Methods, devices, equipment, and storage media for evaluating frequency and damping variations in vehicle-axle coupled systems considering non-classical damping effects.

Abstract

This application provides a method, apparatus, device, and storage medium for evaluating the frequency and damping variations of a vehicle-bridge coupled system considering non-classical damping effects, relating to the field of bridge structural dynamics and structural modal parameter identification technology. The method includes: determining frequency and damping variation information for evaluating the dynamic characteristics of the vehicle-bridge coupled system; constructing dimensionless characterization quantities for frequency and damping variations; calculating evaluation indices to characterize the intensity of the non-classical damping effect in the vehicle-bridge coupled system, quantitatively evaluating the degree of influence of the non-classical damping effect in the vehicle-bridge coupled system; and outputting the evaluation results. This application, by introducing evaluation indices characterizing the degree of non-classical damping in the vehicle-bridge coupled system, analyzes the variation patterns of system frequency and damping parameters within a unified analytical framework, achieving a quantitative analysis of the applicability of existing frequency evaluation theories under non-classical damping conditions.

Description

Technical Field

[0001] This application relates to the field of bridge structural dynamics and structural modal parameter identification technology, and in particular to a method, device, equipment and storage medium for evaluating frequency and damping changes in a vehicle-bridge coupled system that considers non-classical damping effects. Background Technology

[0002] As vital transportation infrastructure connecting different regions and traversing man-made or natural obstacles, bridges inevitably suffer from environmental erosion, traffic loads, and material aging during long-term service, leading to varying degrees of structural performance degradation. To ensure the service safety of bridge structures, various methods for bridge structural health monitoring and condition assessment have been proposed in existing technologies.

[0003] Existing bridge health monitoring technologies typically rely on vibration sensors deployed on the bridge structure or moving vehicles to continuously or indirectly collect dynamic response signals of the bridge during its service life. By analyzing the structural dynamic characteristic parameters in the acquired vibration response, the health status of the bridge structure can be assessed.

[0004] Under actual operating conditions, the vibration response of a bridge mainly originates from the vehicle-bridge coupled vibration process generated when vehicles pass over the bridge. The vehicle and the bridge form a vehicle-bridge coupled system during travel, which exhibits significant time-varying characteristics. Its overall stiffness and mass distribution continuously change with the vehicle's position on the bridge, causing parameters reflecting the bridge's structural dynamics, such as modal frequencies and damping ratios, to change with time and spatial location.

[0005] In existing structural health assessment methods, changes in dynamic parameters such as modal frequencies and damping ratios are often used as important indicators reflecting the performance status of bridge structures. However, under vehicle-bridge coupling conditions, the changes in these parameters are not only related to the state of the bridge structure itself, but are also significantly affected by the vehicle-bridge coupling effect. If this coupling effect is not properly distinguished, it can easily interfere with the assessment of the bridge structure's health status, thereby affecting the accuracy of the assessment results.

[0006] Furthermore, vehicle-bridge coupled systems typically exhibit non-classical damping characteristics during dynamic modeling, requiring complex modal analysis to obtain their modal properties. This complex calculation process presents significant challenges for engineering implementation, thus limiting the practical application of existing methods for evaluating the dynamic characteristics of bridge structures. Summary of the Invention

[0007] This application provides a method, apparatus, device, and storage medium for evaluating the frequency and damping changes of a vehicle-axle coupled system considering non-classical damping effects. It addresses the problem that existing methods for evaluating the frequency evolution of vehicle-axle coupled systems are mostly based on undamped or classical damping assumptions, making it difficult to simultaneously characterize the changes in system frequency and damping parameters. Furthermore, it addresses the issue that when the vehicle damping and bridge damping differ significantly, the vehicle-axle coupled system exhibits non-classical damping characteristics, leading to significant errors in frequency estimation based on undamped theory. By introducing an evaluation index characterizing the degree of non-classical damping in the vehicle-axle coupled system, this application analyzes the variation patterns of system frequency and damping parameters within a unified analytical framework. This enables quantitative analysis of the applicability of existing frequency evaluation theories under non-classical damping conditions and improves the accuracy and reliability of evaluating the dynamic characteristics of vehicle-axle coupled systems.

[0008] Firstly, this application provides a method for evaluating the frequency and damping variations of a vehicle-axle coupling system considering non-classical damping effects, including: Determine the frequency variation and damping variation information used to evaluate the dynamic characteristics of the vehicle-axle coupling system; Based on the frequency change information and damping change information, dimensionless characterization quantities for frequency change and damping change are constructed. Establish the correlation between the dimensionless characterization of frequency change and the dimensionless characterization of damping change, and calculate the evaluation index for characterizing the intensity of nonclassical damping effect in the vehicle-axle coupling system based on the correlation, so as to quantitatively evaluate the influence of nonclassical damping effect in the vehicle-axle coupling system. The output vehicle-axle coupling system yields evaluation results for frequency variation, damping variation, and corresponding non-classical damping effects.

[0009] In one possible design, the frequency variation information and damping variation information are obtained through at least one of the following methods: a) obtaining them based on the collected vehicle-bridge coupled vibration response data using a frequency and damping identification method; b) obtaining them based on the physical parameters of the vehicle and the bridge through theoretical analysis, numerical calculation, or analytical calculation.

[0010] In one possible design, the dimensionless characterization quantity is constructed based on the dimensionless parameters of the vehicle-bridge coupling system, including the mass ratio of the vehicle to the bridge. The frequency ratio of vehicles to bridges Damping ratio of vehicles and bridges and the dimensionless position of the vehicle on the bridge : The mass ratio of the vehicle to the bridge The calculation formula is: (1) in, For vehicle quality, Mass per unit length of the bridge For bridge span; The frequency ratio of the vehicle to the bridge The calculation formula is: (2) in, The vehicle's angular frequency, , This is the vehicle's equivalent stiffness. Bridge angular frequency , The equivalent bending stiffness of the bridge; The damping ratio between the vehicle and the bridge The calculation formula is: (3) in, For vehicle damping ratio, , For the vehicle's equivalent viscous damping, For the bridge damping ratio, , For bridge equivalent viscous damping; The dimensionless position of the vehicle on the bridge The calculation formula is: (4) in, Location of the contact point between the vehicle and the bridge.

[0011] In one possible design, the dimensionless frequency variation characteristic includes the dimensionless frequency variation coefficients of the bridge and vehicle in the vehicle-bridge coupling system. and It is calculated using the following formula: (7) in, The first-order modal function value of a bridge, for a simply supported beam, can be expressed as: In one possible design, the dimensionless characterization of damping variation includes the dimensionless damping ratio scaling factor of the bridge and vehicle in the vehicle-bridge coupling system. and It is calculated using the following formula: (8)

[0012] In one possible design, the evaluation index used to characterize the strength of the nonclassical damping effect in the vehicle-axle coupling system... The calculation formula is: (9) Among them, the evaluation indicators Used to quantitatively determine the applicability of the undamped or classical damping assumptions in the frequency and damping evaluation of vehicle-axle coupling systems: when When the value is less than the first set threshold, it is determined that the non-classical damping effect has a small impact on the estimation of system modal parameters, and it is reasonable to use the assumption of no damping or classical damping for frequency and damping evaluation; when the evaluation index is greater than or equal to the second set threshold, it is determined that the non-classical damping effect is enhanced, and a non-classical damping model is introduced for complex modal analysis.

[0013] In one possible design, the error is calculated via frequency. The degree of influence of non-classical damping effects on the system frequency estimation results is quantified, and the frequency calculation error is mentioned. Calculated using the following formula: (10) in, This represents the instantaneous frequency of the system calculated using the undamped assumption. This represents the pseudo-undamped frequency obtained when considering non-classical damping effects. The larger the value, the more significant the impact of nonclassical damping effect on the system frequency estimation result.

[0014] Secondly, this application provides a device for evaluating the frequency and damping variation of a vehicle-axle coupling system considering non-classical damping effects, the device comprising: The information determination module is configured to determine frequency variation information and damping variation information used to evaluate the dynamic characteristics of the vehicle-axle coupling system. The characterization quantity construction module is configured to construct dimensionless characterization quantities of frequency change and dimensionless characterization quantities of damping change based on the frequency change information and damping change information. The quantitative evaluation module is configured to establish the correlation between the dimensionless characterization of frequency change and the dimensionless characterization of damping change, and to calculate the evaluation index for characterizing the intensity of the non-classical damping effect in the vehicle-bridge coupling system based on the correlation, so as to quantitatively evaluate the influence of the non-classical damping effect in the vehicle-bridge coupling system. The results output module is configured to output the frequency change evaluation results, damping change evaluation results, and corresponding non-classical damping effect evaluation results of the vehicle-bridge coupling system.

[0015] Thirdly, embodiments of this application provide an electronic device, including: at least one processor and a memory; the memory stores computer execution instructions; the at least one processor executes the computer execution instructions stored in the memory, causing the at least one processor to perform the method for evaluating the frequency and damping variation of a vehicle-bridge coupling system considering non-classical damping effects as described in the first aspect and various possible designs of the first aspect.

[0016] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions. When a processor executes the computer-executable instructions, it implements the method for evaluating the frequency and damping changes of a vehicle-bridge coupling system considering non-classical damping effects as described in the first aspect and various possible designs of the first aspect.

[0017] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the method for evaluating frequency and damping changes in a vehicle-bridge coupling system considering non-classical damping effects as described in the first aspect and various possible designs of the first aspect.

[0018] The method, apparatus, equipment, and storage medium for evaluating frequency and damping variations in a vehicle-axle coupling system considering non-classical damping effects provided in this application have at least the following beneficial effects: 1) This application enables a unified evaluation of the frequency and damping parameter variations in a vehicle-axle coupling system, taking into account non-classical damping effects. Specifically, it constructs dimensionless frequency variation coefficients and dimensionless damping scaling coefficients to characterize the evolution of frequency and damping with vehicle position within the same analytical framework.

[0019] 2) This application can evaluate the impact of non-classical damping effects on the dynamic characteristics of the system without performing complex modal eigenvalue analysis. By introducing analytical expressions and dimensionless evaluation indices, the complex complex eigenvalue solution process in traditional non-classical damping analysis can be avoided, significantly reducing computational complexity and improving the operability of engineering applications.

[0020] 3) This application proposes a dimensionless nonclassical damping effect evaluation index, which can be used to determine the applicability of classical damping or undamped assumptions. This evaluation index can quantitatively reflect the degree of influence of nonclassical damping effects on the system frequency and damping estimation results, providing a basis for judging whether a nonclassical damping model needs to be introduced in engineering simulation calculations.

[0021] 4) This application does not rely on the absolute physical dimensions of the vehicle or bridge, and has good versatility and scalability. Through dimensionless processing, the method of this application can be applied to vehicle-bridge coupling systems with different spans and different vehicle parameters, which facilitates comparative analysis between different working conditions.

[0022] 5) This application can perform analytical calculations based on known physical parameters or directly evaluate based on measured vibration response data. Specifically, the method of this application is applicable to both theoretical analysis and numerical simulation scenarios, as well as engineering inspection and structural health monitoring scenarios where only vibration response data is obtained, and has strong engineering practical value. Attached Figure Description

[0023] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0024] Figure 1 This is a schematic diagram of the mechanical model of the vehicle-bridge coupling system provided in the embodiments of this application; Figure 2 A flowchart of a method for evaluating frequency and damping variation in a vehicle-axle coupling system considering non-classical damping effects, provided for embodiments of this application; Figure 3 A comparison diagram of the finite element calculation results of the dimensionless frequency variation coefficient of the bridge and vehicle as a function of the relative position of the vehicle provided in the embodiments of this application and the calculation results of the method in this application. Figure 4 A comparison chart of the finite element calculation results of the dimensionless damping scaling factor of the bridge and vehicle as a function of the relative position of the vehicle provided in the embodiments of this application and the calculation results of the method of this application. Figure 5 The dimensionless nonclassical damping effect evaluation index provided for the embodiments of this application A schematic diagram of the validity verification results; Figure 6 A structural diagram of a device for evaluating the frequency and damping variation of a vehicle-bridge coupling system that considers non-classical damping effects, provided in an embodiment of this application.

[0025] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0026] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0027] The collection, storage, use, processing, transmission, provision, and disclosure of financial data or user data involved in the technical solution of this application all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0028] It should be noted that in the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.

[0029] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0030] This application provides a method for evaluating the frequency and damping variations of a vehicle-axle coupling system considering non-classical damping effects. It employs an analytical calculation-based approach to evaluate these variations. To assess the evolution characteristics of frequency and damping in the vehicle-axle coupling system with changes in vehicle position, the method considers... Figure 1 The diagram illustrates a vehicle-bridge coupled system of a simply supported beam bridge under damped vehicle loading. The vehicle is equivalent to a single-degree-of-freedom vibration system, which includes the vehicle mass. m v Equivalent stiffness k v and equivalent viscous damping c v The bridge is equivalent to a uniform Euler beam, which includes the bridge span. L Equivalent bending stiffness EI b Equivalent viscous damping c b and mass per unit length m b During the process of a vehicle crossing a bridge, the vehicle and the bridge are at the point of contact. x c The interaction occurs at the points of contact, thus forming a vehicle-bridge coupled vibration system.

[0031] It should be noted that the following will revolve around Figure 1 The vehicle-axle coupling system of the simply supported beam bridge under damped vehicle action illustrates in detail the specific implementation process of the method of this application. It is understood that the vehicle-axle coupling system exemplified above is merely exemplary and does not imply that the method of this application must rely on this vehicle-axle coupling system for implementation; other similar vehicle-axle coupling systems can also be applied to the implementation of the method of this application.

[0032] Specifically, such as Figure 2 As shown, the method for evaluating the frequency and damping variation of a vehicle-axle coupling system considering non-classical damping effects can be implemented through the following steps S10~S40.

[0033] S10: Determine the frequency variation information and damping variation information used to evaluate the dynamic characteristics of the vehicle-axle coupling system.

[0034] In some embodiments, frequency variation information and damping variation information for evaluating the dynamic characteristics of the vehicle-axle coupling system are determined, wherein the frequency variation information and damping variation information are obtained by at least one of the following methods: a) Based on the collected vehicle-bridge coupled vibration response data, existing frequency and damping identification methods are used to obtain information on the changes in system frequency and damping; b) Based on the physical parameters of the vehicle and the bridge, the frequency and damping variation assessment method proposed in this application is used to obtain the results through theoretical analysis, numerical calculation or analytical calculation.

[0035] S20: Based on frequency change information and damping change information, construct dimensionless characterization quantities for frequency change and damping change.

[0036] In this embodiment, the purpose of step S20 is to construct dimensionless characterization quantities of frequency and damping changes. Based on the frequency change information and damping change information determined in step S10, dimensionless characterization quantities that reflect the degree of frequency change and damping change in the vehicle-bridge coupling system are constructed respectively. The dimensionless characterization quantities are obtained by normalizing the frequency change parameters and damping change parameters to eliminate the influence of different structural scales and parameter value differences on the evaluation results.

[0037] In some embodiments, in combination with Figure 1 As shown, to avoid the influence of different structural scales and parameter values ​​on the evaluation results, dimensionless parameters are used to characterize the system characteristics. The dimensionless parameters used include the vehicle-to-bridge mass ratio, the vehicle-to-bridge frequency ratio, the vehicle-to-bridge damping ratio, and the dimensionless position of the vehicle on the bridge. The formula for calculating the mass ratio of the vehicle to the bridge is:

[0038] The formula for calculating the frequency ratio of vehicles to bridges is:

[0039] Where the vehicle angular frequency is , For the equivalent stiffness of the vehicle, the angular frequency of the bridge is , The equivalent bending stiffness of the bridge is given by the angular frequency. That is .

[0040] The formula for calculating the damping ratio between the vehicle and the bridge is:

[0041] Vehicle damping ratio satisfies , For the vehicle's equivalent viscous damping, the bridge damping ratio satisfies , This is the equivalent viscous damping for the bridge.

[0042] The formula for calculating the dimensionless position of a vehicle on a bridge is:

[0043] in, Location of the contact point between the vehicle and the bridge.

[0044] Based on the dynamic characteristics of the vehicle-axle coupled system, the dimensionless analytical relationship between the system's frequency and damping changes was derived and determined in advance. This relationship can be used to describe the evolution of frequency and damping in the vehicle-axle coupled system as the vehicle's position changes within a dimensionless parameter space.

[0045] Within this dimensionless framework, the instantaneous damping ratios of the bridge and the vehicle in the vehicle-bridge coupled system are expressed as follows:

[0046] in, and They represent the instantaneous damping ratios of the bridge and the vehicle under vehicle-bridge coupling conditions. and represent the dimensionless damping coefficients. and These represent the dimensionless frequency variation coefficients of the bridge and the vehicle, respectively. , , and Let represent the mass ratio of the vehicle to the bridge, the frequency ratio, the damping ratio, and the dimensionless position of the vehicle on the bridge, respectively. The dimensionless coefficient of frequency variation satisfies:

[0047] and Let represent the instantaneous angular frequencies of the bridge and vehicle under vehicle-bridge coupling conditions. Under the undamped assumption, the dimensionless frequency variation coefficients of the bridge and vehicle in the vehicle-bridge coupling system are... and The specific expression is:

[0048] in, The first-order modal function value of a bridge, for a simply supported beam, can be expressed as: The sign before the radical in the formula is... Decision, when <1 hour, The square root sign in the calculation formula is preceded by a negative sign. The sign before the radical in a calculation is positive; when When the value is greater than 1, the above signs are reversed. The dimensionless damping ratio scaling factor for the bridge and vehicle in a vehicle-bridge coupled system. and The specific expression is:

[0049] When the vehicle mass is relatively small compared to the bridge mass, or when the vehicle's equivalent stiffness approaches zero, the above analytical calculation results can be degenerated into the original damping ratio of the bridge or vehicle, thus being consistent with the results under uncoupled conditions, verifying the rationality of the analytical relationship in typical engineering situations.

[0050] Through the above implementation methods (Equations (7) and (8)), the frequency and damping variation characteristics of the vehicle-bridge coupling system can be quickly obtained based on analytical calculations without the need for complex modal numerical solutions (which can be quantified by dimensionless frequency variation and dimensionless damping variation).

[0051] S30: Establish the correlation between the dimensionless characterization of frequency change and the dimensionless characterization of damping change, and calculate the evaluation index for characterizing the intensity of nonclassical damping effect in the vehicle-axle coupling system based on the correlation, so as to quantitatively evaluate the influence of nonclassical damping effect in the vehicle-axle coupling system.

[0052] In this embodiment, the purpose of step S30 is to evaluate the non-classical damping effect in the vehicle-axle coupling system based on the constructed dimensionless characterization of frequency change and dimensionless characterization of damping change, establish the correlation between the two, and calculate the evaluation index used to characterize the intensity of the non-classical damping effect in the vehicle-axle coupling system. Through the evaluation index, the influence of the non-classical damping effect in the vehicle-axle coupling system is quantitatively evaluated. The evaluation index can serve as a preliminary criterion for whether to adopt complex non-classical damping analysis.

[0053] In some embodiments, to uniformly characterize the combined effect of nonclassical damping on frequency and damping changes in a vehicle-axle coupling system, a dimensionless nonclassical damping effect evaluation index is defined here. The evaluation index is constructed based on dimensionless characteristics of frequency change and dimensionless characteristics of damping change, and its specific form is as follows:

[0054] The dimensionless evaluation index As a purely dimensionless quantity, it does not depend on the absolute dimensions and physical values ​​of the vehicle or bridge, and can be used for comparative analysis of different vehicle-bridge coupling systems under different working conditions. Its parameters can be calculated using the analytical formulas (7) and (8) given here, or directly identified through the collected vibration signals. When When the index approaches 0, the system can be approximated as being suitable for classical damping or undamped theory. A significant increase in the evaluation index indicates a stronger non-classical damping effect, leading to a corresponding increase in the risk of error in frequency and damping estimation using the undamped or classical damping assumptions. For example, when the evaluation index is close to or greater than 1, the use of the undamped or classical damping assumptions may result in non-negligible calculation errors. The evaluation index allows for assessment of the applicability of using the undamped or classical damping assumptions for frequency estimation and evaluates the impact of non-classical damping effects on system modal analysis.

[0055] S40: Outputs the evaluation results of frequency variation, damping variation, and corresponding non-classical damping effect in the vehicle-axle coupling system.

[0056] In this embodiment, the purpose of step S40 is to output the time-varying characteristics and non-classical damping characteristics of the system. Based on the non-classical damping effect evaluation index, the frequency change evaluation result, damping change evaluation result, and corresponding non-classical damping effect evaluation result of the vehicle-axle coupling system are output to characterize the changing features of the dynamic characteristics of the vehicle-axle coupling system and to provide a basis for subsequent structural state evaluation or engineering applications.

[0057] It should be noted that the frequency and damping variation information used to evaluate the non-classical damping effect in the above methods can be derived from direct identification results of vehicle-bridge coupled vibration response data or from theoretical calculation results based on vehicle and bridge physical parameters. This application does not rely on complete physical modeling or detailed parameter acquisition of the vehicle-bridge system; it can still achieve effective evaluation of the non-classical damping effect even when only system response data is available.

[0058] The feasibility and progressiveness of the proposed method will be further illustrated below through two implementation cases.

[0059] Implementation Case 1: Numerical Verification Based on Analytical Computation This implementation case selects a simply supported beam bridge and a single-degree-of-freedom vehicle as the calculation examples, and the parameter settings are as follows.

[0060] Bridge spanL =30m, density of the bridge =2,500 kg / m 3 cross-sectional area =5.3m 2 elastic modulus E =27.5 GPa, moment of inertia I b It is 4.98m 4 Bridge damping ratio With a value of 0.02, the fundamental frequency of the bridge can be calculated to be 5.61 Hz.

[0061] Vehicle body weight m v It is 79,500 kg (corresponding to the axle mass ratio). (0.2), suspension stiffness k v =1.0894×10 8 N / m corresponds to a vehicle frequency of 5.89Hz (corresponding to axle frequency ratio). It is 1.05), vehicle damping ratio It is 0.04 (corresponding to the axle damping ratio). (2).

[0062] The numerical calculations and results are compared below: Assuming the vehicle travels along the bridge, calculate the frequency variation coefficient and damping scaling factor of the vehicle-bridge coupling system at different vehicle positions on the bridge. The variation of the system frequency variation coefficient with vehicle position is as follows: Figure 3 As shown, the damping coefficient varies with vehicle position as follows: Figure 4 As shown.

[0063] in, Figure 3 and Figure 4 Solid symbols in the figure represent the changes in the bridge fundamental frequency due to the vehicle-bridge coupling effect, while hollow symbols represent the changes in the vehicle frequency due to the coupling effect. The analytical calculation results in the figure are obtained by the dimensionless analytical expressions (Equations (7) and (8)) proposed in this application; the finite element results used for comparison are obtained by the mature vehicle-bridge coupling finite element method. This method obtains the system frequency and damping value by constructing the system mass matrix, damping matrix and stiffness matrix and performing complex eigenvalue analysis, and has been widely used in the field of structural dynamics.

[0064] Depend on Figure 3 and Figure 4 It can be seen that when the vehicle is located at the mid-span of the bridge (i.e. When ), the dimensionless frequency variation coefficient and damping scaling coefficient corresponding to the bridge and vehicles are respectively =1.343, =0.745, =0.953 and =1.146. Substituting the above result into the dimensionless nonclassical damping effect evaluation index defined in equation (9), we can calculate the result. =0.09, the value of this evaluation index is much less than 1, indicating that under this operating condition, the non-classical damping effect has a small impact on the estimation of system modal parameters, and it is reasonable to use the classical damping assumption to estimate the system modal parameters. This conclusion can also be drawn from... Figure 3 and Figure 4 The good consistency between the analytical calculation results and the finite element calculation results was verified.

[0065] Regarding the proposed dimensionless nonclassical damping effect evaluation index The applicability and effectiveness under different working conditions and parameter conditions will be further explained in Implementation Case 2.

[0066] Implementation Case 2: Evaluation Index of Dimensionless Nonclassical Damping Effect Validity verification In this implementation case, through numerous numerical examples with various parameter combinations, the dimensionless nonclassical damping effect evaluation index proposed in this application is demonstrated. The effectiveness of [the method] needs to be verified.

[0067] In this embodiment, the following dimensionless parameter combination is considered: the ratio of vehicle mass to bridge mass. Take 6 sets of values, respectively α m =0.5, 1, 2, 3, 4, and 5%. Vehicle-to-bridge frequency ratio. Take 13 sets of values, respectively α f =0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 1.05, 1.1, 1.2, and 1.3. Vehicle-bridge damping ratio. Take 7 sets of values, respectively α ξ =0.5,2.5,5,7.5,10,12.5,15 The above parameter combinations constitute 546 sets of numerical examples for different working conditions.

[0068] The finite element method used for comparison and verification in this embodiment is the same as that in Implementation Case 1. The bridge structural parameters are consistent with those in Implementation Case 1. Different combinations of dimensionless parameters are achieved by adjusting the vehicle parameters in each case. The finite element results are obtained by constructing the mass matrix, damping matrix, and stiffness matrix of the vehicle-bridge coupling system and performing complex modal eigenvalue analysis.

[0069] Evaluation metrics and error definition. To quantify the impact of non-classical damping effects on the system frequency estimation results, a frequency calculation error is introduced. As a comparison metric, the frequency calculation error is defined as the instantaneous frequency obtained under undamped conditions. Compared with the pseudo-undamped frequency obtained by considering non-classical damping effects The relative difference between them is expressed as:

[0070] in, This represents the instantaneous frequency of the system calculated using the undamped assumption. These represent pseudo-undamped frequencies obtained when considering non-classical damping effects; they can all be obtained through complex modal analysis using finite element theory.

[0071] Explanation of indicator meaning: Frequency calculation error The larger the value of , the more significant the influence of nonclassical damping effect on the system frequency estimation results; conversely, when , When the value is small, it indicates that the non-classical damping effect has a weak impact on frequency estimation. In this case, it is reasonable to use the assumption of no damping or classical damping for frequency evaluation. Since this index involves complex modal analysis, it will inevitably involve a large amount of numerical calculation.

[0072] By comparing the aforementioned frequency calculation error with the dimensionless nonclassical damping effect evaluation index proposed in this application... Comparative analysis can further verify the ability of the evaluation index to characterize the strength of non-classical damping effects under different parameter conditions. In this embodiment, it is assumed that the vehicle is located at the mid-span of the bridge.

[0073] like Figure 5 As shown, the evaluation indicators calculated under the above 546 different working conditions are presented. The correspondence between frequency calculation error and other factors. Figure 5 It can be seen that the evaluation indicators The correlation between the frequency calculation error and the index shows a relatively obvious linear trend, indicating that a simpler calculation method is used. It is feasible to estimate the error in frequency calculations that need to be obtained through numerical eigenvalue analysis.

[0074] Furthermore, when evaluation indicators When the calculated result is much less than 1, the corresponding frequency calculation error is also at a small level. It can be considered that the influence of non-classical damping effect on the system frequency estimation can be ignored. At this time, it is reasonable to use the undamped or classical damping assumption for frequency evaluation.

[0075] This application also provides a device for evaluating the frequency and damping changes of a vehicle-axle coupling system considering non-classical damping effects, which is used to implement the method described in the above embodiments, such as... Figure 6 As shown, the device for evaluating the frequency and damping variation of a vehicle-axle coupling system considering non-classical damping effects includes: Information determination module 601 is configured to determine frequency variation information and damping variation information for evaluating the dynamic characteristics of the vehicle-axle coupling system; The characterization construction module 602 is configured to construct a dimensionless characterization quantity for frequency change and a dimensionless characterization quantity for damping change based on the frequency change information and damping change information. The quantitative evaluation module 603 is configured to establish the correlation between the dimensionless characterization of frequency change and the dimensionless characterization of damping change, and calculate the evaluation index for characterizing the intensity of nonclassical damping effect in the vehicle-bridge coupling system based on the correlation, so as to quantitatively evaluate the influence of nonclassical damping effect in the vehicle-bridge coupling system. The output module 604 is configured to output the frequency change evaluation results, damping change evaluation results, and corresponding non-classical damping effect evaluation results of the vehicle-bridge coupling system.

[0076] This application provides an electronic device. The electronic device may include a processor and a memory, wherein the processor and the memory can communicate; exemplarily, the processor and the memory communicate via a communication bus.

[0077] The processor executes computer execution instructions stored in memory, causing the processor to perform the scheme in the above embodiments. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0078] The communication bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. Transceivers are used to enable communication between database access devices and other computers (e.g., clients, read-write libraries, and read-only libraries). Memory may include random access memory (RAM) and may also include non-volatile memory.

[0079] The electronic device provided in this application embodiment can be the terminal device described in the above embodiments.

[0080] This application also provides a computer-readable storage medium storing computer instructions. When the computer instructions are executed on a computer, the computer performs the technical solution of the above-described method for evaluating the frequency and damping changes of a vehicle-bridge coupling system considering non-classical damping effects.

[0081] This application also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When the at least one processor executes the computer program, it can implement the technical solution of the method for evaluating the frequency and damping changes of the vehicle-bridge coupling system considering non-classical damping effects in the above embodiments.

[0082] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0083] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0084] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0085] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods of the various embodiments of this application.

[0086] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.

[0087] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0088] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Architecture (EISA) buses, etc. Buses can be categorized into address buses, data buses, control buses, etc.

[0089] The aforementioned storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0090] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic control unit or main control device.

[0091] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for evaluating frequency and damping variations in a vehicle-axle coupling system considering non-classical damping effects, characterized in that, The method includes: Determine the frequency variation and damping variation information used to evaluate the dynamic characteristics of the vehicle-axle coupling system; Based on the frequency change information and damping change information, dimensionless characterization quantities for frequency change and damping change are constructed. Establish the correlation between the dimensionless characterization of frequency change and the dimensionless characterization of damping change, and calculate the evaluation index for characterizing the intensity of nonclassical damping effect in the vehicle-axle coupling system based on the correlation, so as to quantitatively evaluate the influence of nonclassical damping effect in the vehicle-axle coupling system. The output vehicle-axle coupling system yields evaluation results for frequency variation, damping variation, and corresponding non-classical damping effects.

2. The method for evaluating frequency and damping variations in a vehicle-axle coupling system considering non-classical damping effects according to claim 1, characterized in that, The frequency change information and damping change information are obtained through at least one of the following methods: a) based on the collected vehicle-bridge coupled vibration response data, using a frequency and damping identification method; b) based on the physical parameters of the vehicle and bridge, through theoretical analysis, numerical calculation or analytical calculation.

3. The method for evaluating frequency and damping variations in a vehicle-axle coupling system considering non-classical damping effects according to claim 1, characterized in that, The dimensionless characterization quantity is constructed based on the dimensionless parameters of the vehicle-bridge coupling system, including the mass ratio of the vehicle to the bridge. The frequency ratio of vehicles to bridges Damping ratio of vehicles and bridges and the dimensionless position of the vehicle on the bridge : The mass ratio of the vehicle to the bridge The calculation formula is: (1) in, For vehicle quality, Mass per unit length of the bridge For bridge span; The frequency ratio of the vehicle to the bridge The calculation formula is: (2) in, The vehicle's angular frequency, , This is the vehicle's equivalent stiffness. Bridge angular frequency , The equivalent bending stiffness of the bridge; The damping ratio between the vehicle and the bridge The calculation formula is: (3) in, For vehicle damping ratio, , For the vehicle's equivalent viscous damping, For the bridge damping ratio, , For bridge equivalent viscous damping; The dimensionless position of the vehicle on the bridge The calculation formula is: (4) in, Location of the contact point between the vehicle and the bridge.

4. The method for evaluating frequency and damping variations in a vehicle-axle coupling system considering non-classical damping effects according to claim 3, characterized in that, The dimensionless frequency variation characteristic includes the dimensionless frequency variation coefficients of the bridge and vehicle in the vehicle-bridge coupling system. and It is calculated using the following formula: (7) in, The first-order modal function value of a bridge, for a simply supported beam, can be expressed as: .

5. The method for evaluating frequency and damping variations in a vehicle-axle coupling system considering non-classical damping effects according to claim 4, characterized in that, The dimensionless characterization of damping change includes the dimensionless damping ratio scaling factor of the bridge and vehicle in the vehicle-bridge coupling system. and It is calculated using the following formula: (8)。 6. The method for evaluating frequency and damping variations in a vehicle-axle coupling system considering non-classical damping effects according to claim 5, characterized in that, The evaluation index used to characterize the strength of the nonclassical damping effect in the vehicle-axle coupling system The calculation formula is: (9) Among them, the evaluation indicators Used to quantitatively determine the applicability of the undamped or classical damping assumptions in the frequency and damping evaluation of vehicle-axle coupling systems: when When the value is less than the first set threshold, it is determined that the non-classical damping effect has a small impact on the estimation of system modal parameters, and it is reasonable to use the assumption of no damping or classical damping for frequency and damping evaluation; when the evaluation index is greater than or equal to the second set threshold, it is determined that the non-classical damping effect is enhanced, and a non-classical damping model is introduced for complex modal analysis.

7. The method for evaluating frequency and damping variations of a vehicle-axle coupling system considering non-classical damping effects according to any one of claims 1 to 6, characterized in that, Error calculated using frequency The degree of influence of non-classical damping effects on the system frequency estimation results is quantified, and the frequency calculation error is mentioned. Calculated using the following formula: (10) in, This represents the instantaneous frequency of the system calculated using the undamped assumption. This represents the pseudo-undamped frequency obtained when considering non-classical damping effects. The larger the value, the more significant the impact of nonclassical damping effect on the system frequency estimation result.

8. A device for evaluating the frequency and damping variation of a vehicle-axle coupling system considering non-classical damping effects, characterized in that, The device includes: The information determination module is configured to determine frequency variation information and damping variation information used to evaluate the dynamic characteristics of the vehicle-axle coupling system. The characterization quantity construction module is configured to construct dimensionless characterization quantities of frequency change and dimensionless characterization quantities of damping change based on the frequency change information and damping change information. The quantitative evaluation module is configured to establish the correlation between the dimensionless characterization of frequency change and the dimensionless characterization of damping change, and to calculate the evaluation index for characterizing the intensity of the non-classical damping effect in the vehicle-bridge coupling system based on the correlation, so as to quantitatively evaluate the influence of the non-classical damping effect in the vehicle-bridge coupling system. The results output module is configured to output the frequency change evaluation results, damping change evaluation results, and corresponding non-classical damping effect evaluation results of the vehicle-bridge coupling system.

9. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes the computer execution instructions stored in the memory to implement the method for evaluating the frequency and damping changes of a vehicle-bridge coupling system considering non-classical damping effects as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method for evaluating frequency and damping variations of a vehicle-bridge coupling system considering non-classical damping effects as described in any one of claims 1-7.

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