A vibration isolator and a parameter optimization method of the vibration isolator

Abstract

The application provides a vibration isolator and a parameter optimization method of the vibration isolator. The vibration isolator comprises a bottom plate, a top cover, a first surrounding part extending from the edge of the top cover to a first direction to form the first surrounding part, a second surrounding part extending from a first position of the bottom plate to a second direction to form the second surrounding part, a first spring arranged in the second surrounding part, one end of the first spring being fixedly connected with the bottom plate, a first damping liquid filled in the second surrounding part to cover part of the first spring, and an inertial container located in a containing space formed by the second surrounding part, one end of the inertial container being fixedly connected with the other end of the first spring, and the other end of the inertial container being movably connected with the top cover, so that the inertial container can move in a preset direction relative to the top cover, thereby providing a vibration isolator with better vibration suppression effect and improving the vibration suppression effect of the vibration isolator when the vibration isolator is applied to a floating slab track.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vibration isolators, in particular to a vibration isolator and a parameter optimization method of the vibration isolator. BACKGROUND

[0002] In the prior art, in order to reduce the negative effects of urban rail transit environmental vibration, the subway company has taken many track vibration reduction measures. Among them, the steel spring floating slab track is considered to have excellent vibration reduction effect and is applied to the line section with the most stringent vibration reduction requirements. However, the steel spring floating slab track has no obvious suppression effect on low-frequency vibration. The frequency range in which the steel spring floating slab track plays a vibration isolation role needs to be greater than 1.414 times the natural frequency of the floating slab, so that its suppression effect on low-frequency vibration below 20 Hz is not obvious, and the resonance effect of the floating slab will also cause vibration amplification at about 10 Hz. Therefore, a vibration isolator needs to be used in cooperation to improve the vibration reduction performance of the floating slab track. SUMMARY

[0003] Therefore, the purpose of the present application is to provide a vibration isolator and a parameter optimization method of the vibration isolator, and to provide a vibration isolator with better vibration suppression effect and to improve the vibration suppression effect of the vibration isolator when applied in the floating slab track.

[0004] In a first aspect, an embodiment of the present application provides a vibration isolator, comprising: a bottom disc and a top cover; a first surrounding member extending from the edge of the top cover to a first direction to form the first surrounding member; a second surrounding member extending from a first position of the bottom disc to a second direction to form the second surrounding member, the first direction being opposite to the second direction, and the second surrounding member being located in a containing space formed by the first surrounding member; a first spring arranged in the second surrounding member, one end of the first spring being fixedly connected with the bottom disc; a first damping liquid filled in the second surrounding member to cover part of the first spring; an inertial container located in the containing space formed by the second surrounding member, one end of the inertial container being fixedly connected with the other end of the first spring, and the other end of the inertial container being movably connected with the top cover, so that the inertial container can move in a preset direction relative to the top cover.

[0005] Preferably, the inertial container comprises: a connecting sleeve located in the containing space formed by the second surrounding member and extending from the center of the top cover to the first direction to form the connecting sleeve; a rotating part, an outer wall of the rotating part being movably connected with the extension end of the connecting sleeve; a fixed part, one end of the fixed part being fixedly connected with the other end of the first spring, and the other end of the fixed part being movably connected with the inner wall of the rotating part.

[0006] Preferably, the inertial container further comprises: a bearing arranged at the extension end of the connecting sleeve; and a first ball arranged in the bearing.

[0007] Preferably, an inner thread is formed on the inner wall of the rotating part, the fixing part comprises an end disc and a lead screw formed from the center of the end disc and extending in the second direction, the end disc is fixedly connected with the other end of the first spring, an outer thread is formed on the outer surface of the lead screw and matches the inner thread formed on the inner wall of the rotating part, and the inertial container further comprises: second balls arranged between the outer thread formed on the outer surface of the lead screw and the inner thread formed on the inner wall of the rotating part, so that the lead screw is movably connected with the inner wall of the rotating part.

[0008] Preferably, the vibration isolator further comprises: a third surrounding member extending from the edge of the bottom disc in the second direction to form a containing space, and the second surrounding member is located in the containing space formed by the third surrounding member; a second spring arranged in the containing space between the second surrounding member and the third surrounding member, one end of the second spring being fixedly connected with the bottom disc and the other end of the second spring being fixedly connected with the top cover; and a second damping liquid filled in the containing space between the second surrounding member and the third surrounding member to cover part of the second spring.

[0009] In a second aspect, the embodiments of the present application further provide a parameter optimization method of a vibration isolator, comprising:

[0010] A1: performing spectral element division on a finite half-track model corresponding to a track of a floating plate of the vibration isolator to obtain a plurality of spectral elements, the plurality of spectral elements at least comprising Timoshenko beam spectral elements, continuous support Timoshenko beam spectral elements, spring-damper spectral elements, shear spring spectral elements and inertial container-spring-damper spectral elements, and the spectral elements being connected through nodes;

[0011] A2: for each spectral element, calculating a stiffness matrix corresponding to the spectral element to obtain a total spectral stiffness matrix of the finite half-track model;

[0012] A3: in a simulation simulation platform, determining a first node of a target Timoshenko beam spectral element, and inputting a vertical spectral node load input by the first node and the total spectral stiffness matrix to output a displacement admittance response of the finite half-track model;

[0013] A4: in the simulation simulation platform, using an NSGA-II algorithm, inputting a plurality of preset parameters of the vibration isolator as decision variables, and inputting a set of preset function expressions corresponding to displacement admittance responses output by a second node of a target continuous support Timoshenko beam spectral element in each preset frequency range interval as objective functions, to output a set of all decision variables satisfying a preset condition of the objective functions as an optimization vector solution set;

[0014] A5: determining an optimal vector in the optimization vector solution set as an actual value of the preset parameter corresponding to the vibration isolator.

[0015] Preferably, the finite half-track model at least comprises: a rail, a plurality of floating slabs located below the rail, a plurality of fasteners for connecting the rail and the floating slabs, a plurality of shear hinges arranged between adjacent floating slabs, a plurality of vibration isolators for connecting the floating slabs and the foundation, and a plurality of continuous supports for connecting the foundation and the ground, wherein the step of performing spectral element division on the vibration isolator floating slab track corresponding finite half-track model to obtain a plurality of spectral elements specifically comprises: simulating each section of the rail or the half-section floating slab between two adjacent fasteners as a Timoshenko beam spectral element; simulating each fastener as a spring-damper spectral element; simulating each vibration isolator as a mass-inerter-spring-damper spectral element; simulating each shear hinge as a shear spring spectral element; simulating the non-reflecting boundary condition as a truncated spectral element; and simulating each section of the foundation support between two adjacent vibration isolators as a continuous support Timoshenko beam spectral element.

[0016] Preferably, the step of calculating the stiffness matrix corresponding to each spectral element to obtain the total spectral stiffness matrix of the finite half-track model specifically comprises: obtaining the expression corresponding to each spectral element, and obtaining the physical parameter values of the vibration isolator floating slab track corresponding finite half-track model; for each spectral element, bringing the physical parameter values into the expression corresponding to the spectral element to obtain the stiffness matrix corresponding to the spectral element; converting the element coordinate system in each spectral element into the global coordinate system according to the coordinate transformation mode of the finite element method to obtain the global spectral stiffness matrix; and performing model constraint condition processing on the global spectral stiffness matrix to obtain the total spectral stiffness matrix of the finite half-track model.

[0017] Preferably, the set of all decision variables satisfying the preset condition of the objective function is calculated by the following formula:

[0018]

[0019] wherein x=(b TID ,k TID ,c TID ) is the decision vector, b TID is the mass-inerter coefficient of the mass-inerter, k TID is the spring stiffness of the mass-inerter, c TID is the damping liquid damping of the mass-inerter, f is the frequency, the preset frequency range intervals are [f b1 , f b2 ] and [f b2 , f b3 ] respectively, and f b1 < f b2 < f b3 , R I is the amplitude of the displacement admittance response output by the second node, min F(x) represents taking the minimum value,

[0020] The decision vector value range is

[0021] Preferably, in the step of determining an optimal vector in the optimal vector solution set as the actual value of the corresponding preset parameter of the vibration isolator, specifically comprising: obtaining the optimal solution set front curve according to the mapping relationship between the target vector solution set and the objective function; determining the optimal decision vector according to the slope change of the optimal solution set front curve; for each parameter value in the optimal decision vector, as the actual parameter value of the corresponding preset parameter of the vibration isolator after optimization.

[0022] The vibration isolator provided by the embodiment of the present application comprises a bottom plate, a top cover, a first surrounding member, a second surrounding member, a first spring, first damping liquid and an inertial accumulator. The first surrounding member extends from the edge of the top cover to a first direction to form the first surrounding member. The second surrounding member extends from the first position of the bottom plate to a second direction to form the second surrounding member. The first direction is opposite to the second direction, and the second surrounding member is located in the accommodating space formed by the first surrounding member. The first spring is arranged in the second surrounding member, one end of the first spring is fixedly connected with the bottom plate, the first damping liquid is filled in the second surrounding member to cover part of the first spring, the inertial accumulator is located in the accommodating space formed by the second surrounding member, one end of the inertial accumulator is fixedly connected with the other end of the first spring, and the other end of the inertial accumulator is movably connected with the top cover, so that the inertial accumulator can move relative to the top cover in a preset direction. When the vibration isolator works, the inertia and stiffness characteristics of the structure can be adjusted through the cooperation of the vibration isolator and the first spring, the inertia in the vibration isolator is amplified, the vibration energy is transferred, and the vibration suppression effect of the vibration isolator is improved.

[0023] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the following preferred embodiments are specifically described below, and the accompanying drawings are described in detail as follows. BRIEF DESCRIPTION OF DRAWINGS

[0024] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0025] Figure 1 A structural schematic diagram of a vibration isolator provided by the embodiment of the present application;

[0026] Figure 2 A flowchart of a parameter optimization method of a vibration isolator provided by the embodiment of the present application;

[0027] Figure 3 A structure diagram of a finite half-track model of a TID vibration isolator floating plate track provided by an embodiment of the present application;

[0028] Figure 4 A schematic diagram of spectral element division of a finite half-track model provided by an embodiment of the present application;

[0029] Figure 5 A structure diagram of a mechanical model of a vibration isolator provided by an embodiment of the present application;

[0030] Figure 6 A structure diagram of a periodic half-track model provided by an embodiment of the present application;

[0031] Figure 7 A schematic diagram of spectral element division of a periodic half-track model provided by an embodiment of the present application;

[0032] Figure 8 A flow chart of steps of a total spectral stiffness matrix of a finite half-track model provided by an embodiment of the present application;

[0033] Figure 9 A schematic diagram of a two-node inerter-spring-damper spectral element provided by an embodiment of the present application;

[0034] Figure 10 A schematic diagram of a Pareto front of MOP provided by an embodiment of the present application. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. It should be understood that the drawings in the present application only serve the purpose of illustration and description, and do not serve to limit the protection scope of the present application. In addition, it should be understood that the schematic drawings are not drawn according to the actual proportions. The flow chart shows the operations implemented according to some embodiments of the present application. It should be understood that the operations of the flow chart can not be implemented in sequence, and the steps without logical context relationship can be reversed in sequence or implemented simultaneously. In addition, one or more other operations can be added to the flow chart or one or more operations can be removed from the flow chart under the guidance of the content of the present application.

[0036] In addition, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the accompanying drawings can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0037] In the prior art, in order to reduce the negative effects of urban rail transit environmental vibration, the subway company has taken many track vibration reduction measures. Among them, the steel spring floating slab track is considered to have excellent vibration reduction effect and is applied to the most stringent vibration reduction requirement line section. However, the frequency range of the steel spring floating slab track to play the vibration isolation role needs to be greater than 1.414 times the natural frequency of the floating slab, which causes the suppression effect of the floating slab on low-frequency vibration below 20Hz to be not obvious, and the resonance effect of the floating slab will also cause the vibration at about 10Hz to be amplified, so a vibration isolator needs to be used in cooperation to improve the vibration reduction performance of the floating slab track. In view of the above problems, the embodiments of the present application provide a vibration isolator and a parameter optimization method of the vibration isolator, which are described below through embodiments.

[0038] In order to facilitate the understanding of the present application, the technical solutions provided by the present application will be described in detail below in combination with specific embodiments.

[0039] Figure 1 A structure diagram of a vibration isolator provided by an embodiment of the present application is shown in FIG. 1. Figure 1 A vibration isolator provided by an embodiment of the present application includes a bottom disc 1, a top cover 2, a first surrounding part, a second surrounding part 3, and a TID (tuned inertial damper), and the TID specifically includes a first spring 4, a first damping liquid 5, and an inertial container.

[0040] The first surrounding part extends from the edge of the top cover 2 to a first direction to form a first surrounding part (not shown in the figure). The second surrounding part 3 extends from a first position of the bottom disc 1 to a second direction to form a second surrounding part 3. The first direction is opposite to the second direction, and the second surrounding part 3 is located in the containing space formed by the first surrounding part. The first spring 4 is arranged in the second surrounding part 3, and one end of the first spring 4 is fixedly connected with the bottom disc 1. The first damping liquid 5 is filled in the second surrounding part 3 to cover part of the first spring 4. The second surrounding part 3 and the bottom disc 1 can be integrally formed.

[0041] The inertial container is located in the containing space formed by the second surrounding member 3, one end of the inertial container is fixedly connected with the other end of the first spring 4, and the other end of the inertial container is movably connected with the top cover 2, so that the inertial container can move relative to the top cover 2 in a preset direction.

[0042] The inertial container, the first damping liquid 5 and the first spring 4 together form an inertial damping system, when the vibration isolator works, the inertial and stiffness characteristics of the structure can be adjusted through the cooperation of the vibration isolator and the first spring 4, the inertia inside the vibration isolator is amplified, the vibration energy is transferred, and the vibration suppression effect of the vibration isolator is improved.

[0043] In an embodiment of the present application, the inertial container specifically comprises a connecting sleeve 6, a rotating part 7, a fixed part 8, first rolling balls 9, second rolling balls and a bearing 10.

[0044] The connecting sleeve 6 is located in the containing space formed by the second surrounding member 3 and extends from the center of the top cover 2 to the first direction to form the connecting sleeve 6. The outer wall of the rotating part 7 is movably connected with the extended end of the connecting sleeve 6, and the inner wall of the rotating part 7 is formed with internal threads.

[0045] One end of the fixed part 8 is fixedly connected with the other end of the first spring 4, and the other end of the fixed part 8 is movably connected with the inner wall of the rotating part 7. Specifically, the fixed part 8 comprises an end disc and a lead screw extending from the center of the end disc to the second direction, the end disc is fixedly connected with the other end of the first spring 4, and the outer surface of the lead screw is formed with external threads matched with the internal threads on the inner wall of the rotating part 7. The second rolling balls (not shown in the figure) are arranged between the external threads formed on the outer surface of the lead screw and the internal threads formed on the inner wall of the rotating part 7, so that the lead screw is movably connected with the inner wall of the rotating part 7. The bearing 10 is arranged at the extended end of the connecting sleeve 6, and the first rolling balls 9 are arranged in the bearing 10.

[0046] When the vibration isolator works, the inertial container in the vibration isolator is subjected to force at both ends, a relative linear displacement is generated between the two ends of the inertial container, the vibration energy is converted into the rotary motion of the rotating part 7 through the second rolling balls and the lead screw, so as to realize inertia amplification. The vibration energy is transferred, and the vibration suppression effect of the vibration isolator is improved.

[0047] In an embodiment of the present application, the vibration isolator further comprises a third surrounding member 11, a second spring 12 and a second damping liquid 13.

[0048] The third surrounding part 11 extends from the edge of the bottom plate 1 to the second direction to form the third surrounding part 11, and the second surrounding part 3 is located in the containing space formed by the third surrounding part 11. The third surrounding part 11, the second surrounding part 3 and the bottom plate 1 can be integrally formed. The second spring 12 is arranged in the containing space between the second surrounding part 3 and the third surrounding part 11, one end of the second spring 12 is fixedly connected with the bottom plate 1, and the other end of the second spring 12 is fixedly connected with the top cover 2. The second damping liquid 13 is filled in the containing space between the second surrounding part 3 and the third surrounding part 11 to cover part of the second spring 12.

[0049] In the embodiment of the application, the second spring 12 and the second damping liquid 13 form a main damping system, when the vibration isolator works, the vibration between the inertial damper system formed by the inertial container, the first damping liquid 5 and the first spring 4 and the main damping system is not synchronized, and the asynchronous vibration can amplify the effective deformation of the internal energy dissipation device (that is, the first damping liquid 5), and the energy dissipation effect can further suppress the dynamic response.

[0050] Further, by applying TID to the steel spring floating slab track, a new type of TID vibration isolator floating slab track structure is proposed. On this basis, a periodic half-track model is established, and the spectral element method is used to solve it to reveal the damping mechanism of the TID vibration isolator floating slab track, and a finite half-track model is established, and a multi-objective genetic algorithm is used to realize the optimization of TID parameters.

[0051] As Figure 2 shown, the embodiment of the application also provides a parameter optimization method of a vibration isolator, including:

[0052] A1: performing spectral element division on a finite half-track model corresponding to a vibration isolator floating slab track to obtain a plurality of spectral elements, the plurality of spectral elements at least including Timoshenko beam spectral elements, continuous support Timoshenko beam spectral elements, spring-damper spectral elements, shear spring spectral elements and inertial container-spring-damper spectral elements, and the spectral elements are connected through nodes.

[0053] Figure 3 A structure diagram of a TID vibration isolator floating slab track finite half-track model provided by the embodiment of the application. The vibration isolator floating slab track here refers to a TID vibration isolator floating slab track structure.

[0054] As Figure 3As shown, further, the finite half-track model at least includes: a rail, a plurality of floating slabs located below the rail, a plurality of fasteners for connecting the rail and the floating slabs, a plurality of shear hinges arranged between adjacent floating slabs, a plurality of vibration isolators for connecting the floating slabs and the foundation, and a plurality of continuous supports for connecting the foundation and the ground. Wherein, the step of performing spectral element division on the finite half-track model corresponding to the vibration isolator floating slab track specifically includes:

[0055] Each section of the rail or the half-section floating slab between two adjacent fasteners is simulated as a Timoshenko beam spectral element, each fastener is simulated as a spring-damper spectral element, each vibration isolator is simulated as an inerter-spring-damper spectral element, each shear hinge is simulated as a shear spring spectral element, the non-reflecting boundary condition is simulated as a truncated spectral element, and each section of the foundation support between two adjacent vibration isolators is simulated as a continuous support Timoshenko beam spectral element.

[0056] Figure 4 A finite half-track model spectral element division schematic diagram is provided for the embodiments of the present application. As shown in Figure 4 , the rail is simulated as a Timoshenko beam, the fastener is simplified as a spring-damper, the TID vibration isolator is simplified as an inerter-spring-damper system, the floating slab is also simulated as a Timoshenko beam, the length of each floating slab is 8 times the fastener spacing, the shear hinge between the floating slabs is simulated as a shear spring, and the foundation is simplified as a continuous support Timoshenko beam. In order to reduce the influence of elastic wave reflection on the calculation results, the non-reflecting boundary condition is applied at both ends of the long rail.

[0057] In the embodiments of the present application, the mechanical model of the vibration isolator can be as shown in Figure 5 . In the figure, b TID , k TID and c TID are the inerter coefficient of the inerter, the spring (i.e., the first spring) stiffness of the inerter, and the damping liquid damping (i.e., the first damping liquid) of the inerter, k ss and c ss are the second spring stiffness and the second damping liquid damping, u1, u2 and u3 are the displacements of nodes 1-3, and f1 and f2 are the forces at both ends of the TID. The motion equations are established for nodes 1-3 respectively, and the following equations are obtained:

[0058]

[0059] In practical applications, floating slab tracks with added vibration isolators can be considered as one-dimensional periodic structures. Therefore, the flexural wave propagation characteristics of TID (Temperature Isolator) floating slab tracks can be studied using periodic structure elastic wave analysis methods. Based on periodic structure theory, a periodic semi-track model based on a double-layer point-supported beam structure is established, such as... Figure 6 The diagram shown is a structural schematic of a periodic half-orbit model provided in an embodiment of this application.

[0060] Figure 6 In the model, the periodic half-track consists of a rail, two sets of fasteners, a half-section floating plate, and a vibration isolator.

[0061] Furthermore, the spectral element method is used to divide the periodic half-orbit model into spectral units. Figure 7 This is a schematic diagram illustrating the spectral unit division of a periodic half-orbit model provided in an embodiment of this application. Figure 7 As shown, the rails and floating slabs can be simulated using Timoshenko beams, with a length equal to twice the fastener spacing. The fasteners can be simplified to springs, and the vibration isolators to an inertia container-spring system. The lower foundation is considered as a fixed constraint. Based on Bloch's theorem, a periodic connection is established between the two ends of the model. The model only considers vertical displacement and rotational degrees of freedom about the transverse axis, and the periodic half-track model of the steel spring floating slab track can be obtained by removing the components corresponding to TIDs from the model.

[0062] The rails are divided into 3 Timoshenko beam element types, the floating slab into 4 Timoshenko beam element types, each fastener into one spring element type, and the TID isolator into one inertial container-spring element type. The resulting model contains 10 element types and 10 nodes, with node numbers... Figure 7 The bid was successful.

[0063] It should be noted that since the introduction of damping can suppress the propagation of free elastic waves within the passband and thus change the band structure, the damping factor is not considered in the periodic half-track model to analyze the inherent elastic wave transmission characteristics of the TID isolator floating slab track. The physical parameters corresponding to the model are shown in Table 1. Table 1 is shown below:

[0064]

[0065]

[0066] A2: For each spectral element, calculate the stiffness matrix corresponding to that spectral element to obtain the total spectral stiffness matrix of the finite half-track model.

[0067] Figure 8 A flowchart illustrating the steps involved in creating the total spectral stiffness matrix for a finite half-orbit model, as provided in this application embodiment.Figure 8 As shown, for each spectral element, the stiffness matrix corresponding to the spectral element is calculated to obtain the total spectral stiffness matrix of the finite half-track model, specifically comprising:

[0068] B1: Obtain the expression corresponding to each spectral element, and obtain the physical parameter values of the finite half-track model corresponding to the isolator floating plate track.

[0069] Specifically, the physical parameter values of the finite half-track model refer to the physical parameter values in the TID in the TID.

[0070] B2: For each spectral element, the physical parameter values are brought into the expression corresponding to the spectral element to obtain the stiffness matrix corresponding to the spectral element;

[0071] B3: According to the coordinate transformation mode of the finite element method, the element coordinate system in each spectral element is converted into the global coordinate system to obtain the global spectral stiffness matrix;

[0072] B4: The global spectral stiffness matrix is subjected to model constraint condition processing to obtain the total spectral stiffness matrix of the finite half-track model.

[0073] In existing research, the stiffness matrix expressions of other types of spectral elements except the inertial container-spring spectral element have been derived. Figure 9 A schematic diagram of a two-node inertial container-spring-damper spectral element provided by the embodiment of the present application. For the two-node inertial container-spring(-damper) spectral element, the definitions of the spectral node load and displacement are as shown in Figure 9 , wherein U1 and F1 are the spectral node displacement and load at node 1, respectively, U2 and F2 are the spectral node displacement and load at node 2, respectively, S is a preset spectral stiffness matrix, and the inertial container-spring-damper spectral element stiffness matrix expression S ISD The expression of (ω) is:

[0074]

[0075]

[0076] Obviously, let c TID = 0 to obtain the inertial container-spring spectral element stiffness matrix. Then, the stiffness matrix of each spectral element is calculated according to the parameters shown in Table 1. The spectral element stiffness matrix in the element coordinate system is converted to the global coordinate system using the same coordinate transformation mode as the finite element method, and then assembled into the overall spectral stiffness matrix, while the model constraint condition processing is completed, finally obtaining the overall spectral stiffness matrix of the model, and obtaining the relationship between the model spectral node load vector and the displacement vector, denoted as formula one, the expression of formula one is as follows:

[0077] F = S(ω)U;

[0078] where S(ω) is the global spectral stiffness matrix, ω is the circular frequency, U is the spectral nodal displacement vector of the global model, and F is the spectral nodal load vector of the global model.

[0079] For the periodic half-track model, equation one can be refined as:

[0080]

[0081] where U i = (u i , θ i ) is the spectral nodal displacement vector of node i (=1-10), u i is the vertical displacement, θ i is the rotation angle, F j = (F j , M j ) is the spectral nodal load vector of node j (=1-10), F j is the vertical force, and M j is the bending moment. The spectral stiffness matrix S(ω) is divided into 10x10 sub-matrices S ij according to the node number. In order to establish the transfer relationship between the left end node and the right end node of the model, the combination of the refinement of equation one can be obtained as:

[0082]

[0083] where,

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] Since nodes 3-8 are not subjected to external loads (i.e. F M = 0), we have:

[0100]

[0101] where,

[0102]

[0103] Subsequently, according to the transfer relationship between the two end nodes:

[0104]

[0105] where t(ω) is the spectral transfer matrix, and the formula of t(ω) is:

[0106]

[0107] In addition, combined with the Bloch theorem, we have:

[0108]

[0109] where k is the one-dimensional Bloch wave vector (i.e. wave number), and the periodic constant l is equal to the model length (i.e. twice the fastener spacing), and finally we can get the standard eigenvalue problem about k and ω:

[0110] |t(ω)-e -ikl I| = 0,

[0111] where I is the unit matrix.

[0112] By solving this eigenvalue problem, we can get the band structure represented by k and ω. Since t(ω) is an 8x8 matrix, the characteristic solution contains 8 band curves, which respectively represent 4 pairs of elastic waves propagating in the periodic semi-orbit model. It has been verified that the TID vibration isolator floating slab track produces a controllable band gap in the low frequency range, which can suppress the propagation of bending waves in the floating slab, reduce the vertical amplitude of the floating slab, and reduce the force transmitted to the foundation by the vibration isolator.

[0113] A3: In the simulation platform, a first node of a target Timoshenko beam spectral element is determined, and a vertical spectral node load input by the first node and a total spectral stiffness matrix are input to output a displacement admittance response of a finite half-track model. Specifically, in order to reduce the influence of elastic wave reflection on the calculation result, a non-reflection boundary condition is applied at both ends of a long steel rail. A vertical simple harmonic point load is applied at a corresponding first node at a mid-span rail in the middle of the model, and the dynamic response of different track components is calculated. Only vertical displacement and rotation around the horizontal axis are considered in the model. At the same time, a finite half-track model of a steel spring floating slab track can be obtained by removing the TID element in the model. The simulation platform can be Matlab, etc.

[0114] A4: In the simulation platform, the NSGA-II algorithm is used, a plurality of preset parameters of the vibration isolator are input as decision variables, a set of preset function expressions corresponding to the displacement admittance response output by a second node of the target continuous support Timoshenko beam spectral element in each preset frequency range interval is input as an objective function, a set of all decision variables satisfying the preset condition of the objective function is output as an optimized vector solution set.

[0115] Further, the set of all decision variables satisfying the preset condition of the objective function is calculated by the following method, and the preset condition is described by the following formula:

[0116]

[0117] wherein x=(b TID ,k TID ,c TID ) is a decision vector, b TID is a mass inerter coefficient of the inerter, k TID is a spring stiffness of the inerter, c TID is a damping liquid damping of the inerter, f is a frequency, the preset frequency range intervals are [f b1 , f b2 ] and [f b2 , f b3 ] respectively, and f b1 <f b2 <f b3 , R I is an amplitude of the displacement admittance response output by the second node, and min F(x) represents taking the minimum value,

[0118] The decision vector has a value range of

[0119] It can be understood that the selection of the TID vibration isolator parameters should not only consider the improvement of the low-frequency damping performance, but also comprehensively consider the broadband damping performance. The parameter selection is a multi-objective optimization problem (MOP). Since the TID vibration isolator is obtained by adding a TID on the basis of the existing steel spring vibration isolator structure, in order to change the original components of the structure as little as possible, the MOP decision variables are the TID related parameters, that is, b TID , k TID and c TID , and the second spring stiffness k ss and the second damping liquid damping c ss are not involved in optimization. In this embodiment, the optimization objective of the TID parameter MOP is to simultaneously reduce the root mean square values of the base displacement admittance amplitudes in the frequency ranges of 1-30 Hz and 30-100 Hz. Wherein, F(x) is the objective vector, x=(b TID , k TID , c TID ) is the decision vector, f is the frequency, f b1 =1 Hz, f b2 =30 Hz and f b3 =100 Hz are the calculation boundary frequencies.

[0120] Wherein, the mathematical description formula of the multi-objective optimization problem is:

[0121]

[0122]

[0123] A5: Determine an optimal vector in the optimization vector solution set as the actual value of the corresponding preset parameter of the vibration isolator.

[0124] Further, the step of determining an optimal vector in the optimization vector solution set as the actual value of the corresponding preset parameter of the vibration isolator, specifically comprises:

[0125] According to the mapping relationship between the objective vector solution set and the objective function, the optimal solution set front curve is obtained. According to the slope change of the optimal solution set front curve, the optimal decision vector is determined. For each parameter value in the optimal decision vector, it is used as the actual parameter value of the corresponding preset parameter of the optimized vibration isolator.

[0126] Specifically, Figure 10 is a schematic diagram of a function corresponding to the Pareto front of the MOP provided by the embodiment of the application. The above MOP is solved by using NSGA-II, and the Pareto front (i.e. the image of the optimization vector solution set in the objective function space) is as shown in Figure 10 .

[0127] It can be understood that the calculation results of the steel spring floating slab track are taken as the demarcation point (the intersection of the two straight lines), and the plane formed by the target vector is divided into four regions A-D. For the optimal solution set in region A, the root mean square value of the base displacement admittance amplitude in the range of 1-30 Hz is reduced, and the root mean square value in the range of 30-100 Hz is increased. In region B, the root mean square value in the ranges of 1-30 Hz and 30-100 Hz is reduced, and if there is an optimal solution in this region, it is an ideal solution. The cases of regions C and D are opposite to those of regions A and B, respectively. It can be known that the optimal vector solution set falls in region A, indicating that when the low-frequency damping performance of the TID vibration isolator floating slab track is improved, the medium and high-frequency damping performance will be deteriorated to a certain extent. Figure 10 Figure 10

[0128] It can be known that when the Pareto frontier curve changes in the direction of reducing the root mean square value in the range of 1-30 Hz, the absolute value of the slope gradually increases, the deterioration of the medium and high-frequency damping performance is increasingly serious, and the optimal values of the decision variables b TID ,k TID ,c TID are continuously increased. Compared with the calculation results of the steel spring floating slab track, the low-frequency damping performance near the yellow point in the figure is greatly improved, the deterioration of the medium and high-frequency damping performance is smaller, and the values of the decision variables are easy to manufacture and realize, so the Pareto frontier point at this place is selected as the final optimization result, and the preset parameter values in the optimal decision vector are b TID = 274 kg, k TID = 1.06 x 10 6 N / m, and c TID = 7433 N·s / m.

[0129] The optimal solution of the TID parameters is substituted into the finite half-track model to calculate the base displacement admittance amplitude of the steel spring floating slab track and the TID vibration isolator floating slab track in the middle of the model. For the steel spring floating slab track, the displacement admittance amplitude curves of the floating slab and the steel rail have similar variation trends and characteristic frequencies to the base curve, but the amplitude values are different.

[0130] It can be known that the TID makes the first wave peak of the displacement admittance amplitude curves of the floating slab and the steel rail move to the low-frequency direction, the peak value is significantly weakened, and the amplitude in the band gap range is also significantly reduced. At the same time, each wave peak caused by the high-order vertical bending resonance of the floating slab and the steel rail is weakened. In the frequency range above 70 Hz, the curves of the two track forms are almost coincident, which shows that the TID has almost no effect on the medium and high-frequency vibration characteristics of the floating slab and the steel rail. It can be known that the suppression of the band gap on the bending wave weakens the influence of the low-frequency resonance, and the TID vibration isolator floating slab track not only improves the low-frequency damping performance, but also weakens the vibration response of the track components. ​​

[0131] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described system, device and unit can refer to the corresponding processes in the foregoing method embodiments, which will not be repeated here.

[0132] In several embodiments provided in the present application, it should be understood that the disclosed system, device and method can be implemented in other ways. The above-described device embodiments are only schematic, for example, the division of units is only a logical function division, and actual implementation can have another division manner, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some communication interfaces, devices or units, and can be electrical, mechanical or other forms.

[0133] The units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e., can be located in one place, or can be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the embodiment.

[0134] In addition, each functional unit in each embodiment of the present application can be integrated in one processing unit, or each unit can exist physically, or two or more units can be integrated in one unit.

[0135] If the functions are realized in the form of software function units and sold or used as independent products, they can be stored in a non-volatile computer readable memory executable by a processor. Based on this understanding, the technical solutions of the present application or the essential part or part of the technical solutions that make contributions to the prior art can be embodied in the form of a software product. The computer software product is stored in a memory and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the embodiments of the method of the present application. The foregoing memory includes: a U disk, a mobile hard disk, a read-only memory (Read-Only Memory, ROM), a random access memory (Random Access Memory, RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0136] Finally, it should be noted that the above-described embodiments are merely specific embodiments of the present application, which are used to illustrate the technical solutions of the present application, but not to limit the same. The protection scope of the present application is not limited thereto. Although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that any skilled person in the art can still modify or easily think of changes to the technical solutions recorded in the foregoing embodiments, or make equivalent replacements to some of the technical features, within the technical scope disclosed by the present application. The modifications, changes or replacements do not make the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method of parameter optimization of an isolator, characterized in that, The method comprises the following steps: A1: performing spectral element division on a finite half-track model corresponding to a floating slab track of an isolator to obtain a plurality of spectral elements, wherein the plurality of spectral elements at least include Timoshenko beam spectral elements, continuous support Timoshenko beam spectral elements, spring-damper spectral elements, shear spring spectral elements and inertial container-spring-damper spectral elements, and the spectral elements are connected through nodes; A2: for each spectral element, calculating a stiffness matrix corresponding to the spectral element to obtain a total spectral stiffness matrix of the finite half-track model; A3: in a simulation platform, determining a first node of a target Timoshenko beam spectral element, inputting a vertical spectral node load input by the first node and the total spectral stiffness matrix to output a displacement admittance response of the finite half-track model; A4: in the simulation platform, inputting a plurality of preset parameters of the isolator as decision variables, inputting a set of preset function expressions corresponding to displacement admittance responses output by a second node of a target continuous support Timoshenko beam spectral element in each preset frequency range interval as objective functions to output a set of all decision variables satisfying preset conditions of the objective functions as an optimization vector solution set; A5: determining an optimal vector in the optimization vector solution set as an actual value of the preset parameters corresponding to the isolator; The finite half-track model at least includes a steel rail, a plurality of floating slabs located below the steel rail, a plurality of fasteners for connecting the steel rail and the floating slabs, a plurality of shear hinges arranged between adjacent floating slabs, a plurality of isolators for connecting the floating slabs and the foundation, and a plurality of continuous supports for connecting the foundation and the ground, wherein the step of performing spectral element division on the finite half-track model corresponding to the floating slab track of the isolator to obtain a plurality of spectral elements specifically comprises: simulating each section of the steel rail or the half-section floating slab between two adjacent fasteners as a Timoshenko beam spectral element; simulating each fastener as a spring-damper spectral element; simulating each isolator as an inertial container-spring-damper spectral element; simulating each shear hinge as a shear spring spectral element; simulating a non-reflecting boundary condition as a truncated spectral element; simulating each section of the foundation support between two adjacent isolators as a continuous support Timoshenko beam spectral element.

2. The method of claim 1, wherein, The step of calculating, for each spectral element, a stiffness matrix corresponding to the spectral element to obtain a total spectral stiffness matrix of the finite half-track model specifically comprises: obtaining an expression corresponding to each spectral element and obtaining physical parameter values of the finite half-track model corresponding to the floating slab track of the isolator; for each spectral element, bringing the physical parameter values into the expression corresponding to the spectral element to obtain a stiffness matrix corresponding to the spectral element; converting an element coordinate system in each spectral element into a global coordinate system according to a coordinate transformation mode of the finite element method to obtain a global spectral stiffness matrix; performing model constraint condition processing on the global spectral stiffness matrix to obtain a total spectral stiffness matrix of the finite half-track model.

3. The method of claim 1, wherein, The set of all decision variables satisfying the preset condition of the target function is calculated in the following manner: The preset condition is described by the following formula: ； wherein ( b TID , k TID , c TID ) is a decision vector, b TID is a compliance coefficient of the compliance element, k TID is a spring stiffness of the compliance element, c TID is a damping liquid damping of the compliance element, is a frequency, the predetermined frequency range intervals being respectively f b1 , f b2 ] and f b2 , f b3 ] and f b1 f b2 f b3 , R I is an amplitude of the displacement admittance response output by the second node, denotes taking the minimum value,​​ 。 4. The method of claim 1, wherein, The step of determining an optimal vector from the set of optimal vector solutions as the actual value of the corresponding preset parameter of the vibration isolator specifically includes: According to the mapping relationship between the set of target vector solutions and the target function, an optimal solution set front curve is obtained; According to the slope change of the optimal solution set front curve, an optimal decision vector is determined; For each parameter value in the optimal decision vector, the actual parameter value of the corresponding preset parameter of the optimized vibration isolator is obtained.

5. An isolator characterized by, The parameter optimization method is suitable for the vibration isolator of claims 1-4, and the vibration isolator comprises: a bottom plate and a top cover; a first enclosing member extending from the edge of the top cover in a first direction to form the first enclosing member; a second enclosing member extending from the first position of the bottom plate in a second direction to form the second enclosing member, the first direction being opposite to the second direction, and the second enclosing member being located in the accommodating space formed by the first enclosing member; a first spring arranged in the second enclosing member, one end of the first spring being fixedly connected with the bottom plate; a first damping liquid filled in the second enclosing member to cover part of the first spring; an inertial container located in the accommodating space formed by the second enclosing member, one end of the inertial container being fixedly connected with the other end of the first spring, and the other end of the inertial container being movably connected with the top cover, so that the inertial container can move in a preset direction relative to the top cover.

6. The vibration isolator of claim 5, wherein The inertial container comprises: a connecting sleeve located in the accommodating space formed by the second enclosing member and extending from the center of the top cover in a first direction to form the connecting sleeve; a rotating part, the outer wall of the rotating part being movably connected with the extension end of the connecting sleeve; a fixed part, one end of the fixed part being fixedly connected with the other end of the first spring, and the other end of the fixed part being movably connected with the inner wall of the rotating part.

7. The vibration isolator of claim 6, wherein The inertial container further comprises: a bearing arranged at the extension end of the connecting sleeve; a first rolling ball arranged in the bearing.

8. The vibration isolator of claim 6, wherein An inner thread is formed on the inner wall of the rotating part, the fixed part comprises an end disc and a lead screw extending from the center of the end disc in a second direction, the end disc being fixedly connected with the other end of the first spring, and an outer thread being formed on the outer surface of the lead screw and matching with the inner thread on the inner wall of the rotating part, the inertial container further comprises: a second rolling ball arranged between the outer thread formed on the outer surface of the lead screw and the inner thread formed on the inner wall of the rotating part, so that the lead screw and the inner wall of the rotating part are movably connected.

9. The vibration isolator of claim 5, wherein The vibration isolator further comprises: a third enclosing member extending from the edge of the bottom plate in a second direction to form the third enclosing member, and the second enclosing member being located in the accommodating space formed by the third enclosing member; A second spring is arranged in the accommodating space between the second enclosing member and the third enclosing member, one end of the second spring is fixedly connected with the bottom cover, and the other end of the second spring is fixedly connected with the top cover; A second damping liquid is filled in the accommodating space between the second enclosing member and the third enclosing member to cover part of the second spring.

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