle damper contact model is constructed based on the structural parameters and modal excitation frequency of the particle damper; based on the cumulative energy method, according to the particle structure energy consumption, rail structure energy consumption, and measured rail modal damping ratio corresponding to each order of modal excitation frequency, obtaining the additional damping ratio of the particle damper corresponding to each order of modal excitation frequency; based on multiple additional damping ratios and the measured multi-order modal damping ratio of the rail, analyzing the particle damper in the rail to obtain a target performance analysis result, where the target performance analysis result includes a multi-order rail response analysis result.

[0038] Figure 1 The application scenario diagram of the method for analyzing the performance of a particle damper of a rail according to the embodiments of the present disclosure is shown.

[0039] As Figure 1As shown, the application scenario according to this embodiment may include an excitation device 101, a target track 102, and a processor 103. The excitation device 101 is used to send an excitation signal to the target track 102.

[0040] The user can use the excitation device 101 to interact with the target track 102 and the processor 103 to receive or send signals, etc.

[0041] The processor 103 may be a processor that receives various structural parameter information. For example, it receives and processes the parameters of the track and the particle damper obtained after the excitation device 101 acts on the target track 102 (only for example). The processor 103 can analyze and process data such as the received parameters of the track and the particle damper, and feedback the processing results (such as obtaining or generating relevant analysis data according to user requests, etc.) to the terminal device.

[0042] It should be noted that the method for analyzing the performance of the particle damper of the steel rail provided by the embodiments of the present invention can generally be executed by the processor 103. Correspondingly, the device for analyzing the performance of the particle damper of the steel rail provided by the embodiments of the present invention can generally be set in the processor 103. The method for analyzing the performance of the particle damper of the steel rail provided by the embodiments of the present invention can also be executed by a processor or a processor cluster different from the processor 103 and capable of communicating with the excitation device 101, the target track 102, and / or the processor 103. Correspondingly, the device for analyzing the performance of the particle damper of the steel rail provided by the embodiments of the present invention can also be set in a processor or a processor cluster different from the processor 103 and capable of communicating with the excitation device 101, the target track 102, and / or the processor 103.

[0043] It should be understood, Figure 1 The numbers of the excitation device, the target track, and the processor in

[0044] are merely illustrative. According to the implementation requirements, there can be any number of excitation devices, target tracks, and processors. Figure 1 The following will be based on Figures 2 - 6 the described scenario, and will describe in detail the method for analyzing the performance of the particle damper of the steel rail of the disclosed embodiments through

[0045] Figure 2 shows a flowchart of the method for analyzing the performance of the particle damper of the steel rail according to the embodiments of the present disclosure.

[0046] As Figure 2 shown, the method for analyzing the performance of the particle damper of the steel rail in this embodiment includes operations S210 to S250.

[0047] In operation S210, a finite element model of the steel rail particles is obtained and the measured multi-order modal damping ratios of the steel rail are obtained.

[0048] According to an embodiment of the present disclosure, the finite element model of the rail particles is a model obtained by simulating the rail installed with a particle damper.

[0049] According to an embodiment of the present disclosure, since the established finite element model of the rail particles is approximately equivalent to the actual rail installed with a particle damper, the measurement of the multi-order rail modal damping ratio can be obtained after a modal test on the rail installed with a particle damper, or can be obtained after a modal test on the finite element model of the rail particles. The multi-order rail modal damping ratios obtained after the modal test on the rail installed with a particle damper and the multi-order rail modal damping ratios obtained after the modal test on the finite element model of the rail particles are equal.

[0050] In operation S220, by applying multi-order modal excitation frequencies to the finite element model of the rail particles, the rail structural energy consumption of the rail corresponding to each of the multi-order modal excitation frequencies and the housing displacement excitation of the particle damper are obtained.

[0051] According to an embodiment of the present disclosure, the rail structural energy consumption characterizes the structural energy consumption of the rail including the particle damper, and the housing displacement excitation can characterize the vibration displacement generated due to vibration.

[0052] For example, multi-period first-order modal excitation frequencies, multi-period second-order modal excitation frequencies, and multi-period third-order modal excitation frequencies are respectively applied to the finite element model of the rail particles to obtain the rail structural energy consumption of the rail corresponding to any period of the first-order modal excitation frequency and the housing displacement excitation of the particle damper, the rail structural energy consumption of the rail corresponding to any period of the second-order modal excitation frequency and the housing displacement excitation of the particle damper, and the rail structural energy consumption of the rail corresponding to any period of the third-order modal excitation frequency and the housing displacement excitation of the particle damper.

[0053] In operation S230, multiple housing displacement excitations are applied to the particle damper contact model, and the particle structural energy consumption of the particle damper corresponding to each order of modal excitation frequency is determined by the discrete element method.

[0054] According to an embodiment of the present disclosure, the particle damper contact model is constructed based on the structural parameters of the particle damper and the modal excitation frequency.

[0055] According to an embodiment of the present disclosure, the housing displacement excitations corresponding to each order of modal excitation frequency obtained by applying multi-order modal excitation frequencies to the finite element model of the rail particles are respectively applied to the particle damper contact model, so as to determine the particle structural energy consumption of the particle damper corresponding to each order of modal excitation frequency according to the discrete element method.

[0056] In operation S240, based on the cumulative energy method, the additional damping ratios of the particle damper corresponding to each order of modal excitation frequency are obtained according to the particle structure energy dissipation, the rail structure energy dissipation, and the measured rail modal damping ratio corresponding to each order of modal excitation frequency.

[0057] According to an embodiment of the present disclosure, by analyzing information such as the collision and friction between particles in the particle damper, the force exerted by the particles on the housing, and the external force received by the housing, etc., it is convenient to describe the vibration reduction performance of the particle damper in multiple aspects and dimensions, and an accurate additional damping ratio is obtained.

[0058] In operation S250, based on multiple additional damping ratios and the measured multi-order rail modal damping ratios, the particle damper in the rail is analyzed to obtain the target performance analysis result.

[0059] According to an embodiment of the present disclosure, the target performance analysis result includes the multi-order rail response analysis result.

[0060] According to an embodiment of the present disclosure, the obtained additional damping ratios corresponding to each order of modal excitation frequency are added to the linear measured multi-order rail modal damping ratios, so that the non-linear damping ratio of the particle damper is equivalent to the linear damping ratio of the entire structure of the rail including the particle damper. Furthermore, the vibration reduction performance of the particle damper can be analyzed, and according to the ideal state information, the rail response analysis results corresponding to each order of modal excitation frequency are obtained, that is, the multi-order rail response analysis results.

[0061] According to an embodiment of the present disclosure, by first obtaining a finite element model of rail particles and measuring the multi-order modal damping ratios of the rail, and then applying multi-order modal excitation frequencies to the finite element model of the rail particles, the rail structure energy dissipation of the rail corresponding to each order of modal excitation frequency and the housing displacement excitation of the particle damper are obtained. Thereby, the obtained multiple housing displacement excitations are applied to the constructed particle damper contact model to determine the particle structure energy dissipation of the particle damper corresponding to each order of modal excitation frequency by using the discrete element method. Then, based on the cumulative energy method, according to the particle structure energy dissipation, the rail structure energy dissipation corresponding to each order of modal excitation frequency, and the measured rail modal damping ratio obtained above, the additional damping ratio of the particle damper corresponding to each order of modal excitation frequency is calculated. The multiple additional damping ratios are added to the measured multi-order rail modal damping ratios to obtain a linear damping ratio that can be equivalent to the rail including the particle damper, thereby analyzing the particle damper in the rail to obtain the target performance analysis result. It realizes that by based on the energy method, damping ratio calculation, model acquisition and simulation verification, when the particle damper on the rail is subjected to impact excitation, the information such as the collision and friction between particles inside the particle damper, the force of the particles on the housing, and the external force received by the housing caused by the vibration is analyzed, comprehensively and accurately describes the vibration reduction mechanism and vibration reduction performance of the particle damper in the rail, obtains the accurate additional damping ratio of the particle damper, and at the same time analogizes the relationship between the additional damping ratio provided by the particle damper and the dissipated energy, so as to add it to the measured multi-order rail modal damping ratio (linear damping ratio) of the original rail to obtain the linear damping ratio of the entire structure that can be equivalent to the rail including the particle damper, which is convenient for performance analysis and obtains the target performance analysis result with excellent effect and high accuracy.

[0062] According to an embodiment of the present disclosure, further, the method of the present disclosure has strong adaptability and can adapt to different types of excitation conditions and particle materials, and can thus effectively handle vibration problems in a variety of frequency ranges, especially the performance analysis of particle dampers under dynamic loads such as random excitation. Through equivalent linearization processing, a complex nonlinear system can be simplified into a linear model, thereby reducing the computational complexity, improving the processing efficiency of performance analysis and the robustness of the model, reducing the processing cost and resource consumption rate, and can quickly evaluate the influence of different design parameters (such as particle filling rate, particle size, etc.) on the damping and vibration reduction effect, so as to facilitate the optimal design of the structure of the particle damper, so that the particle damper can play an excellent vibration reduction effect on the rail and can be widely applied to industrial production and other aspects.

[0063] According to an embodiment of the present disclosure, the method for obtaining a finite element model of rail particles and measuring the multi-order modal damping ratios of the rail includes the following operations.

[0064] According to an embodiment of the present disclosure, an equivalent damping block corresponding to the particle damper is obtained.

[0065] According to an embodiment of the present disclosure, the mass parameter of the equivalent damping block is equal to the mass parameter of the particle damper.

[0066] According to an embodiment of the present disclosure, the mass parameter of the equivalent damping block can be calculated according to formula (1), and formula (1) is shown as follows.

[0067] (1);

[0068] Wherein, M can represent the mass parameter of the equivalent damping block, M c can represent the mass of the housing of the particle damper, M' can represent the mass of the particles in the particle damper, n can represent the number of particles, can represent the filling rate of the particles in the particle damper.

[0069] According to an embodiment of the present disclosure, according to the predetermined installation position information of the particle damper, the equivalent damping block is installed in the rail to obtain a rail installed with the equivalent damping block.

[0070] According to an embodiment of the present disclosure, since the mass parameter of the equivalent damping block is equal to the mass parameter of the particle damper, that is, the equivalent damping block is approximated as a particle damper, so that installing the equivalent damper at the predetermined installation position on the rail is equivalent to installing the particle damper at the predetermined installation position on the rail, which is convenient for analyzing the vibration reduction performance of various different types of particle dampers.

[0071] According to an embodiment of the present disclosure, a modal test is performed on the rail installed with the equivalent damping block to obtain the measured rail modal information of the rail.

[0072] According to an embodiment of the present disclosure, the measured modal information includes measuring multiple-order rail modal frequencies, measuring multiple-order rail modal vibration modes, and measuring multiple-order rail modal damping ratios.

[0073] According to an embodiment of the present disclosure, according to the obtained measured multiple-order rail modal frequencies, measured multiple-order rail modal vibration modes, and measured multiple-order rail modal damping ratios of the rail, it is convenient to train and adjust parameter information such as boundary parameters in the initial rail particle finite element model during the process of establishing the model to obtain an accurate rail particle finite element model, and the actually measured multiple-order rail modal damping ratio obtained by measurement can be used as the original damping ratio of the original rail, so that the additional damping ratio obtained subsequently can be added to the accurate original damping ratio to obtain a linear damping ratio that can be equivalent to the entire structure of the rail including the particle damper.

[0074] According to an embodiment of the present disclosure, based on the measured modal information, a rail particle finite element model is obtained according to the rail parameters of the rail and the structural parameters of the equivalent damping block.

[0075] According to an embodiment of the present disclosure, by obtaining an equivalent damping block corresponding to a particle damper, and according to the predetermined installation position information of the particle damper, the equivalent damping block is installed at a predetermined position of the rail. A modal test is performed on the rail installed with the equivalent damping block to obtain the measured rail modal information of the rail. Based on the measured modal information, according to the rail parameters of the rail and the structural parameters of the equivalent damping block, a rail particle finite element model is constructed, realizing the simplification of a complex non-linear model system into a linear model, reducing the work complexity. At the same time, using an equivalent mass block to replace the particle damper, the equivalent damping block can be arbitrarily replaced and changed according to the parameters of the particle damper, improving the processing efficiency and facilitating the construction of the model.

[0076] According to an embodiment of the present disclosure, based on the measured rail modal information, the method for obtaining a rail particle finite element model according to the rail parameters of the rail and the structural parameters of the equivalent damping block includes the following operations.

[0077] According to an embodiment of the present disclosure, a rail particle initial model is constructed according to the rail parameters of the rail and the structural parameters of the equivalent damping block.

[0078] According to an embodiment of the present disclosure, the rail parameters may include parameter information such as the material, structure, and weight of the rail, but are not limited thereto. The structural parameters of the equivalent damping block may include structural parameter information such as the weight of the particles, the weight of the housing, the filling rate of the particles, the number of particles, and the size of the equivalent mass block, but are not limited thereto.

[0079] According to an embodiment of the present disclosure, a modal test is performed on the rail particle initial model to obtain intermediate modal information.

[0080] According to an embodiment of the present disclosure, the intermediate modal information includes intermediate multi-order rail modal damping ratios.

[0081] According to an embodiment of the present disclosure, based on the measured multi-order rail modal damping ratios and the intermediate multi-order rail modal damping ratios, the rail particle initial model is adjusted to obtain a rail particle finite element model.

[0082] According to an embodiment of the present disclosure, in the case where the difference between the measured multi-order rail modal damping ratios and the intermediate multi-order rail modal damping ratios is greater than a predetermined threshold or even the measured multi-order rail modal damping ratios and the intermediate multi-order rail modal damping ratios are not equal, the model parameters and boundary constraint conditions of the rail particle initial model are adjusted and set, so as to obtain a rail particle finite element model that can output a difference between the intermediate multi-order rail modal damping ratios and the measured multi-order rail modal damping ratios less than the predetermined threshold or even the measured multi-order rail modal damping ratios are equal to the intermediate multi-order rail modal damping ratios after the modal experiment.

[0083] According to an embodiment of the present disclosure, an initial rail particle model is constructed based on the rail parameters of the rail and the structural parameters of the equivalent damping block. A modal test is performed on the initial rail particle model to obtain the intermediate multi-order rail modal damping ratios. The measured multi-order rail modal damping ratios are compared with the intermediate multi-order rail modal damping ratios, so as to adjust the initial rail particle model, and a finite element model of the rail particles is obtained, realizing the construction of a model of the rail that can accurately include particle dampers. Through the verification and comparison of the actually measured modal data and the data obtained from the tests on the model, the model parameters and boundary constraint conditions are continuously adjusted to obtain the initial rail particle model.

[0084] According to an embodiment of the present disclosure, a method for obtaining the rail structural energy consumption of the rail and the housing displacement excitation of the particle damper corresponding to each order of modal excitation frequency in the multi-order modal excitation frequencies by applying the multi-order modal excitation frequencies to the finite element model of the rail particles includes the following operations.

[0085] According to an embodiment of the present disclosure, the multi-order modal excitation frequencies are applied to the finite element model of the rail particles to obtain the rail modal cumulative energy consumption values and the housing displacement excitations corresponding to each order of modal excitation frequency.

[0086] According to an embodiment of the present disclosure, each order of modal excitation frequency applied to the finite element model of the rail particles is the multi-period each order of modal excitation frequency. For example, a first-order modal excitation frequency including 5 periods is applied to the finite element model of the rail particles, and a second-order modal excitation frequency including 10 periods is applied to the finite element model of the rail particles.

[0087] According to an embodiment of the present disclosure, after applying the multi-order modal excitation frequencies to the finite element model of the rail particles, the vibration displacements generated by the particle damper at the multi-order modal excitation frequencies are obtained. According to the vibration displacements corresponding to each order of modal excitation frequency, a vibration displacement function is obtained, thereby generating the housing displacement excitation.

[0088] For example, the first-order modal excitation frequency, the second-order modal excitation frequency, and the third-order modal excitation frequency can be respectively applied to the finite element model of the rail particles to obtain the rail modal cumulative energy consumption value and the vibration displacement of the particle damper at the first-order modal excitation frequency, the rail modal cumulative energy consumption value and the vibration displacement of the particle damper at the second-order modal excitation frequency, and the rail modal cumulative energy consumption value and the vibration displacement of the particle damper at the third-order modal excitation frequency. According to the vibration displacements of the particle damper at the first-order modal excitation frequency, the second-order modal excitation frequency, and the third-order modal excitation frequency respectively, the vibration displacement functions corresponding to each order of modal excitation frequency are obtained, thereby generating the housing displacement excitation at the first-order modal excitation frequency, the housing displacement excitation at the second-order modal excitation frequency, and the housing displacement excitation at the third-order modal excitation frequency.

[0089] According to an embodiment of the present disclosure, the finite element method is used to extract and process the cumulative energy dissipation values of multiple rail modes, and the cumulative energy dissipation time history curves of the rail corresponding to the excitation frequencies of each order of mode are obtained.

[0090] According to an embodiment of the present disclosure, the cumulative energy dissipation time history curve of the rail mode characterizes the cumulative energy dissipation value continuously output by the rail installed with the particle damper within a predetermined period.

[0091] According to an embodiment of the present disclosure, based on the cumulative energy dissipation time history curves of the rail corresponding to the excitation frequencies of each order of mode, the structural energy dissipation of the rail corresponding to the excitation frequencies of each order of mode is obtained.

[0092] According to an embodiment of the present disclosure, since the modal excitation frequencies applied to the rail particle finite element model are all multi-period modal excitation frequencies, it is only necessary to obtain the cumulative energy dissipation time history curve of the rail mode within one period based on the cumulative energy dissipation value of the rail mode within one period, so as to obtain the structural energy dissipation of the rail corresponding to the excitation frequencies of each order of mode under one period.

[0093] According to an embodiment of the present disclosure, by applying multi-order modal excitation frequencies to the rail particle finite element model, the cumulative energy dissipation values of the rail mode and the shell displacement excitation corresponding to the excitation frequencies of each order of mode can be obtained. Then, the finite element method is used to extract and process the cumulative energy dissipation values of multiple rail modes to obtain the cumulative energy dissipation time history curves of the rail corresponding to the excitation frequencies of each order of mode. The structural energy dissipation of the rail corresponding to the excitation frequencies of each order of mode is obtained from the cumulative energy dissipation time history curves of the rail corresponding to the excitation frequencies of each order of mode, realizing the acquisition of the structural energy dissipation of the rail containing the particle damper under each order of modal excitation frequency, so as to calculate the additional damping ratio of the particle damper using the obtained structural energy dissipation.

[0094] Figure 3 A schematic diagram showing the cumulative energy dissipation time history curve of the rail mode of the rail according to an embodiment of the present disclosure is shown.

[0095] As Figure 3 shown, Figure 3 The cumulative energy dissipation time history curve of the rail mode is shown. The abscissa can be characterized as time, and the ordinate can be characterized as the energy dissipation value. It can be seen from the figure that when any order of modal excitation frequency is applied to the rail particle finite element model, the longer the time of applying the excitation frequency, the more the cumulative energy dissipation of the rail mode.

[0096] According to an embodiment of the present disclosure, the particle damper contact model includes a shell model and a particle model located inside the shell model.

[0097] According to an embodiment of the present disclosure, based on parameter information of a particle damper, such as particle parameters, damper parameters, the vibration displacement function (displacement response) of the particle damper at the first-order modal excitation frequency, and the first-order modal excitation frequency, a Hertz contact model, i.e., a particle damper contact model, is constructed.

[0098] According to an embodiment of the present disclosure, the method for determining the energy dissipation of the particle structure of the particle damper corresponding to each order of modal excitation frequency by applying a plurality of housing displacement excitations to the particle damper contact model through the discrete element method includes the following operations.

[0099] According to an embodiment of the present disclosure, for any one of the multi-order modal excitation frequencies,

[0100] According to an embodiment of the present disclosure, a housing displacement excitation corresponding to any one of the modal excitation frequencies is applied to the housing model to obtain the resultant excitation force and the particle force received by the housing model.

[0101] According to an embodiment of the present disclosure, the resultant excitation force represents the driving force exerted on the housing model by the housing displacement excitation, and the particle force represents the force exerted on the housing model by the particle model.

[0102] According to an embodiment of the present disclosure, the method for obtaining the resultant excitation force and the particle force received by the housing model by applying a housing displacement excitation corresponding to any one of the modal excitation frequencies to the housing model includes the following operations.

[0103] According to an embodiment of the present disclosure, a housing displacement excitation corresponding to any one of the modal excitation frequencies is applied to the housing model to obtain the housing model displacement information.

[0104] According to an embodiment of the present disclosure, the housing model displacement information can be obtained according to the expression of formula (2).

[0105] (2);

[0106] Wherein, u can represent the housing model displacement information, A can represent the amplitude of the housing, w can represent the angular frequency of the housing, t can represent the time, can represent the phase difference of the housing, and B can represent the offset of the housing.

[0107] According to an embodiment of the present disclosure, by performing a derivative process on the housing model displacement information, the housing acceleration response information of the housing model is obtained.

[0108] According to an embodiment of the present disclosure, the housing acceleration response information can be obtained according to the expression of formula (3).

[0109] (3);

[0110] Among them, it can be characterized as the housing acceleration response information.

[0111] According to an embodiment of the present disclosure, based on the housing acceleration response information and the mass information of the housing model, the resultant exciting force acting on the housing model is obtained.

[0112] According to an embodiment of the present disclosure, the resultant exciting force acting on the housing model can be calculated according to formula (4), and formula (4) is shown as follows.

[0113] (4);

[0114] Among them, it can be characterized as the resultant exciting force acting on the housing model.

[0115] According to an embodiment of the present disclosure, when a housing displacement excitation is applied to the housing model, by differentiating the housing model displacement information, the housing acceleration response information is obtained, so that based on the housing acceleration response information and the mass of the housing, the resultant exciting force acting on the housing model is obtained, fully considering the influence of the external force acting on the housing model under the structural parameters of the particle damper on its damping effect.

[0116] According to an embodiment of the present disclosure, based on the particle structure parameter information and the particle displacement parameter information of the particle model, the particle force acting on the housing model is obtained.

[0117] According to an embodiment of the present disclosure, the particle model may include I particles, where I is a positive integer greater than 1.

[0118] According to an embodiment of the present disclosure, the method for obtaining the particle force acting on the housing model based on the particle structure parameter information and the particle displacement parameter information of the particle model includes the following operations.

[0119] According to an embodiment of the present disclosure, for the i-th particle among the I particles, based on the particle structure parameter information and the particle displacement parameter information, the normal resultant force and the tangential resultant force between the I - 1 particles other than the i-th particle and the i-th particle among the I particles are obtained, where 1 ≤ i ≤ I.

[0120] According to an embodiment of the present disclosure, the particle structure parameter information may include parameters such as Young's modulus, Poisson's ratio, shear modulus, elastic coefficient of the particle material, particle radius, particle mass, etc. of the particle material, but is not limited to the above information. The particle displacement parameter information may include parameters such as the normal relative velocity, tangential relative velocity of the particles, normal overlap amount between particles or between particles and the inner cavity wall of the housing, distance between any two particles, tangential relative displacement, etc. under the housing displacement excitation, but is not limited to the above information.

[0121] According to an embodiment of the present disclosure, the normal resultant force between any one of the I - 1 particles other than the i-th particle and the i-th particle among the I particles can be calculated according to Equation (5), and Equation (5) is as follows.

[0122] (5);

[0123] where, F n1 can be characterized as the normal resultant force between any one of the I - 1 particles other than the i-th particle and the i-th particle among the I particles, F kn can be characterized as the normal elastic force between any one of the I - 1 particles other than the i-th particle and the i-th particle among the I particles, F cn can be characterized as the normal viscous damping force between any one of the I - 1 particles other than the i-th particle and the i-th particle among the I particles, r can be characterized as the particle radius, E can be characterized as the Young's modulus of the particle material, v can be characterized as the Poisson's ratio of the particle material, D ij can be characterized as the distance between the centers of the spheres of any one of the I - 1 particles other than the i-th particle and the i-th particle among the I particles, m can be characterized as the particle mass, k n can be characterized as the elastic coefficient of the particle, v n can be characterized as the normal relative velocity of the particle.

[0124] According to an embodiment of the present disclosure, the normal resultant force between the I - 1 particles other than the i-th particle and the i-th particle among the I particles can be obtained from the sum of the normal resultant forces between each of the I - 1 particles other than the i-th particle and the i-th particle.

[0125] According to an embodiment of the present disclosure, the tangential resultant force between any one of the I - 1 particles other than the i-th particle and the i-th particle among the I particles can be calculated according to Equation (6), and Equation (6) is as follows.

[0126] (6);

[0127] where, F t1 can be characterized as the tangential resultant force between any one of the I - 1 particles other than the i-th particle and the i-th particle among the I particles, F kt can be characterized as the tangential acting force between any one of the I - 1 particles other than the i-th particle and the i-th particle among the I particles, F ctIt can be characterized as the tangential viscous damping force between any one of the I - 1 particles other than the i-th particle and the i-th particle among the I particles. G can be characterized as the shear modulus of the particle material, D n It can be characterized as the normal overlap between particles or between a particle and the inner cavity wall of the shell, D t It can be characterized as the tangential relative displacement of the particle under the excitation of the shell displacement, v t It can be characterized as the tangential relative velocity of the particle under the excitation of the shell displacement.

[0128] According to an embodiment of the present disclosure, the tangential resultant force between the I - 1 particles other than the i-th particle and the i-th particle among the I particles can be obtained according to the sum of the tangential resultant forces between each of the I - 1 particles other than the i-th particle and the i-th particle.

[0129] According to an embodiment of the present disclosure, based on the normal resultant force and tangential resultant force between the I - 1 particles and the i-th particle, the particle control equation and the motion state equation of the i-th particle are constructed.

[0130] According to an embodiment of the present disclosure, the particle control equation of the i-th particle can be obtained according to formula (7), and the motion state equation of the i-th particle can be represented according to formula (8).

[0131] (7);

[0132] Where, m i It can be characterized as the particle mass of the i-th particle, p i It can be characterized as the displacement vector of the i-th particle under the action of the shell displacement excitation, k i It can be characterized as the total number of particles in contact with the i-th particle. j can be characterized as the j-th particle among the total number of particles in contact with the i-th particle, F n It can be characterized as the sum of the normal resultant forces between each of the I - 1 particles other than the i-th particle and the i-th particle among the I particles, F t It can be characterized as the sum of the tangential resultant forces between each of the I - 1 particles other than the i-th particle and the i-th particle among the I particles, It can be characterized as the angular velocity of rotation of the i-th particle under the action of the shell displacement excitation. R can be characterized as the radius of rotation of the i-th particle under the action of the shell displacement excitation, g can be characterized as the acceleration due to gravity.

[0133] (8);

[0134] Where, I i It can be characterized as the moment of inertia of the i-th particle, can be characterized as the angular displacement vector of the i-th particle under the action of the housing displacement excitation, T ij can be characterized as the torque exerted on the i-th particle by the tangential contact force of the j-th particle.

[0135] According to an embodiment of the present disclosure, based on the particle control equation and the motion state equation of the i-th particle, and according to the normal resultant force and the tangential resultant force between the I-1 particles and the i-th particle, the force exerted by the i-th particle on the housing model is obtained.

[0136] According to an embodiment of the present disclosure, based on the sum of the forces exerted by the I particles on the housing model, the particle force received by the housing model is obtained.

[0137] According to an embodiment of the present disclosure, the above operations are performed on each particle to obtain the force exerted by each particle on the housing model, and the sum of the forces exerted by each particle on the housing model is processed to obtain the total particle force received by the housing model.

[0138] According to an embodiment of the present disclosure, for the i-th particle among the I particles, according to the particle structure parameter information and the particle displacement parameter information, the normal resultant force and the tangential resultant force between the I-1 particles other than the i-th particle and the i-th particle in the I particles are obtained. According to the normal resultant force and the tangential resultant force between the I-1 particles and the i-th particle, the particle control equation and the motion state equation of the i-th particle are constructed. Then, based on the particle control equation and the motion state equation of the i-th particle, and according to the normal resultant force and the tangential resultant force between the I-1 particles and the i-th particle, the force exerted by the i-th particle on the housing model is obtained. The sum of the forces exerted by each particle on the housing model is processed to obtain the particle force received by the housing model. It is realized that under the action of the housing displacement excitation, the normal resultant force and the tangential resultant force between the particles during the movement are fully considered, so as to obtain the accurate particle force on the housing due to the collision and friction of the particles, so as to fully consider the influence of the forces generated by the particle filling rate, particle size, collision and friction on the damping effect, obtain the additional damping ratio of the accurate particle damper, and then accurately analyze the vibration reduction performance of the particle damper, improving the calculation efficiency.

[0139] According to an embodiment of the present disclosure, a shell displacement excitation corresponding to any order modal excitation frequency is applied to the shell model to obtain the shell model displacement information. Then, the obtained shell model displacement information is differentiated to obtain the shell acceleration response information of the shell model. Based on the shell acceleration response information and the mass information of the shell model, the resultant excitation force received by the shell model is obtained. And based on the particle structure parameter information and particle displacement parameter information of the relevant particle model, the particle force exerted on the shell model is obtained. It realizes that under the action of the shell displacement excitation, the total resultant excitation force received by the shell, the total particle force exerted by the particles on the shell, and the relevant structure parameters of the particles and the shell are fully integrated to obtain the accurate result of the force analysis of the shell model, so as to obtain the additional damping ratio according to the result of the force analysis of the shell model.

[0140] Figure 4 FIG. shows a schematic diagram of the particle force exerted by the particles on the shell in the particle damper according to an embodiment of the present disclosure. Figure 5 FIG. shows a schematic diagram of the shell model displacement of the particle damper according to an embodiment of the present disclosure.

[0141] As Figure 4 shown, Figure 4 FIG. shows the particle force exerted by the particles on the shell. The abscissa can represent time, and the ordinate can represent the applied particle force. It can be seen from the figure that when a multi-periodic shell displacement excitation is applied to the particle damper contact model, the particle force exerted by the particles on the shell changes periodically in the same manner as the multi-periodic shell displacement excitation. When the shell displacement excitation in a certain period is large, the change of the particle force exerted by the particles on the shell is also periodic and the force is large. When the shell displacement excitation in a certain period is small, the change of the particle force exerted by the particles on the shell is also periodic but the force is small.

[0142] As Figure 5 shown, Figure 5 FIG. shows the shell model displacement of the particle damper. The abscissa can represent time, and the ordinate can represent the displacement distance. When a multi-periodic shell displacement excitation is applied to the particle damper contact model, the displacement distance of the shell model changes periodically as the application time of the shell displacement excitation increases.

[0143] According to an embodiment of the present disclosure, it can be seen from Figure 4 and Figure 5 that the periodic change of the shell model displacement and the periodic change of the particle force exerted by the particles on the shell are approximately the same.

[0144] According to an embodiment of the present disclosure, based on the resultant excitation force and the particle force, the resultant external force received by the shell model is obtained.

[0145] According to an embodiment of the present disclosure, a curve fitting is performed on the function of the particle force using the discrete element method to obtain a fitting curve of the particle force.

[0146] According to an embodiment of the present disclosure, the fitting curve of the particle force can be obtained according to the expression of formula (9).

[0147] (9);

[0148] where s can represent the fitting curve of the particle force, A' can represent the amplitude of the particle, can represent the angular frequency of the particle, can represent the phase difference of the particle.

[0149] According to an embodiment of the present disclosure, the sum of the fitting values obtained from the fitting curve of the particle force and the excitation resultant force is calculated to obtain the resultant external force received by the housing model. Among them, since both the particle force and the excitation resultant force are multi-periodic forces, the resultant external force obtained is also a multi-periodic force.

[0150] According to an embodiment of the present disclosure, integral processing is performed on the resultant external force and the displacement information of the housing model to obtain the external work done on the housing model corresponding to any order modal excitation frequency.

[0151] According to an embodiment of the present disclosure, the displacement information of the housing model represents the displacement generated by the housing model under the drive of the housing displacement excitation.

[0152] According to an embodiment of the present disclosure, integral processing is performed on the information in any one period of the multi-periodic resultant external force and the multi-periodic displacement information of the housing model to obtain the external work done on the housing model corresponding to any order modal excitation frequency. Among them, any one period can be the last period.

[0153] According to an embodiment of the present disclosure, the external work done on the housing model can be calculated according to formula (10), and formula (10) is shown as follows.

[0154] (10);

[0155] where E d can represent the external work done, T1 can represent the initial time of any one period, T2 can represent the end time of any one period, f d can represent the resultant external force.

[0156] According to an embodiment of the present disclosure, based on the external work done corresponding to each order modal excitation frequency and the change in mechanical energy of the particle model corresponding to each order modal excitation frequency, the particle energy dissipation value of the particle damper corresponding to each order modal excitation frequency is obtained.

[0157] According to an embodiment of the present disclosure, the change in mechanical energy includes the change in kinetic energy and the change in potential energy of the particle model.

[0158] According to an embodiment of the present disclosure, a method for obtaining the energy dissipation of the particle structure of the particle damper contact model corresponding to each modal excitation frequency based on the work done by the external force corresponding to each modal excitation frequency and the change in mechanical energy of the particle model corresponding to each modal excitation frequency includes the following operations.

[0159] According to an embodiment of the present disclosure, the discrete element method is used to calculate the change in kinetic energy corresponding to each modal excitation frequency based on the particle structure parameter information, particle mass information, and particle motion velocity information corresponding to each modal excitation frequency of the particle model.

[0160] According to an embodiment of the present disclosure, the kinetic energy can be calculated according to formula (11), and formula (11) is shown as follows.

[0161] (11);

[0162] Wherein, E k can be characterized as kinetic energy, I can be characterized as I particles, and V i can be characterized as the velocity of the i-th particle.

[0163] According to an embodiment of the present disclosure, the change in kinetic energy can be obtained by subtracting the kinetic energy corresponding to the initial time of the period with the same period as the obtained work done by the external force from the kinetic energy corresponding to the termination time of the period with the same period as the obtained work done by the external force.

[0164] According to an embodiment of the present disclosure, the discrete element method is used to calculate the change in potential energy corresponding to each modal excitation frequency based on the particle structure parameter information, gravitational acceleration, and particle motion position corresponding to each modal excitation frequency.

[0165] According to an embodiment of the present disclosure, the potential energy can be calculated according to formula (12), and formula (12) is shown as follows.

[0166] (12);

[0167] Wherein, Ep can be characterized as potential energy, and h i can be characterized as the position information of the i-th particle in the shell model.

[0168] According to an embodiment of the present disclosure, the change in potential energy can be obtained by subtracting the potential energy corresponding to the initial time of the period with the same period as the obtained work done by the external force from the potential energy corresponding to the termination time of the period with the same period as the obtained work done by the external force.

[0169] According to an embodiment of the present disclosure, the energy dissipation of the particle structure of the particle damper contact model is obtained based on the difference between the work done by the external force corresponding to each order of modal excitation frequency and the change in kinetic energy and the change in potential energy corresponding to each order of modal excitation frequency.

[0170] According to an embodiment of the present disclosure, the difference obtained by subtracting the change in kinetic energy corresponding to any one period of each order of modal excitation frequency from the work done by the external force corresponding to any one period of each order of modal excitation frequency, and then subtracting the change in potential energy corresponding to any one period of each order of modal excitation frequency is the energy dissipation of the particle structure corresponding to each order of modal excitation frequency. For example, the difference obtained by subtracting the change in kinetic energy corresponding to the 5th period of the first-order modal excitation frequency from the work done by the external force corresponding to the 5th period of the first-order modal excitation frequency, and then subtracting the change in potential energy corresponding to the 5th period of the first-order modal excitation frequency is the energy dissipation of the particle structure corresponding to the first-order modal excitation frequency. The difference obtained by subtracting the change in kinetic energy corresponding to the 10th period of the second-order modal excitation frequency from the work done by the external force corresponding to the 10th period of the second-order modal excitation frequency, and then subtracting the change in potential energy corresponding to the 10th period of the second-order modal excitation frequency is the energy dissipation of the particle structure corresponding to the second-order modal excitation frequency.

[0171] According to an embodiment of the present disclosure, for any one order of modal excitation frequency among multiple orders of modal excitation frequencies, a shell displacement excitation corresponding to any one order of modal excitation frequency is applied to the shell model to obtain the resultant excitation force and particle force received by the shell model, and based on this, the resultant external force received by the shell model is obtained. Then, integral processing is performed on the resultant external force and the shell model displacement information to obtain the work done by the external force of the shell model. Further, based on the particle structure parameter information, particle mass information, and particle motion velocity information corresponding to each order of modal excitation frequency of the particle model using the discrete element method, the change in kinetic energy corresponding to each order of modal excitation frequency is obtained. Based on the particle structure parameter information, gravitational acceleration, and particle motion position corresponding to each order of modal excitation frequency, the change in potential energy corresponding to each order of modal excitation frequency is obtained. Based on the difference between the work done by the external force corresponding to each order of modal excitation frequency and the change in kinetic energy and the change in potential energy, the energy dissipation of the particle structure of the particle damper contact model is obtained. It realizes a full analysis of the influence of various parameters such as particle filling rate, particle size, and force on the damping effect, and at the same time, a full analysis of the energy consumed by particle collisions and friction is also carried out, so as to accurately describe the vibration reduction mechanism of the particle damper and obtain the accurate energy dissipation of the particle structure of the particle damper contact model, which is equivalent to the energy dissipation of the particle structure of the particle damper located on the rail, in order to obtain the non-linear additional damping ratio within a variety of excitation frequency ranges.

[0172] Figure 6 Shows a schematic diagram of the total kinetic energy and total potential energy of the particles in the particle damper according to an embodiment of the present disclosure.

[0173] As shown Figure 6 in Figure 6 the figure, the total kinetic energy and total potential energy of the particles in the particle damper are shown. The abscissa can be characterized as time, and the ordinate can be characterized as the total kinetic energy and total potential energy. A period can be characterized between the two circles in the figure. The sum of the kinetic energy change and potential energy change can be obtained by subtracting the total kinetic energy and total potential energy corresponding to the points in the first circle from the total kinetic energy and total potential energy corresponding to the points in the second circle. The kinetic energy and potential energy also change periodically.

[0174] According to an embodiment of the present disclosure, a method for analyzing a particle damper in a rail and obtaining a target performance analysis result based on a plurality of additional damping ratios and measuring multi-order rail modal damping ratios includes the following operations.

[0175] According to an embodiment of the present disclosure, the additional damping ratios corresponding to the modal excitation frequencies of each order are added to the measured multi-order rail modal damping ratios to obtain multi-order target rail modal damping ratios.

[0176] According to an embodiment of the present disclosure, the additional damping ratio can be calculated according to formula (13), and formula (13) is shown as follows.

[0177] (13);

[0178] Wherein, can be characterized as the additional damping ratio, can be characterized as the measured rail modal damping ratio, can be characterized as the energy dissipation of the particle structure, E c can be characterized as the energy dissipation of the rail structure.

[0179] According to an embodiment of the present disclosure, the measured rail modal damping ratios of each order in adding the additional damping ratios corresponding to the modal excitation frequencies of each order to the measured multi-order rail modal damping ratios are used to obtain the target rail modal damping ratios of each order. For example, the additional damping ratio corresponding to the first-order modal excitation frequency is added to the measured first-order rail modal damping ratio to obtain the first-order target rail modal damping ratio, and the additional damping ratio corresponding to the second-order modal excitation frequency is added to the measured second-order rail modal damping ratio to obtain the second-order target rail modal damping ratio.

[0180] According to an embodiment of the present disclosure, based on predetermined rail state information, multi-order rail response analysis results corresponding to the multi-order target rail modal damping ratios are evaluated according to the multi-order target rail modal damping ratios.

[0181] For example, based on the predetermined rail state information of the ideal first order, an evaluation is performed according to the difference between the first order target rail modal damping ratio and the predetermined rail state information of the first order, and a first order rail response analysis result corresponding to the first order target rail modal damping ratio is obtained. Based on the predetermined rail state information of the ideal second order, an evaluation is performed according to the difference between the second order target rail modal damping ratio and the predetermined rail state information of the first order, and a second order rail response analysis result corresponding to the second order target rail modal damping ratio is obtained.

[0182] According to an embodiment of the present disclosure, the rail response analysis result may include whether the particle damper of the current particle parameter structure has a performance that meets the expected vibration reduction effect, and the adjustment and optimization direction of the relevant particle structure parameters of the particle damper.

[0183] According to an embodiment of the present disclosure, by adding the additional damping ratio corresponding to each order of modal excitation frequency to the measured multi-order rail modal damping ratio, a multi-order target rail modal damping ratio is obtained. Based on the predetermined rail state information, according to the multi-order target rail modal damping ratio, a multi-order rail response analysis result corresponding to the multi-order target rail modal damping ratio is evaluated, realizing the influence under the consideration of various structural parameters, force conditions and various excitation conditions, obtaining an accurate non-linear additional damping ratio, and through equivalent linearization processing, adding the non-linear additional damping ratio to the measured multi-order rail modal damping ratio (linear damping ratio) of the original rail, obtaining a linear damping ratio that can be equivalent to the entire structure of the rail including the particle damper, thereby simplifying the non-linear system into a linear model, reducing the calculation complexity, improving the processing efficiency of performance analysis and the robustness of the model, reducing the processing cost and resource consumption rate, so as to facilitate the analysis according to the predetermined rail state information and obtain a multi-order target rail modal damping ratio with excellent effect and high accuracy.

[0184] Figure 7 The structural block diagram of the device for performance analysis of the particle damper of the rail according to an embodiment of the present disclosure is shown.

[0185] As Figure 7 shown, the device for performance analysis of the particle damper of the rail in this embodiment includes: an acquisition module 710, a first obtaining module 720, a determination module 730, a second obtaining module 740, and an analysis module 750.

[0186] The acquisition module 710 is configured to acquire a rail particle finite element model and a measured multi-order rail modal damping ratio, wherein the rail particle finite element model is a model obtained by simulating a rail installed with a particle damper. The acquisition module 710 can be used to perform the operation S210 described above, and will not be elaborated here.

[0187] The first obtaining module 720 is configured to obtain the rail structure energy dissipation of the rail and the housing displacement excitation of the particle damper corresponding to each modal excitation frequency in the multi-order modal excitation frequencies by applying multi-order modal excitation frequencies to the finite element model of the rail particles. The first obtaining module 720 can be used to perform the operation S220 described above, which will not be elaborated here.

[0188] The determination module 730 is configured to apply a plurality of housing displacement excitations to the particle damper contact model, and determine the particle structure energy dissipation of the particle damper corresponding to each modal excitation frequency by the discrete element method, where the particle damper contact model is constructed according to the structural parameters of the particle damper and the modal excitation frequency. The determination module 730 can be used to perform the operation S230 described above, which will not be elaborated here.

[0189] The second obtaining module 740 is configured to obtain the additional damping ratio of the particle damper corresponding to each modal excitation frequency based on the cumulative energy method according to the particle structure energy dissipation, the rail structure energy dissipation, and the measured rail modal damping ratio corresponding to each modal excitation frequency. The second obtaining module 740 can be used to perform the operation S240 described above, which will not be elaborated here.

[0190] The analysis module 750 is configured to analyze the particle damper in the rail based on a plurality of additional damping ratios and the measured multi-order rail modal damping ratios to obtain a target performance analysis result, where the target performance analysis result includes a multi-order rail response analysis result. The analysis module 750 can be used to perform the operation S250 described above, which will not be elaborated here.

[0191] According to an embodiment of the present disclosure, the first obtaining module 720 includes: a first application sub-module, a first extraction sub-module, and a first obtaining sub-module.

[0192] The first application sub-module is configured to apply multi-order modal excitation frequencies to the finite element model of the rail particles to obtain the rail modal cumulative energy dissipation value and the housing displacement excitation corresponding to each modal excitation frequency.

[0193] The first extraction sub-module is configured to perform extraction processing on a plurality of rail modal cumulative energy dissipation values by the finite element method to obtain a rail modal cumulative energy dissipation time history curve corresponding to each modal excitation frequency, where the rail modal cumulative energy dissipation time history curve represents the modal cumulative energy dissipation value continuously output by the rail installed with the particle damper within a predetermined period.

[0194] The first obtaining sub-module is configured to obtain the rail structure energy dissipation corresponding to each modal excitation frequency according to the rail modal cumulative energy dissipation time history curve corresponding to each modal excitation frequency.

[0195] According to an embodiment of the present disclosure, the determination module 730 includes: a second obtaining sub-module and a third obtaining sub-module.

[0196] The second obtaining sub-module is configured to, for any one of the multi-order modal excitation frequencies, apply a shell displacement excitation corresponding to the any one of the multi-order modal excitation frequencies to the shell model, and obtain an excitation resultant force and a particle acting force received by the shell model, where the excitation resultant force represents the driving force received by the shell model due to the shell displacement excitation, and the particle acting force represents the acting force of the particle model received by the shell model; obtain an external force resultant force received by the shell model according to the excitation resultant force and the particle acting force; perform an integration process on the external force resultant force and the shell model displacement information to obtain the external work of the shell model corresponding to the any one of the multi-order modal excitation frequencies, where the shell model displacement information represents the displacement generated by the shell model driven by the shell displacement excitation.

[0197] The third obtaining sub-module is configured to obtain the particle structure energy dissipation of the particle damper corresponding to each order of modal excitation frequency according to the external work corresponding to each order of modal excitation frequency and the change in mechanical energy of the particle model corresponding to each order of modal excitation frequency.

[0198] According to an embodiment of the present disclosure, the second obtaining sub-module includes: a first application unit, a first derivative unit, a first obtaining unit, and a second obtaining unit.

[0199] The first application unit is configured to apply a shell displacement excitation corresponding to any one of the multi-order modal excitation frequencies to the shell model to obtain shell model displacement information.

[0200] The first derivative unit is configured to obtain the shell acceleration response information of the shell model by performing a derivative process on the shell model displacement information.

[0201] The first obtaining unit is configured to obtain the excitation resultant force received by the shell model according to the shell acceleration response information and the mass information of the shell model.

[0202] The second obtaining unit is configured to obtain the particle acting force received by the shell model according to the particle structure parameter information and the particle displacement parameter information of the particle model.

[0203] According to an embodiment of the present disclosure, the second obtaining unit includes: a first obtaining sub-unit, a first constructing sub-unit, a second obtaining sub-unit, and a third obtaining sub-unit.

[0204] The first obtaining sub-unit is configured to, for the i-th particle among the I particles, obtain the normal resultant force and the tangential resultant force between the I-1 particles other than the i-th particle and the i-th particle among the I particles according to the particle structure parameter information and the particle displacement parameter information, where 1 ≤ i ≤ I.

[0205] The first construction subunit is configured to construct the particle control equation and the motion state equation of the \(i\)-th particle according to the normal resultant force and the tangential resultant force between the \(I - 1\) particles and the \(i\)-th particle.

[0206] The second obtaining subunit is configured to obtain the force exerted by the \(i\)-th particle on the housing model based on the particle control equation and the motion state equation of the \(i\)-th particle according to the normal resultant force and the tangential resultant force between the \(I - 1\) particles and the \(i\)-th particle.

[0207] The third obtaining subunit is configured to obtain the particle force received by the housing model according to the sum of the forces exerted by the \(I\) particles on the housing model.

[0208] According to an embodiment of the present disclosure, the third obtaining sub-module includes: a first calculation unit, a second calculation unit, and a third obtaining unit.

[0209] The first calculation unit is configured to calculate the change in kinetic energy corresponding to each order of modal excitation frequency by using the discrete element method according to the particle structure parameter information, the particle mass information of the particle model, and the particle motion velocity information corresponding to each order of modal excitation frequency.

[0210] The second calculation unit is configured to calculate the change in potential energy corresponding to each order of modal excitation frequency by using the discrete element method according to the particle structure parameter information, the gravitational acceleration, and the particle motion position corresponding to each order of modal excitation frequency.

[0211] The third obtaining unit is configured to obtain the energy dissipation of the particle structure of the particle damper contact model according to the external work corresponding to each order of modal excitation frequency and the difference between the change in kinetic energy and the change in potential energy corresponding to each order of modal excitation frequency.

[0212] According to an embodiment of the present disclosure, the analysis module 750 includes: a first adding sub-module and a first evaluation sub-module.

[0213] The first adding sub-module is configured to add the additional damping ratio corresponding to each order of modal excitation frequency to the measured multi-order rail modal damping ratio to obtain the multi-order target rail modal damping ratio;

[0214] The first evaluation sub-module is configured to evaluate and obtain the multi-order rail response analysis results corresponding to the multi-order target rail modal damping ratio based on the predetermined rail state information according to the multi-order target rail modal damping ratio.

[0215] According to an embodiment of the present disclosure, the obtaining module 710 includes: a first obtaining sub-module, a first installation sub-module, a first test sub-module, and a fourth obtaining sub-module.

[0216] The first obtaining sub-module is configured to obtain an equivalent damping block corresponding to the particle damper, wherein the mass parameter of the equivalent damping block is equal to the mass parameter of the particle damper.

[0217] The first installation sub-module is configured to install an equivalent damping block in a rail according to the predetermined installation position information of the particle damper, so as to obtain a rail installed with the equivalent damping block.

[0218] The first test sub-module is configured to perform a modal test on the rail installed with the equivalent damping block to obtain the measured rail modal information of the rail, where the measured modal information includes measured multi-order rail modal frequencies, measured multi-order rail modal vibration modes, and measured multi-order rail modal damping ratios.

[0219] The fourth obtaining sub-module is configured to obtain a rail particle finite element model based on the measured modal information, according to the rail parameters of the rail and the structural parameters of the equivalent damping block.

[0220] According to an embodiment of the present disclosure, the fourth obtaining sub-module includes: a first construction sub-module, a second test sub-module, and a first adjustment sub-module.

[0221] The first construction sub-module is configured to construct an initial rail particle model according to the rail parameters of the rail and the structural parameters of the equivalent damping block.

[0222] The second test sub-module is configured to perform a modal test on the initial rail particle model to obtain intermediate modal information, where the intermediate modal information includes intermediate multi-order rail modal damping ratios.

[0223] The first adjustment sub-module is configured to adjust the initial rail particle model based on the measured multi-order rail modal damping ratios and the intermediate multi-order rail modal damping ratios to obtain a rail particle finite element model.

[0224] According to an embodiment of the present disclosure, any plurality of modules among the acquisition module 710, the first obtaining module 720, the determination module 730, the second obtaining module 740, and the analysis module 750 may be combined and implemented in one module, or any one of them may be split into multiple modules. Alternatively, at least part of the functions of one or more of these modules may be combined with at least part of the functions of other modules and implemented in one module. According to an embodiment of the present disclosure, at least one of the acquisition module 710, the first obtaining module 720, the determination module 730, the second obtaining module 740, and the analysis module 750 may be at least partially implemented as a hardware circuit, such as a field programmable gate array (FPGA), a programmable logic array (PLA), a system on chip, a system on substrate, a system on package, an application specific integrated circuit (ASIC), or any other reasonable manner that can integrate or package circuits, etc., implemented by hardware or firmware, or implemented in any one of the three implementation manners of software, hardware, and firmware, or in an appropriate combination of any several of them. Alternatively, at least one of the acquisition module 710, the first obtaining module 720, the determination module 730, the second obtaining module 740, and the analysis module 750 may be at least partially implemented as a computer program module, and when the computer program module is run, it can execute corresponding functions.

[0225] Figure 8 A block diagram of an electronic device showing a method for performance analysis of a particle damper for a steel rail according to an embodiment of the present disclosure.

[0226] As Figure 8 shown, the electronic device according to an embodiment of the present disclosure includes a processor 801, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 802 or a program loaded from a storage section 808 into a random access memory (RAM) 803. The processor 801 may include, for example, a general microprocessor (such as a CPU), an instruction set processor, and / or a related chipset, and / or a dedicated microprocessor (such as an application specific integrated circuit (ASIC)), etc. The processor 801 may also include on-board memory for caching purposes. The processor 801 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present disclosure.

[0227] In the RAM 803, various programs and data required for the operation of the electronic device are stored. The processor 801, the ROM 802, and the RAM 803 are connected to each other via a bus 804. The processor 801 performs various operations of the method flow according to the embodiments of the present disclosure by executing the programs in the ROM 802 and / or the RAM 803. It should be noted that the programs may also be stored in one or more memories other than the ROM 802 and the RAM 803. The processor 801 may also perform various operations of the method flow according to the embodiments of the present disclosure by executing the programs stored in the one or more memories.

[0228] According to an embodiment of the present disclosure, the electronic device may further include an input / output (I / O) interface 805, and the input / output (I / O) interface 805 is also connected to the bus 804. The electronic device may further include one or more of the following components connected to the I / O interface 805: an input portion 806 including a keyboard, a mouse, etc.; an output portion 807 including, for example, a cathode ray tube (CRT), a liquid crystal display (LCD), etc. and a speaker, etc.; a storage portion 808 including a hard disk, etc.; and a communication portion 809 including a network interface card such as a LAN card, a modem, etc. The communication portion 809 performs communication processing via a network such as the Internet. A drive 810 is also connected to the I / O interface 805 as needed. A removable medium 811, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 810 as needed so that a computer program read from it can be installed into the storage portion 808 as needed.

[0229] The present disclosure also provides a computer-readable storage medium, which may be included in the device / device / system described in the above embodiments; or may exist separately without being assembled into the device / device / system. The above computer-readable storage medium carries one or more programs, and when the one or more programs are executed, the method according to the embodiments of the present disclosure is implemented.

[0230] According to an embodiment of the present disclosure, the computer-readable storage medium may be a non-volatile computer-readable storage medium, for example, it may include but is not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above. In the present disclosure, the computer-readable storage medium may be any tangible medium that contains or stores a program, and this program can be used by or in combination with an instruction execution system, apparatus, or device. For example, according to an embodiment of the present disclosure, the computer-readable storage medium may include one or more memories other than the above-described ROM 802 and / or RAM 803 and / or ROM 802 and RAM 803.

[0231] An embodiment of the present disclosure also includes a computer program product, which includes a computer program that contains program code for executing the method shown in the flowchart. When the computer program product runs in a computer system, the program code is used to enable the computer system to implement the method for performance analysis of the particle damper of the steel rail provided by the embodiment of the present disclosure.

[0232] When the computer program is executed by the processor 801, it executes the above functions defined in the system / apparatus of the embodiment of the present disclosure. According to an embodiment of the present disclosure, the above-described systems, apparatuses, modules, units, etc. can be implemented by computer program modules.

[0233] In one embodiment, the computer program may rely on tangible storage media such as optical storage devices and magnetic storage devices. In another embodiment, the computer program may also be transmitted and distributed in the form of a signal on a network medium, and be downloaded and installed through the communication part 809, and / or be installed from the removable medium 811. The program code included in the computer program can be transmitted by any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination of the above.

[0234] In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 809, and / or be installed from the removable medium 811. When the computer program is executed by the processor 801, it executes the above functions defined in the system of the embodiment of the present disclosure. According to an embodiment of the present disclosure, the above-described systems, devices, apparatuses, modules, units, etc. can be implemented by computer program modules.

[0235] Those skilled in the art will appreciate that the features recited in the various embodiments of the present disclosure can be combined or / and combined in various ways, even if such combinations or combinations are not explicitly recited in the present disclosure. In particular, without departing from the spirit and teachings of the present disclosure, the features recited in the various embodiments of the present disclosure can be combined and / or combined in various ways. All such combinations and / or combinations fall within the scope of the present disclosure.

Claims

1. A method for analyzing the performance of a particle damper of a rail, comprising: Obtaining a rail particle finite element model and measuring multi-order rail modal damping ratios, wherein the rail particle finite element model is a model obtained by simulating a rail with a particle damper installed; Applying multi-order modal excitation frequencies to the rail particle finite element model, obtaining rail structure energy consumption of the rail and shell displacement excitation of the particle damper corresponding to each modal excitation frequency in the multi-order modal excitation frequencies; Applying a plurality of shell displacement excitations to the particle damper contact model, and determining the particle structure energy dissipation of the particle damper corresponding to each order of the modal excitation frequency by discrete element method, wherein the particle damper contact model is constructed according to the structural parameters of the particle damper and the modal excitation frequency; Based on the cumulative energy method, according to the particle structure energy consumption corresponding to the each-order modal excitation frequency, the rail structure energy consumption and the measured rail modal damping ratio, the additional damping ratio of the particle damper corresponding to the each-order modal excitation frequency is obtained; Based on the plurality of the additional damping ratios and the measured multi-order rail modal damping ratios, the particle damper in the rail is analyzed to obtain a target performance analysis result, wherein the target performance analysis result includes a multi-order rail response analysis result.

2. The method according to claim 1, wherein: The method of applying multi-order modal excitation frequencies to the rail particle finite element model to obtain the rail structure energy consumption of the rail and the shell displacement excitation of the particle damper corresponding to each modal excitation frequency in the multi-order modal excitation frequencies comprises: Applying the multi-order modal excitation frequencies to the rail particle finite element model to obtain the rail modal cumulative energy consumption value and the shell displacement excitation corresponding to the respective modal excitation frequencies; The finite element method is used to extract and process a plurality of the rail modal cumulative energy consumption values ​​to obtain a rail modal cumulative energy consumption time history curve corresponding to each order of the modal excitation frequency, wherein the rail modal cumulative energy consumption time history curve represents the modal cumulative energy consumption value continuously output by the rail equipped with the particle damper within a predetermined period of time; According to the rail modal cumulative energy consumption time history curve corresponding to the respective modal excitation frequencies, the rail structure energy consumption corresponding to the respective modal excitation frequencies is obtained.

3. The method according to claim 1, wherein: The particle damper contact model includes a shell model and a particle model located inside the shell model; The step of applying a plurality of shell displacement excitations to the particle damper contact model and determining the particle structure energy consumption of the particle damper corresponding to each order modal excitation frequency by discrete element method comprises: For any modal excitation frequency among the multiple modal excitation frequencies, Applying the shell displacement excitation corresponding to the any-order modal excitation frequency to the shell model to obtain the excitation resultant force and particle action force on the shell model, wherein the excitation resultant force represents the driving force exerted on the shell model by the shell displacement excitation, and the particle action force represents the force exerted on the shell model by the particle model; Obtaining the resultant external force on the shell model according to the excitation resultant force and the particle action force; Integrating the resultant external force and the shell model displacement information to obtain the external force work of the shell model corresponding to any modal excitation frequency, wherein the shell model displacement information represents the displacement of the shell model driven by the shell displacement excitation; According to the external force work corresponding to the various modal excitation frequencies and the mechanical energy variation of the particle model corresponding to the various modal excitation frequencies, the particle structure energy consumption of the particle damper corresponding to the various modal excitation frequencies is obtained.

4. The method according to claim 3, wherein: The step of applying the shell displacement excitation corresponding to any order modal excitation frequency to the shell model to obtain the excitation resultant force and particle action force on the shell model includes: Applying the shell displacement excitation corresponding to the any-order modal excitation frequency to the shell model to obtain the shell model displacement information; By performing a derivation process on the displacement information of the shell model, the shell acceleration response information of the shell model is obtained; Obtaining the excitation resultant force received by the shell model according to the shell acceleration response information and the mass information of the shell model; The particle force acting on the shell model is obtained according to the particle structure parameter information and the particle displacement parameter information of the particle model.

5. The method according to claim 4, wherein: The particle model includes I particles, where I is a positive integer greater than 1; The step of obtaining the particle force acting on the shell model according to the particle structure parameter information and the particle displacement parameter information of the particle model comprises: For the i-th particle among the I particles, according to the particle structure parameter information and the particle displacement parameter information, obtain the normal resultant force and the tangential resultant force between the i-th particle and I-1 particles other than the i-th particle among the I particles, wherein 1≤i≤I; Constructing a particle control equation and a motion state equation of the i-th particle according to the normal resultant force and the tangential resultant force between the i-1 particle and the i-th particle; Based on the particle control equation and the motion state equation of the i-th particle, and according to the normal resultant force and the tangential resultant force between the I-1 particle and the i-th particle, the force of the i-th particle on the shell model is obtained; According to the sum of the forces acting on the shell model by the I particles, the force acting on the shell model by the particles is obtained.

6. The method according to claim 3, wherein: The mechanical energy variation includes the kinetic energy variation and potential energy variation of the particle model; The step of obtaining the particle structure energy consumption of the particle damper contact model corresponding to each order of modal excitation frequency according to the external force work corresponding to each order of modal excitation frequency and the mechanical energy change of the particle model corresponding to each order of modal excitation frequency comprises: The kinetic energy variation corresponding to each order of modal excitation frequency is calculated using a discrete element method according to the particle structure parameter information of the particle model, the particle mass information and the particle motion speed information corresponding to each order of modal excitation frequency; The potential energy variation corresponding to each order of modal excitation frequency is calculated by using a discrete element method according to the particle structure parameter information, gravitational acceleration and the particle motion position corresponding to each order of modal excitation frequency; The particle structure energy consumption of the particle damper contact model is obtained according to the external force work corresponding to the various modal excitation frequencies and the difference between the kinetic energy change and the potential energy change corresponding to the various modal excitation frequencies.

7. The method according to claim 1, wherein: The particle damper in the rail is analyzed based on the plurality of additional damping ratios and the measured multi-order rail modal damping ratios to obtain a target performance analysis result, including: Adding the additional damping ratio corresponding to each order modal excitation frequency to the measured multi-order rail modal damping ratio to obtain a multi-order target rail modal damping ratio; Based on the predetermined rail state information and according to the multi-order target rail modal damping ratios, the multi-order rail response analysis results corresponding to the multi-order target rail modal damping ratios are evaluated and obtained.

8. The method according to claim 1, wherein: The method of obtaining a rail particle finite element model and measuring a multi-order rail modal damping ratio comprises: Acquire an equivalent damping block corresponding to the particle damper, wherein a mass parameter of the equivalent damping block is equal to a mass parameter of the particle damper; According to the predetermined installation position information of the particle damper, the equivalent damping block is installed in the rail to obtain the rail with the equivalent damping block installed; Performing a modal test on the rail with the equivalent damping block installed thereon to obtain measured rail modal information of the rail, wherein the measured modal information includes measured multi-order rail modal frequencies, measured multi-order rail modal vibration shapes, and measured multi-order rail modal damping ratios; Based on the measured modal information, the rail particle finite element model is obtained according to rail parameters of the rail and structural parameters of the equivalent damping block.

9. The method according to claim 8, wherein: The method of obtaining the rail particle finite element model based on the measured rail modal information and according to rail parameters of the rail and structural parameters of the equivalent damping block comprises: constructing an initial model of rail particles according to rail parameters of the rail and structural parameters of the equivalent damping block; Performing a modal test on the initial model of the rail particles to obtain intermediate modal information, wherein the intermediate modal information includes intermediate multi-order rail modal damping ratios; Based on the measured multi-order rail modal damping ratio and the intermediate multi-order rail modal damping ratio, the rail particle initial model is adjusted to obtain the rail particle finite element model.

10. A device for analyzing the performance of a particle damper of a rail, comprising: An acquisition module, used for acquiring a rail particle finite element model and measuring multi-order rail modal damping ratios, wherein the rail particle finite element model is a model obtained by simulating a rail with a particle damper installed; A first obtaining module is used to obtain the rail structure energy consumption of the rail and the shell displacement excitation of the particle damper corresponding to each modal excitation frequency in the multi-order modal excitation frequency by applying multi-order modal excitation frequencies to the rail particle finite element model; A determination module, used for applying a plurality of shell displacement excitations to a particle damper contact model, and determining the particle structure energy consumption of the particle damper corresponding to each order of the modal excitation frequency by a discrete element method, wherein the particle damper contact model is constructed based on the structural parameters of the particle damper and the modal excitation frequency; The second obtaining module is used to obtain the additional damping ratio of the particle damper corresponding to the respective order modal excitation frequencies based on the energy consumption of the particle structure, the energy consumption of the rail structure and the measured rail modal damping ratio corresponding to the respective order modal excitation frequencies based on the cumulative energy method; An analysis module is used to analyze the particle damper in the rail based on the plurality of additional damping ratios and the measured multi-order rail modal damping ratios to obtain a target performance analysis result, wherein the target performance analysis result includes a multi-order rail response analysis result.

11. An electronic device, comprising: one or more processors; a storage device for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors execute the method according to any one of claims 1 to 9.

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