Vehicle-bridge Coupled Vibration Analysis Method and System Based on Time History Array Interaction Iteration

Abstract

The present invention relates to the technical field of vehicle-bridge coupled vibration analysis, and particularly to a vehicle-bridge coupled vibration analysis method based on time history array interactive iteration, including: analyzing the bridge subsystem based on the ANSYS platform to obtain the initial response time history array of the bridge; sharing data between the ANSYS platform and the MATLAB platform, analyzing the vehicle subsystem on the MATLAB platform, and obtaining the equivalent road surface roughness time history array according to the obtained initial response time history array of the bridge; performing a coupled analysis on the bridge subsystem and the vehicle subsystem, and obtaining the vibration responses of the bridge and the vehicle according to the equivalent road surface roughness time history array. By using the data sharing between MATLAB and ANSYS, the vehicle subsystem and the bridge subsystem are respectively analyzed, and then the coupled analysis of the vehicle and bridge subsystems is performed to obtain the vibration responses of the bridge and the vehicle. Avoiding the integration iteration of time steps improves the operation efficiency. The present invention also provides a vehicle-bridge coupled vibration analysis system based on time history array interactive iteration.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle-bridge coupled vibration analysis, and particularly to a vehicle-bridge coupled vibration analysis method and system based on time history array interactive iteration. Background Art

[0002] When vehicles such as automobiles or trains pass over a bridge, they impact the bridge, causing the bridge to vibrate. The vibration of the bridge in turn affects the smoothness and safety of the running vehicles. The vehicle and the bridge form a unified coupled vibration system that influences and correlates with each other. Studying the vehicle and the bridge separately cannot correctly reflect their vibration responses.

[0003] Currently, in the research on vehicle-bridge coupled vibration, the main approach is to establish the overall dynamic equation of the vehicle and the bridge and solve the dynamic responses of the vehicle and the bridge simultaneously. This method well solves the coupling problem of the vehicle and the bridge, but it is necessary to correct the mass, stiffness, and damping matrices of the overall dynamic equation at each integration step. For trains, it is also necessary to first predict the "hunting wave" of the train operation. Another method treats the vehicle and the bridge as two subsystems and uses an iterative method to separately obtain the dynamic responses of the vehicle and the bridge through the coordination relationship between the two systems. For this method, when establishing the damping matrix of the vehicle model for an automobile, it is necessary to know in advance the magnitude of the vertical force, and the vertical force is solved through iteration. Therefore, at each time step, not only iteration is required, but also the damping matrix needs to be corrected at each iteration step. When solving the wheel-rail force for a train, it is necessary to know in advance the displacement and velocity of the wheel set and the rail, and the displacement and velocity of the wheel set and the rail are unknowns themselves. Therefore, it is necessary to first assume the displacement and velocity values and then continuously iterate until convergence to the true solution.

[0004] The above analysis methods are specifically implemented by compiling their own step-by-step numerical integration programs. Like any numerical integration method, the accuracy of the step-by-step integration method depends on the length of the time increment taken, and it is an iterative integration for the time step. And in order to perform reliable analysis, the time increment must be short enough for the above analysis methods, resulting in a large amount of computation. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the present invention proposes a vehicle-bridge coupled vibration analysis method and system based on time history array interactive iteration, which improves the operation efficiency.

[0006] In the first aspect, the present invention provides a vehicle-bridge coupled vibration analysis method based on time history array interactive iteration.

[0007] In the first implementable mode, a vehicle-bridge coupling vibration analysis method based on time history array interaction iteration includes: analyzing the bridge subsystem based on the ANSYS platform to obtain the initial response time history array of the bridge; the ANSYS platform sharing the initial response time history array of the bridge with MATLAB, and the MATLAB platform analyzing the vehicle subsystem based on the initial response time history array of the bridge to obtain the equivalent road surface roughness time history array; performing a coupling analysis on the bridge subsystem and the vehicle subsystem, and obtaining the vibration responses of the bridge and the vehicle according to the equivalent road surface roughness time history array.

[0008] Combined with the first implementable mode, in the second implementable mode, obtaining the initial response time history array of the bridge includes: based on the ANSYS platform, performing finite element modeling according to the preset bridge structure information; determining the initial action time history matrix of the vehicle on the bridge; applying the excitation of the initial action time history matrix of the vehicle on the bridge in the bridge structure model to obtain the initial response time history array of the bridge.

[0009] Combined with the second implementable mode, in the third implementable mode, determining the initial action time history matrix of the vehicle on the bridge includes: determining the initial action time history matrix of the bridge on the vehicle according to the vehicle motion equation; determining the initial action time history matrix of the vehicle on the bridge according to the initial action time history matrix of the bridge on the vehicle.

[0010] Combined with the second implementable mode, in the fourth implementable mode, applying the excitation of the initial action time history matrix of the vehicle on the bridge in the bridge structure model to obtain the initial response time history array of the bridge includes: successively extracting the responses of the contact points between the front and rear axles of the vehicle and the bridge main girder, and the responses of four relevant nodes of the bridge main girder by using the interpolation method; forming the initial response time history array of the bridge with the responses of the contact points between the front and rear axles of the vehicle and the bridge main girder and the responses of the four relevant nodes of the bridge main girder.

[0011] Combined with the first implementable mode, in the fifth implementable mode, obtaining the equivalent road surface roughness time history array according to the initial response time history array of the bridge shared by the ANSYS platform includes: on the MATLAB platform, obtaining the equivalent road surface roughness time history array according to the initial response time history array of the bridge and the preset simulated road surface roughness time history.

[0012] Combined with the first implementation, in the sixth implementation, obtaining the vibration responses of the bridge and the vehicle according to the equivalent road surface roughness time history array includes: obtaining the bridge vibration response time history array according to the equivalent road surface roughness time history array; determining whether the bridge vibration response time history array converges; in the case where the bridge vibration response time history array does not converge, obtaining an updated equivalent road surface roughness time history array according to the bridge vibration response time history array, and repeating the above process with the updated equivalent road surface roughness time history array as the equivalent road surface roughness time history array; in the case where the bridge vibration response time history array converges, obtaining the vehicle vibration response time history array.

[0013] Combined with the sixth implementation, in the seventh implementation, obtaining the bridge vibration response time history array according to the equivalent road surface roughness time history array includes: obtaining the time history matrix of the bridge's action on the vehicle at the vehicle-bridge contact point according to the equivalent road surface roughness time history array; determining the time history matrix of the vehicle's action on the bridge according to the time history matrix of the bridge's action on the vehicle; obtaining the bridge vibration response time history array according to the time history matrix of the vehicle's action on the bridge.

[0014] Combined with the sixth implementation, in the eighth implementation, obtaining the time history matrix of the bridge's action on the vehicle at the vehicle-bridge contact point according to the equivalent road surface roughness time history array includes:

[0015] By calculating obtaining the time history matrix of the bridge's action on the vehicle at the vehicle-bridge contact point;

[0016] where, f vbzi is the vertical action time history matrix borne by the wheel, f vbhi is the lateral action time history matrix borne by the wheel, C lzi is the vertical damping coefficient at the tire-road surface contact point, K lzi is the stiffness coefficient at the tire-road surface contact point; is the vertical speed of the road surface at the wheel-road surface contact point, Z ci is the vertical displacement of the road surface at the wheel-road surface contact point; is the vertical speed of the wheel at the wheel-road surface contact point, Z si is the vertical displacement of the wheel at the wheel-road surface contact point; C hi is the lateral damping coefficient at the tire-road surface contact point, K hi is the elastic coefficient at the tire-road surface contact point; is the lateral speed of the road surface at the wheel-road surface contact point, Y ci is the lateral displacement of the road surface at the wheel-road surface contact point; is the lateral speed of the wheel at the wheel-road surface contact point, Y si is the lateral displacement of the wheel at the wheel-road surface contact point.

[0017] Combined with the seventh implementation manner, in the ninth implementation manner, when the time history array of the bridge vibration response converges, obtaining the time history array of the vehicle vibration response includes:

[0018] When the time history array of the bridge vibration response converges, obtaining the time history array of the vehicle vibration response according to the time history matrix of the action of the bridge on the vehicle.

[0019] In a second aspect, the present invention provides a vehicle-bridge coupling vibration analysis system based on time history array interaction iteration.

[0020] In the tenth implementation manner, the vehicle-bridge coupling vibration analysis system based on time history array interaction iteration includes: a bridge subsystem analysis module configured to analyze the bridge subsystem based on the ANSYS platform to obtain the initial response time history array of the bridge; a vehicle subsystem analysis module configured to share data between the ANSYS platform and the MATLAB platform, the MATLAB platform obtains the initial response time history array of the bridge, and analyzes the vehicle subsystem, and obtains the equivalent road surface unevenness time history array according to the initial response time history array of the bridge; a coupling analysis module configured to perform a coupling analysis on the bridge subsystem and the vehicle subsystem, and obtain the vibration responses of the bridge and the vehicle according to the equivalent road surface unevenness time history array.

[0021] As can be seen from the above technical solutions, the beneficial technical effects of the present invention are as follows:

[0022] 1. Combining and making full use of the efficient matrix calculation function of the MATLAB platform and the professional modeling, finite element calculation, and pre- and post-processing functions of the ANSYS structural analysis software, regarding the vehicle and the bridge as an interacting and unified system, using the data sharing between MATLAB and ANSYS, analyzing the vehicle subsystem and the bridge subsystem respectively, and then performing a coupling analysis on the vehicle subsystem and the bridge subsystem, and finally obtaining the vibration responses of the bridge and the vehicle. In this way, the integration iteration of the time step is avoided, the amount of calculation is reduced, and the calculation efficiency is improved.

[0023] 2. Utilizing the powerful matrix calculation function of MATLAB, performing data exchange and update in the form of a time history array, only need to set the time step according to the total time of the vehicle crossing the bridge at the beginning, avoiding the stability sensitivity of the time increment of the step-by-step integration method, and greatly improving the calculation efficiency; similarly, for complex vehicles and multiple vehicles, the time history array method is nothing more than an increase in the number of matrix columns and arrays, and the modeling can be easily realized, with general applicability and expandability. Description of the Drawings

[0024] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0025] Figure 1 Schematic diagram of a vehicle-bridge coupling vibration analysis method based on time history array interactive iteration provided by the present invention;

[0026] Figure 2 Flowchart of obtaining the vibration responses of bridges and vehicles provided by the present invention;

[0027] Figure 3 Schematic structural diagram of a vehicle-bridge coupling vibration analysis system based on time history array interactive iteration provided by the present invention;

[0028] Figure 4 Schematic diagram of a simply supported beam model with a constant force moving at a uniform speed provided by the present invention;

[0029] Figure 5-a Curve graph of the mid-span displacement calculated by applying the theoretical solution of Krylov provided by the present invention;

[0030] Figure 5-b Curve graph of the mid-span displacement calculated by applying the literature solution provided by the present invention;

[0031] Figure 5-c Curve graph of the mid-span displacement calculated by using the analysis method of the present application provided by the present invention. Specific Embodiments

[0032] The following will describe in detail the embodiments of the technical solutions of the present invention with reference to the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and thus are only examples and cannot be used to limit the protection scope of the present invention.

[0033] It should be noted that unless otherwise specified, the technical terms or scientific terms used in this application should have the ordinary meanings understood by those skilled in the art to which the present invention belongs.

[0034] In some embodiments, vehicle information and relevant parameters of the bridge structure are preset and corresponding data files are formed for platform call. The highway grade information is preset, and the road surface unevenness is simulated and generated at any time according to the highway grade information, and a data file is formed for platform call.

[0035] Combined Figure 1 As shown, this embodiment provides a vehicle-bridge coupling vibration analysis method based on time history array interactive iteration, including:

[0036] Step S01: Analyze the bridge subsystem based on the ANSYS platform to obtain the initial response time history array of the bridge;

[0037] Step S02: After data sharing between the ANSYS platform and the MATLAB platform, the MATLAB platform analyzes the vehicle subsystem, and obtains the equivalent road surface roughness time history array according to the initial response time history array of the bridge shared by the ANSYS platform;

[0038] Step S03: Perform a coupled analysis of the bridge subsystem and the vehicle subsystem, and obtain the vibration responses of the bridge and the vehicle according to the equivalent road surface roughness time history array.

[0039] Combining and making full use of the efficient matrix calculation function of the MATLAB (matrix & laboratory) platform and the professional modeling, finite element calculation, and pre- and post-processing functions of the ANSYS (Analysis of Systems) structural analysis software, regarding the vehicle and the bridge as an interacting and unified system, using the data sharing between MATLAB and ANSYS, analyze the vehicle subsystem and the bridge subsystem respectively, and then perform a coupled analysis of the vehicle subsystem and the bridge subsystem, and finally obtain the vibration responses of the bridge and the vehicle. Avoiding the integration iteration of time steps improves the operation efficiency.

[0040] Optionally, obtaining the initial response time history array of the bridge includes: based on the ANSYS platform, performing finite element modeling according to the preset bridge structure information; the initial action time history matrix of the vehicle on the bridge; applying the excitation of the initial action time history matrix of the vehicle on the bridge in the bridge structure model to obtain the initial response time history array of the bridge.

[0041] In some embodiments, on the ANSYS platform, call the data file corresponding to the preset bridge structure related parameters, perform finite cloud modeling, and obtain the bridge structure model.

[0042] Optionally, determining the initial action time history matrix of the vehicle on the bridge includes: determining the initial action time history matrix of the bridge on the vehicle according to the vehicle motion equation; determining the initial action time history matrix of the vehicle on the bridge according to the initial action time history matrix of the bridge on the vehicle.

[0043] Optionally, the vehicle motion equation is expressed by the following formula:

[0044]

[0045] In the above formula, M v is the total mass of the vehicle, C v is the damping, K v is the stiffness matrix, is the acceleration of the vehicle, is the speed of the vehicle, u v is the displacement of the vehicle, f vb is the time history matrix of the force exerted by the bridge on the vehicle.

[0046] When conducting a unified analysis of the vehicle and the bridge, the mass, stiffness matrix, and damping of the vehicle motion equation change as the vehicle moves on the bridge. When using a unified coupled motion equation, the coefficient matrix needs to be regenerated and decomposed at each time step in the analysis; at the same time, as the number of vehicles on the bridge increases, the coupled degrees of freedom also increase, resulting in an increase in the computational workload and making programming more difficult. In this application, taking the contact point between the wheel and the bridge deck as the boundary, the vehicle and the bridge are regarded as two subsystems, and the vehicle subsystem and the bridge subsystem are analyzed separately, and then balance iteration is carried out according to the coupling relationship between the two subsystems. In this way, the coefficient matrices of the respective motion equations of the vehicle and the bridge remain unchanged at each time step, greatly reducing the computational difficulty. Moreover, by utilizing the powerful matrix calculation function of MATLAB and performing data exchange and update in the form of a time history array, only the time step needs to be set according to the total time for the vehicle to cross the bridge at the beginning, avoiding the stable sensitivity of the step-by-step integration method to the time increment, and further improving the computational efficiency; similarly, for complex vehicles and multiple vehicles, the time history array method is nothing more than an increase in the number of matrix columns and arrays, and the modeling can be easily realized, with general applicability and expandability.

[0047] Optionally, according to the principle of interaction, the force exerted by the bridge on the vehicle is equal in magnitude and opposite in direction to the force exerted by the vehicle on the bridge. According to the initial time history matrix f of the force exerted by the bridge on the vehicle vb the initial time history matrix of the force exerted by the vehicle on the bridge can be obtained.

[0048] In some embodiments, the initial acceleration of the vehicle the initial speed and the initial displacement are all 0. Substituting the initial acceleration, initial speed, and initial displacement into the vehicle motion equation, the initial time history matrix of the force exerted by the bridge on the vehicle is obtained as 0. According to the principle of interaction, the initial time history matrix f of the force exerted by the vehicle on the bridge bv 0 (t) is 0.

[0049] Optionally, when applying the excitation of the initial vehicle-bridge action time history matrix in the bridge structure model, an initial bridge response time history array is obtained, including: successively extracting the responses of the contact points between the front and rear axles of the vehicle and the bridge main girder, and the responses of four relevant nodes of the bridge main girder by using the interpolation method; and forming an initial bridge response time history array from the responses of the contact points between the front and rear axles of the vehicle and the bridge main girder and the responses of the four relevant nodes of the bridge main girder. In this way, the entire process of multiple vehicles traveling on and off the bridge with different vehicle speeds, spacings, etc. can be considered, the geometric and mechanical relationship transmission at the vehicle-bridge contact points can be realized, and the accuracy and applicability of the analysis are improved.

[0050] In some embodiments, after obtaining the initial vehicle-bridge action time history matrix, the initial bridge response time history array is calculated by using ANSYS transient analysis. When extracting the results, the responses of the contact points between the front and rear axles of the vehicle and the bridge main girder, and the responses of four relevant nodes of the bridge main girder are successively extracted by using the interpolation method, and an initial bridge response time history array is formed from the responses of the contact points between the front and rear axles of the vehicle and the bridge main girder and the responses of the four relevant nodes of the bridge main girder.

[0051] Optionally, an equivalent road surface roughness time history array is obtained, including: on the MATLAB platform, an equivalent road surface roughness time history array is obtained according to the initial bridge response time history array and the simulated road surface roughness time history.

[0052] In some embodiments, on the MATLAB platform, after combining the initial bridge response time history array and the simulated road surface roughness time history, an equivalent road surface roughness time history array is formed. The equivalent road surface roughness time history array is expressed as where is the comprehensive response of the bridge vertical deformation and the road surface roughness, is the vertical acceleration of the road surface at the wheel-road contact point, is the vertical velocity of the road surface at the wheel-road contact point, Z ci is the vertical displacement of the road surface at the wheel-road contact point; is the comprehensive response of the bridge lateral deformation and the road surface roughness, is the lateral acceleration of the road surface at the wheel-road contact point, is the lateral velocity of the road surface at the wheel-road contact point, Y ci is the lateral displacement of the road surface at the wheel-road contact point.

[0053] Optionally, the vibration responses of the bridge and the vehicle are obtained according to the equivalent road surface unevenness time history array, including: obtaining the bridge vibration response time history array according to the equivalent road surface unevenness time history array; determining whether the bridge vibration response time history array converges; in the case where the bridge vibration response time history array does not converge, obtaining an updated equivalent road surface unevenness time history array according to the bridge vibration response time history array, and repeating the above process with the updated equivalent road surface unevenness time history array as the new equivalent road surface unevenness time history array; in the case where the bridge vibration response time history array converges, obtaining the vehicle vibration response time history array.

[0054] Optionally, obtaining the bridge vibration response time history array according to the equivalent road surface unevenness time history array includes: obtaining the time history matrix of the action of the bridge on the vehicle at the vehicle-bridge contact point according to the equivalent road surface unevenness time history array; determining the time history matrix of the action of the vehicle on the bridge according to the time history matrix of the action of the bridge on the vehicle; obtaining the bridge vibration response time history array according to the time history matrix of the action of the vehicle on the bridge.

[0055] Optionally, the time history matrix of the action of the bridge on the vehicle at the vehicle-bridge contact point is obtained by the following formula:

[0056]

[0057] In the above formula, f vbzi is the vertical action time history matrix borne by the wheel, f vbhi is the lateral action time history matrix borne by the wheel, C lzi is the vertical damping coefficient at the tire-road surface contact point, K lzi is the stiffness coefficient at the tire-road surface contact point; is the vertical speed of the road surface at the wheel-road surface contact point, Z ci is the vertical displacement of the road surface at the wheel-road surface contact point; is the vertical speed of the wheel at the wheel-road surface contact point, Z si is the vertical displacement of the wheel at the wheel-road surface contact point; C hi is the lateral damping coefficient at the tire-road surface contact point, K hi is the elastic coefficient at the tire-road surface contact point; is the lateral speed of the road surface at the wheel-road surface contact point, Y ci is the lateral displacement of the road surface at the wheel-road surface contact point; is the lateral speed of the wheel at the wheel-road surface contact point, Y si is the lateral displacement of the wheel at the wheel-road surface contact point.

[0058] In some embodiments, according to the interaction principle, the time history matrix of the action of the vehicle on the bridge f vb is determined from the time history matrix of the action of the bridge on the vehicle f bv. On the ANSYS platform, when applying the time history matrix f of the vehicle's action on the bridge to the bridge structure model, the excitation of bv is obtained, and the bridge vibration response array is obtained. bv Among them, is the acceleration of the bridge structure updated for the nth time, is the velocity of the bridge structure updated for the nth time, and is the displacement of the bridge structure updated for the nth time. The ANSYS platform shares the bridge vibration response array with the MATLAB platform. The MATLAB platform analyzes the vehicle subsystem based on the bridge vibration response time history array and obtains the updated equivalent road surface unevenness time history array. Among them, is the acceleration of the bridge structure updated for the nth time, is the velocity of the bridge structure updated for the nth time, is the displacement of the bridge structure updated for the nth time. The ANSYS platform shares the bridge vibration response array with the MATLAB platform. The MATLAB platform analyzes the vehicle subsystem according to the bridge vibration response time history array and obtains the updated equivalent road surface unevenness time history array.

[0059] Optionally, when the bridge vibration response time history array converges, the vehicle vibration response time history array is obtained, including: when the bridge vibration response time history array converges, the vehicle vibration response time history array is obtained according to the time history matrix of the bridge's action on the vehicle.

[0060] In some embodiments, given the time history matrix f of the bridge's action on the vehicle vb , the Runge-Kutta method of the MATLAB platform is used to solve the vehicle motion equation to obtain the vehicle vibration response time history array . vb Among them, is the acceleration of the vehicle updated for the nth time, is the velocity of the vehicle updated for the nth time, and is the displacement of the vehicle updated for the nth time. Obtain the vehicle vibration response time history array Among them, is the acceleration of the vehicle updated for the nth time, is the velocity of the vehicle updated for the nth time, is the displacement of the vehicle updated for the nth time.

[0061] As shown in combination with Figure 2 , in some embodiments, the process of obtaining the vibration responses of the bridge and the vehicle includes: Figure 2 Step S11: Based on the ANSYS platform, finite element modeling is performed according to the preset bridge structure information to determine the initial time history matrix of the vehicle's action on the bridge. The excitation of the initial time history matrix of the vehicle's action on the bridge is applied to the bridge structure model, and the initial bridge response time history array is obtained;

[0062] Step S12: On the MATLAB platform, based on the initial bridge response time history array and the preset simulated road surface unevenness time history, the equivalent road surface unevenness time history array is obtained;

[0063] Step S13: According to the equivalent road surface unevenness time history array, the time history matrix of the bridge's action on the vehicle at the vehicle-bridge contact point is obtained;

[0064] Step S14: According to the time history matrix of the bridge's action on the vehicle, the time history matrix of the vehicle's action on the bridge is determined;

[0065] Step S14: Determine the time history matrix of the vehicle's action on the bridge according to the time history matrix of the bridge's action on the vehicle;

[0066] Step S15: Obtain the bridge vibration response time history array according to the vehicle-to-bridge action time history matrix;

[0067] Step S16: Determine whether the bridge vibration response time history array converges; if the bridge vibration response time history array does not converge, execute Step S17; if the bridge vibration response time history array converges, execute Step S18;

[0068] Step S17: Obtain the updated equivalent road surface unevenness time history array according to the bridge vibration response time history array, and use the updated equivalent road surface unevenness time history array as the equivalent road surface unevenness time history array to return to Step S13;

[0069] Step S18: Obtain the vehicle vibration response time history array according to the bridge-to-vehicle action time history matrix.

[0070] In this way, by performing data exchange and update in the form of time history arrays, only need to set the time step according to the total time of the vehicle crossing the bridge at the beginning, generally set to 1 / 500 to meet the accuracy requirements, avoiding the stability sensitivity of the step-by-step integration method to time increments, and greatly improving the operation efficiency; moreover, for complex vehicles and multiple vehicles, the time history array method is nothing more than an increase in the number of matrix columns and arrays, and the modeling can be easily realized, with universal applicability and expandability.

[0071] Combined with Figure 3 As shown, this embodiment provides a vehicle-bridge coupling vibration analysis system based on time history array interaction iteration, including a bridge subsystem analysis module 101, a vehicle subsystem analysis module 102, and a coupling analysis module 103. The bridge subsystem analysis module 101 is configured to analyze the bridge subsystem based on the ANSYS platform to obtain the initial bridge response time history array; the vehicle subsystem analysis module 102 is configured to share the initial bridge response time history array by the ANSYS platform with the MATLAB platform, and the MATLAB platform analyzes the vehicle subsystem according to the initial bridge response time history array to obtain the equivalent road surface unevenness time history array; the coupling analysis module 103 is configured to perform coupling analysis on the bridge subsystem and the vehicle subsystem, and obtain the vibration responses of the bridge and the vehicle according to the equivalent road surface unevenness time history array.

[0072] By making use of the efficient matrix calculation function of the MATLAB platform and the professional modeling, finite element calculation, and pre- and post-processing functions of the ANSYS structural analysis software, the vehicle and the bridge are regarded as an interacting and unified system. The motion equations of the vehicle and bridge subsystems are established respectively. Through the mechanical balance and geometric compatibility conditions between the vehicle and the bridge, data intercommunication and iteration are realized, and the subsystems are solved interactively. Finally, a consistent vehicle-bridge coupling vibration analysis result is obtained. In this way, global analysis is not required, thus avoiding the operation of a huge system matrix, and improving the operation efficiency. Data exchange and update are realized through the time history array method, further improving the operation efficiency. The integration iteration for time steps is avoided, and the convergence parameter does not need to be adjusted repeatedly, thus improving the convergence speed. At the same time, more complex vehicle bodies can be simulated, and the applicability is stronger.

[0073] Fully utilize and combine the technical advantages of the existing software platform, and develop the required algorithm functions on this basis, which has broad application prospects. In contrast, self-written programs are more complex, and it is impossible or very difficult to establish complex bridge models, so the application is restricted. The ANSYS preprocessing module provides a powerful solid modeling and meshing tool, and its rich element library can support most structures to build accurate finite element models according to needs. Secondly, ANSYS also specifically sets up data interfaces with some well-known large general analysis software, facilitating data exchange. In addition, the ANSYS postprocessor can perform various convenient operations on the analysis results. The above advantages make it very suitable as the operating platform for self-developed programs.

[0074] In some embodiments, the verification process of the vehicle-bridge coupling vibration analysis method based on time history array interactive iteration of the present application is as follows:

[0075] The bridge analysis model is a simply supported beam with a span L = 1.1938 m as shown in Figure 4 and a cross-sectional area A = 0.51e-2 m 2 (constant cross-section), moment of inertia I = 0.9448e-8 m 4 , material elastic modulus E = 10.4804e10 N / m 2 , material ρ = 2.9602e3 kg / m 3 . The bridge finite element model is simulated by 100 beam4 elements, and the influence of bridge damping is not considered.

[0076] Optionally, the theoretical calculation formula for the natural vibration frequency of the constant cross-section simply supported beam is:

[0077]

[0078] Substituting the defined parameters of the bridge into the above formula can obtain the theoretical natural vibration frequency of the bridge analysis model.

[0079] Table 1 shows the first 10 vibration frequencies (Hz) of the simply supported beam

[0080]

[0081]

[0082] In some embodiments, the first 100 modes of the bridge are calculated using the analysis method of the present application. Table 1 lists the frequencies of the first 10 modes among them. In addition, the solutions obtained by (Yang Jianrong, 2008) using his self-written program are also listed in Table 1. As shown in Table 1, the theoretical solution corresponding to serial number 1 is 8.93, the literature solution is 8.93, and the solution calculated using the present analysis method is 8.93; the theoretical solution corresponding to serial number 5 is 223.16, the literature solution is 223.12, and the solution calculated using the present analysis method is 223.12; the theoretical solution corresponding to serial number 10 is 892.63, the literature solution is 892.04, and the solution calculated using the present analysis method is 892.06. Comparing the first 10 vibration frequencies of the bridge model, the calculation results using the present analysis method are almost exactly the same as the theoretical frequencies

[0083] Optionally, the velocity parameter α is defined as α = T / τ, where T is the first vibration period of the bridge, and τ represents the time taken for the vehicle to cross the bridge. Thus, the velocity parameter can also be expressed as α = TV / L, where L is the bridge span and V is the vehicle speed. When the moving constant force F = 52.9442 N crosses the bridge at different vehicle speeds, the dynamic response of the bridge is calculated using the present analysis method

[0084] Figure 5-a To calculate the mid-span displacement curve graph using the theoretical solution of Krylov Figure 5-b To calculate the mid-span displacement curve graph using the literature solution (Yang Jianrong, 2008) Figure 5-c To calculate the mid-span displacement curve graph using the present analysis method, the calculation results of the three methods are almost exactly the same. The above calculation results show that the analysis method of the present application is correct in calculating the dynamic response of the bridge under the action of a moving constant force

[0085] The example analysis shows that the present analysis method can obtain high-precision and reliable numerical results only through one interactive iteration, greatly improving the operation speed

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the various embodiments of the present invention, and they should all be covered within the scope of the claims and the specification of the present invention.

Claims

1. A vehicle-bridge coupling vibration analysis method based on time-history array interaction iteration, characterized in that Including: Analyze the bridge subsystem based on the ANSYS platform to obtain the initial response time history array of the bridge; The ANSYS platform shares the initial response time history array of the bridge with the MATLAB platform, and the MATLAB platform analyzes the vehicle subsystem according to the initial response time history array of the bridge to obtain the equivalent road surface unevenness time history array; Conduct a coupling analysis on the bridge subsystem and the vehicle subsystem, and obtain the vibration responses of the bridge and the vehicle according to the equivalent road surface unevenness time history array; Among them, obtaining the vibration responses of the bridge and the vehicle according to the equivalent road surface unevenness time history array includes: Obtain the bridge vibration response time history array according to the equivalent road surface unevenness time history array; Judge whether the bridge vibration response time history array converges; In the case where the bridge vibration response time history array does not converge, obtain the updated equivalent road surface unevenness time history array according to the bridge vibration response time history array, and use the updated equivalent road surface unevenness time history array as the equivalent road surface unevenness time history array to repeat the above process; In the case where the bridge vibration response time history array converges, obtain the vehicle vibration response time history array; Among them, obtaining the bridge vibration response time history array according to the equivalent road surface unevenness time history array includes: Obtain the time history matrix of the bridge's action on the vehicle at the vehicle-bridge contact point according to the equivalent road surface unevenness time history array; Determine the time history matrix of the vehicle's action on the bridge according to the time history matrix of the bridge's action on the vehicle; Obtain the bridge vibration response time history array according to the time history matrix of the vehicle's action on the bridge; Among them, obtaining the time history matrix of the bridge's action on the vehicle at the vehicle-bridge contact point according to the equivalent road surface unevenness time history array includes: By calculation Obtain the action time history matrix of the axle on the vehicle at the axle contact point; Among them, f vbzi is the vertical action time history matrix borne by the wheel, f vbhi is the lateral action time history matrix borne by the wheel, C lzi is the vertical damping coefficient at the contact point between the tire and the road surface, K lzi is the stiffness coefficient at the contact point between the tire and the road surface; is the vertical speed of the road surface at the contact point between the wheel and the road surface, Z ci is the vertical displacement of the road surface at the contact point between the wheel and the road surface; Z si is the vertical displacement of the wheel at the contact point between the wheel and the road surface; C hi is the lateral damping coefficient at the contact point between the tire and the road surface, K hi is the elastic coefficient at the contact point between the tire and the road surface; is the lateral speed of the road surface at the contact point between the wheel and the road surface, Y ci is the lateral displacement of the road surface at the contact point between the wheel and the road surface; is the lateral speed of the wheel at the contact point between the wheel and the road surface, Y si is the lateral displacement of the wheel at the contact point between the wheel and the road surface.

2. The method according to claim 1, characterized in that, Obtaining the initial response time history array of the bridge includes: Based on the ANSYS platform, perform finite element modeling according to the preset bridge structure information; determine the initial action time history matrix of the vehicle on the bridge; apply the excitation of the initial action time history matrix in the bridge structure model to obtain the initial response time history array of the bridge.

3. The method according to claim 2, wherein Determining the initial action time history matrix of the vehicle on the bridge includes: Determine the initial action time history matrix of the bridge on the vehicle according to the vehicle motion equation; Determine the initial action time history matrix of the vehicle on the bridge according to the initial action time history matrix of the bridge on the vehicle.

4. The method according to claim 2, characterized in that Applying the excitation of the initial action time history matrix in the bridge structure model to obtain the initial response time history array of the bridge includes: Use the interpolation method to sequentially extract the responses of the contact points between the front and rear axles of the vehicle and the bridge main girder, as well as the responses of four relevant nodes of the bridge main girder; Combine the responses of the contact points between the front and rear axles of the vehicle and the bridge main girder and the responses of four relevant nodes of the bridge main girder to form the initial response time history array of the bridge.

5. The method according to claim 1, characterized in that Obtaining the equivalent road surface unevenness time history array includes: On the MATLAB platform, obtain the equivalent road surface unevenness time history array according to the initial response time history array of the bridge and the preset simulated road surface unevenness time history.

6. The method according to claim 1, characterized in that In the case where the bridge vibration response time history array converges, obtaining the vehicle vibration response time history array includes: In the case where the bridge vibration response time history array converges, obtain the vehicle vibration response time history array according to the time history matrix of the bridge's action on the vehicle.

7. A vehicle-bridge coupling vibration analysis system based on time-history array interactive iteration, characterized in that, Including: The bridge subsystem analysis module is configured to analyze the bridge subsystem based on the ANSYS platform to obtain an array of bridge initial response time histories; The vehicle subsystem analysis module is configured such that the ANSYS platform shares the array of bridge initial response time histories with the MATLAB platform, and the MATLAB platform analyzes the vehicle subsystem based on the array of bridge initial response time histories to obtain an array of equivalent road surface unevenness time histories; The coupling analysis module is configured to perform a coupling analysis on the bridge subsystem and the vehicle subsystem, and obtain the vibration responses of the bridge and the vehicle according to the array of equivalent road surface unevenness time histories; Among them, obtaining the vibration responses of the bridge and the vehicle according to the array of equivalent road surface unevenness time histories includes: Obtaining an array of bridge vibration response time histories according to the array of equivalent road surface unevenness time histories; Judging whether the array of bridge vibration response time histories converges; In the case where the array of bridge vibration response time histories does not converge, obtaining an updated array of equivalent road surface unevenness time histories according to the array of bridge vibration response time histories, and repeating the above process with the updated array of equivalent road surface unevenness time histories as the array of equivalent road surface unevenness time histories; In the case where the array of bridge vibration response time histories converges, obtaining an array of vehicle vibration response time histories; Among them, obtaining an array of bridge vibration response time histories according to the array of equivalent road surface unevenness time histories includes: Obtaining a time history matrix of the action of the bridge on the vehicle at the vehicle-bridge contact point according to the array of equivalent road surface unevenness time histories; Determining a time history matrix of the action of the vehicle on the bridge according to the time history matrix of the action of the bridge on the vehicle; Obtaining an array of bridge vibration response time histories according to the time history matrix of the action of the vehicle on the bridge; Among them, obtaining a time history matrix of the action of the bridge on the vehicle at the vehicle-bridge contact point according to the array of equivalent road surface unevenness time histories includes: By calculation Obtain the time history matrix of the action of the axle on the vehicle at the axle contact point; Among them, f vbzi is the vertical action time history matrix borne by the wheel, and f vbhi is the lateral action time history matrix borne by the wheel. C lzi is the vertical damping coefficient at the contact point between the tire and the road surface, and K lzi is the stiffness coefficient at the contact point between the tire and the road surface; is the vertical speed of the road surface at the contact point between the wheel and the road surface, and Z ci is the vertical displacement of the road surface at the contact point between the wheel and the road surface; Z si is the vertical displacement of the wheel at the contact point between the wheel and the road surface; C hi is the lateral damping coefficient at the contact point between the tire and the road surface, and K hi is the elastic coefficient at the contact point between the tire and the road surface; is the lateral speed of the road surface at the contact point between the wheel and the road surface, and Y ci is the lateral displacement of the road surface at the contact point between the wheel and the road surface; is the lateral speed of the wheel at the contact point between the wheel and the road surface, and Y si is the lateral displacement of the wheel at the contact point between the wheel and the road surface.

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