Fast simulation method and system for vehicle-bridge coupling vibration based on sliding window domain decomposition method

Abstract

This invention discloses a rapid vehicle-track-bridge coupled vibration simulation method and system based on the sliding window domain decomposition method, which is used to achieve efficient analysis of the vibration of vehicle-track-bridge coupled systems. This invention introduces a sliding window computation mechanism in the spatial dimension to locally model the dynamic response of the track structure, establishing the computational region only within the vehicle's neighborhood, thereby reducing the number of system degrees of freedom and the computational scale of vehicle-track-bridge coupled vibration analysis. By setting a transferable time-varying interface in the time dimension, the computational window can be dynamically updated along the track direction as the vehicle runs, thus enabling continuous calculation of time-varying dynamics problems of vehicle-track-bridge coupled systems. This invention verifies the energy stability of the proposed method through theoretical derivation and numerical examples, thereby ensuring the numerical stability and computational reliability of the method in long-term dynamic response analysis.

Description

Technical Field

[0001] This invention relates to a rapid vehicle-track-bridge coupled vibration simulation method and system based on the sliding window domain decomposition method, belonging to the field of structural dynamics analysis technology. Background Technology

[0002] In the dynamic analysis of the vehicle-track-bridge system, due to the mobility and impact of the train load, and the differences in structural characteristics of the vehicle, track, and bridge subsystems, the vehicle, track, and bridge system exhibit obvious zoning characteristics.

[0003] Existing technologies typically treat vehicles, tracks, and bridges as separate subsystems for solution, achieving system coupling through contact force or displacement coordination conditions. However, many existing methods require iterative calculation of interface forces or displacements to achieve coordination between subsystems, relying on pre-defined convergence criteria. When the vehicle, track, and bridge system exhibits strong nonlinearity or when interface conditions change over time, iterative calculations may encounter convergence difficulties. Furthermore, some methods lack a unified energy analysis framework, making it difficult to guarantee numerical stability in long-term dynamic calculations.

[0004] To overcome the aforementioned problems, existing research has proposed a non-iterative energy-conserving partitioning strategy. This strategy constructs a non-iterative solution process by applying continuity conditions at the interfaces of sub-regions, thereby avoiding iterative calculations of interface forces and ensuring the energy conservation characteristics of the system to a certain extent. However, in this type of method, the track subsystem is usually modeled as a complete structure. Since the track structure has a large length along the track direction, its dynamic model often contains a large number of degrees of freedom. As the track length increases, the computational scale of the system increases rapidly, leading to a significant decrease in computational efficiency.

[0005] In vehicle-track-bridge systems, the dynamic response of the bridge structure is usually the focus of engineering analysis, while the track structure, far from the vehicle's operating area, has a relatively small impact on the system's dynamic response. Therefore, while ensuring computational accuracy, modeling the dynamics of the track structure only within a limited range near the vehicle, thereby reducing the system's degrees of freedom, is an effective approach to improve computational efficiency. Existing research has proposed truncating a local region of the track structure and dynamically updating this region as the vehicle moves, thus ensuring that the calculations remain focused on the track area near the vehicle.

[0006] However, existing local modeling methods are mostly designed for vehicle-track systems or employ specific solution methods such as modal superposition, which have limited applicability when dealing with complex boundary conditions, structural inhomogeneities, or nonlinear problems. Furthermore, these methods are typically not combined with zonal dynamics methods, lacking a unified mechanism for handling interface coupling relationships and energy stability among multiple subsystems such as vehicles, tracks, and bridges.

[0007] Therefore, how to combine the idea of ​​localized modeling of track structures with the partitioned dynamics method while ensuring the accuracy and numerical stability of dynamic response calculations, in order to reduce the computational scale of track subsystems and improve the computational efficiency of vehicle-track-bridge system dynamic analysis, has become a technical problem that needs to be solved in this field. Summary of the Invention

[0008] Objective: To overcome the shortcomings of existing vehicle-track-bridge system dynamic analysis methods, such as large degrees of freedom of the track subsystem, low computational efficiency, and the reliance on iterative solutions and difficulty in guaranteeing numerical stability in some partitioning methods, this invention provides a rapid vehicle-track-bridge coupled vibration simulation method and system based on the sliding window domain decomposition method. By constructing a locally updated computational region in the track structure that dynamically updates with vehicle operation, and combining it with a partitioned dynamic modeling strategy, efficient coupled computation between the vehicle, track, and bridge subsystems is achieved, reducing the computational scale while ensuring the stability and accuracy of dynamic response calculation.

[0009] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0010] Firstly, a rapid vehicle-rail-bridge coupled vibration simulation method based on the sliding window domain decomposition method includes the following steps:

[0011] Step 1: Divide the vehicle-track-bridge coupled system into vehicle subsystem, track subsystem and bridge subsystem, and obtain the matrix and state variables corresponding to each subsystem.

[0012] Step 2: Construct the initial window position based on the window position parameters, and determine the values ​​of the variable mapping operation matrix and the windowed orbit matrix under the initial window based on the matrices corresponding to each subsystem.

[0013] Step 3: Based on the matrices and state variables corresponding to each subsystem, as well as the values ​​of the variable mapping operation matrix under the initial window and the windowed orbital matrix, solve the incremental dynamic equations of each subsystem within the window to obtain the dynamic response of each subsystem within the window.

[0014] Step 4: Take the track response without window segment as the dynamic response of the bridge subsystem without window segment, and combine the dynamic response of the bridge subsystem without window segment with the dynamic responses of each subsystem within the window to obtain the dynamic response of the entire track.

[0015] Step 5: Update the window position parameters and advance the window's start and end points forward by one track unit simultaneously.

[0016] Step 6: Compare the current window endpoint index with the bridge preset endpoint index to determine whether the window has completely passed the bridge segment. If the current window endpoint index is less than the bridge preset endpoint index, the window is still on the bridge, and the process proceeds to the next window, repeating steps 3 to 6. Otherwise, the algorithm ends.

[0017] In a second aspect, a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a rapid vehicle-rail-bridge coupled vibration simulation method based on the sliding window domain decomposition method as described in any of the first aspects.

[0018] Thirdly, a computer device comprising:

[0019] Memory is used to store instructions.

[0020] A processor is configured to execute the instructions, causing the computer device to perform operations as described in any of the first aspects of a rapid vehicle-rail-bridge coupled vibration simulation method based on the sliding window domain decomposition method.

[0021] Beneficial Effects: The fast vehicle-track-bridge coupled vibration simulation method and system based on the sliding window domain decomposition method provided by this invention are used to achieve efficient analysis of the vibration of vehicle-track-bridge coupled systems. This invention introduces a sliding window computation mechanism in the spatial dimension to locally model the dynamic response of the track structure, establishing the computational region only within the vehicle's neighborhood, thereby reducing the number of system degrees of freedom and the computational scale of vehicle-track-bridge coupled vibration analysis. By setting a transferable time-varying interface in the time dimension, the computational window can be dynamically updated along the track direction as the vehicle runs, thus enabling continuous calculation of time-varying dynamics problems of vehicle-track-bridge coupled systems. Theoretical derivation of the proposed method and verification of its energy stability through numerical examples ensure the numerical stability and computational reliability of the method in long-term dynamic response analysis. Compared with existing technologies, this invention has the following beneficial effects:

[0022] (1) By introducing a sliding window calculation mechanism into the track structure, dynamic modeling is performed only on the track structure within the vehicle's neighborhood, thereby significantly reducing the degree of freedom of the track subsystem and reducing the computational load of vehicle-track-bridge coupling analysis.

[0023] (2) By setting a track calculation window that is dynamically updated with the vehicle's movement, the calculation area is always matched with the vehicle's position, thereby improving calculation efficiency while ensuring calculation accuracy.

[0024] (3) By using the partitioned dynamic modeling method, the coupling solution between vehicle, track and bridge subsystems can be realized, so that the complex system can be decomposed into multiple substructures for calculation, thereby improving the overall solution efficiency.

[0025] (4) By performing energy stability analysis on the algorithm, the proposed method can maintain numerical stability in long-term dynamic response calculation, thereby improving the reliability of the calculation results. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating a rapid vehicle-track-bridge coupled vibration simulation method based on the sliding window domain decomposition method according to the present invention.

[0027] Figure 2 This is an example diagram illustrating the concept of a sliding window.

[0028] Figure 3 This diagram illustrates a comparison of the displacement responses of the NP-SW (sliding window domain decomposition) method and the NECP (non-sliding window domain decomposition) method. Figure 3 Figure (a) shows a schematic diagram of the evolution of the overall response over time; Figure 3 Figure (b) is a magnified view of the area near the window removal area.

[0029] Figure 4 This is a schematic diagram of the vehicle-local track-bridge vertical system.

[0030] Figure 5 This diagram illustrates a comparison of the computation time of the NECP method, the traditional global method, and the NP-SW method under different bridge span conditions for the same window length (50 meters). Detailed Implementation

[0031] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0032] The present invention will be further described below with reference to specific embodiments.

[0033] Example 1:

[0034] This embodiment introduces a fast vehicle-track-bridge coupled vibration simulation method based on the sliding window domain decomposition method, which is used for dynamic response analysis of vehicle-track-bridge coupled systems, such as... Figure 1 As shown, it includes the following steps:

[0035] Step 1: Initialize system parameters:

[0036] The vehicle-track-bridge coupled system is divided into vehicle subsystems, track subsystems, and bridge subsystems, and the necessary calculation matrices and state variables are prepared. These include the mass matrix, stiffness matrix, damping matrix, and equivalent stiffness matrix of the vehicle subsystem, track subsystem, and bridge subsystem; the interface solution matrix; the invariant mapping operation matrix; the window position parameters; and the initial dynamic response.

[0037] Step 2: Determine the values ​​of the variable parameters in the initial window:

[0038] Construct the initial window position based on the window position parameters from step one, and determine the values ​​of the variable mapping operation matrix and the windowed orbital matrix under the initial window.

[0039] Step 3: Calculate the subsystem response within the window:

[0040] Based on the parameters obtained in steps one and two, the dynamic response of each subsystem within the window is solved within the current time step.

[0041] Step 4: Synthesize the full orbital response:

[0042] Since the track response outside the window was not calculated, the track response without the window segment was taken from the dynamic response of the bridge subsystem. The dynamic response of the bridge subsystem was then combined with the dynamic response of the track subsystem inside the window to obtain the dynamic response of the entire track.

[0043] Step 5: Move the window:

[0044] Update the window position parameters to advance the window's start and end points forward by one orbital unit.

[0045] Step Six: Determine if the window has left the bridge:

[0046] The current window endpoint index is compared with the bridge preset endpoint index to determine whether the window has completely passed the bridge segment. If the current window endpoint index is less than the bridge preset endpoint index, the window is still on the bridge, and steps three to six are repeated; otherwise, the algorithm ends.

[0047] Furthermore, the vehicle subsystem is denoted by V, the track subsystem by R, and the bridge subsystem by Br. The mass matrix, damping matrix, stiffness matrix, and equivalent stiffness matrix of the vehicle, track, and bridge subsystems are denoted by M, respectively. k C k K k and K * k , express.

[0048] Furthermore, construct the invariant mapping operation matrix. , , and .

[0049] Wherein, the invariant mapping operation matrix , It can be done through general formula symbols Let represent a Boolean matrix used to extract the degrees of freedom in subsystem j that are connected to interface l, which connects subsystems j and k. The superscript j·k denotes a pair of subsystems connected through interface l, where ... This indicates that j and k can take values ​​from V, R, and Br, where V represents the vehicle subsystem, R represents the track subsystem, and Br represents the bridge subsystem. The subscript l indicates the interface number.

[0050]

[0051] in: Let represent the interface degrees of freedom of subsystems j and k in the i-th row and j-th column of the Boolean matrix at the interface l.

[0052] The Boolean matrix representing the degrees of freedom of the vehicle subsystem and the track subsystem at interface 1.

[0053] The Boolean matrix represents the degrees of freedom of the interface between the track subsystem and the bridge subsystem at interface 2.

[0054] Based on the above definition and The addition of the subscript 'a' indicates the placement position of the vehicle within the sliding window, such as... Figure 2 As shown, because the vehicles need to move relative to each other on the track, there exists and Representing time respectively The Boolean matrix of the degrees of freedom of the vehicle subsystem and track subsystem corresponding to train position 'a' within the sliding window at interface interface 1, and the time step. The Boolean matrix of the degrees of freedom of the vehicle subsystem and track subsystem at interface 1, corresponding to train position a+1 within the sliding window. Since the vehicle and track calculation windows move forward synchronously by one track unit, and the track structure satisfies the uniformity assumption along the track direction, the relative positions of the vehicle and local track units within the sliding window remain unchanged. and It is also an invariant mapping operation matrix.

[0055] The initial dynamic response includes: initial values ​​of displacement dynamic response. Initial value of velocity dynamic response and initial value of acceleration dynamic response ,in, .

[0056] The window parameters include: the starting position s0 of the left endpoint of the window, and the ending position s of the left endpoint of the window. f The starting position e0 and the ending position e0 of the right endpoint of the window. f .

[0057] Furthermore, the variable mapping matrix It is complete According to the window The resulting windowed mapping matrix. The specific operation involves retrieving the matrix. Corresponding window A new matrix consisting of rows and all columns. .in, This represents the window corresponding to the position 's' of the left endpoint and the position 'e' of the right endpoint, where... , .

[0058] Furthermore, the windowed orbital matrix includes: a windowed orbital subsystem mass matrix. Stiffness matrix of windowed orbital subsystem and the damping matrix of the windowed orbital subsystem Similarly, the corresponding part of the original matrix is ​​extracted based on the degree of freedom index within the window.

[0059] Furthermore, step three specifically includes:

[0060] Step 3.1: Construct the incremental dynamic equation, the expression of which is as follows:

[0061]

[0062] In the formula, For the mass matrix of the vehicle subsystem, For vehicle subsystem The incremental acceleration of power response at all times For the damping matrix of the vehicle subsystem, For vehicle subsystem Increment of velocity dynamic response at any moment For the stiffness matrix of the vehicle subsystem, For vehicle subsystem Increment of displacement dynamic response at time intervals For vehicle subsystem The increment of interface force at any moment For vehicle subsystem The increment of external force at all times This represents the portion of the compensation term that acts on the vehicle as the system transitions from time-varying to time-invariant.

[0063] For the windowed orbital subsystem mass matrix, For window orbital subsystem The incremental acceleration of power response at all times For the damping matrix of the windowed orbital subsystem, For window orbital subsystem Increment of velocity dynamic response at any moment For the stiffness matrix of the windowed orbital subsystem, For window orbital subsystem Increment of displacement dynamic response at time intervals For window orbital subsystem The increment of interface force at any moment For window orbital subsystem The increment of external force at all times This represents the portion of the compensation term that acts on the track after the system transitions from time-varying to time-invariant.

[0064] For the mass matrix of the bridge subsystem, For bridge subsystem The incremental acceleration of power response at all times For the damping matrix of the bridge subsystem, For bridge subsystem Increment of velocity dynamic response at any moment For the stiffness matrix of the bridge subsystem, For bridge subsystem Increment of displacement dynamic response at time intervals For bridge subsystem The increment of interface force at any moment For bridge subsystem The increment of external force at any given moment.

[0065] in:

[0066]

[0067]

[0068] In the formula: The Boolean matrix of the interface degrees of freedom of the vehicle subsystem and the track subsystem at interface 1. For a moment Boolean matrix of the degrees of freedom of the vehicle subsystem and track subsystem corresponding to train position a+1 within the sliding window at interface interface 1. For a moment Boolean matrix of the degrees of freedom of the vehicle subsystem and track subsystem corresponding to train position a within the sliding window at interface interface 1. For window orbital subsystem Momentary displacement dynamic response Represents the contact stiffness constant between the wheel and the track. This represents the contact damping constant between the wheel and the track. T is the transpose matrix. The Boolean matrix representing the degrees of freedom of the interface between the vehicle subsystem and the track subsystem at interface 0. For vehicle subsystem Momentary displacement dynamic response.

[0069] in:

[0070]

[0071]

[0072] In the formula: For the kth subsystem The increment of the displacement dynamic response at any given moment. For the kth subsystem Real-time speed and dynamic response, The kth subsystem Constant acceleration dynamic response.

[0073] For the kth subsystem Constantly accelerating the incremental change in power response, For the kth subsystem The increment of velocity dynamic response at any moment According to the Newmark time integration scheme, β and γ are integration constants, typically taken as 0.25 and 0.5 respectively. This represents the integration time step.

[0074] Step 3.2: Transform the incremental dynamic equations into incremental kinematic equations in equivalent stiffness form, the expression of which is as follows:

[0075]

[0076] in: The equivalent stiffness matrix of the vehicle subsystem, For vehicle subsystem Increment of velocity dynamic response at any moment For vehicle subsystem Real-time speed and dynamic response For vehicle subsystem It accelerates power response at all times.

[0077] The equivalent stiffness matrix of the windowed orbital subsystem, For window orbital subsystem Increment of velocity dynamic response at any moment For window orbital subsystem Real-time speed and dynamic response For window orbital subsystem Real-time speed and dynamic response.

[0078] The equivalent stiffness matrix of the bridge subsystem, For bridge subsystem Increment of velocity dynamic response at any moment For bridge subsystem Real-time speed and dynamic response For bridge subsystem It accelerates power response at all times.

[0079] In the formula, , The expression is as follows:

[0080]

[0081] In the formula, The expression is as follows:

[0082]

[0083] Step 3.3: Obtain the velocity increments of the vehicle subsystem, track subsystem, and bridge subsystem under the action of external forces. , as well as And the interface solution matrices G1, G2, H1 and H2.

[0084] The expression is as follows:

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] in, For vehicle subsystem The increment of external force at all times For the corrected equivalent stiffness matrix of the vehicle subsystem, The compensation term resulting from the system's transition from time-varying to time-invariant applies to the vehicle's portion. The equivalent stiffness matrix of the vehicle subsystem, For vehicle subsystem Real-time speed and dynamic response For vehicle subsystem It accelerates power response at all times.

[0093] For window orbital subsystem The increment of external force at all times The compensation term resulting from the transformation from time-varying to time-invariant applies to the portion of the orbit. What is the corrected equivalent stiffness matrix of the orbital subsystem for windowing? For window orbital subsystem The incremental acceleration of power response at all times For window orbital subsystem Increment of velocity dynamic response at any moment The equivalent stiffness matrix of the windowed orbital subsystem, This is the stiffness matrix of the windowed orbital subsystem.

[0094] For bridge subsystem The increment of external force at all times For the corrected equivalent stiffness matrix of the bridge subsystem, The equivalent stiffness matrix of the bridge subsystem, For the stiffness matrix of the bridge subsystem, For bridge subsystem Always accelerate power response, For bridge subsystem Real-time speed and dynamic response.

[0095] For a moment Boolean matrix of the degrees of freedom of the vehicle subsystem and track subsystem corresponding to train position a+1 within the sliding window at interface interface 1. To represent the Boolean matrix of the interface degrees of freedom of the track subsystem and the bridge subsystem at interface 2, A Boolean matrix representing the degrees of freedom of the vehicle subsystem and the track subsystem at interface 1. Let T be the Boolean matrix of the interface degrees of freedom of the orbital subsystem and bridge subsystem of window w(e,s) at interface 2, where T represents the transpose matrix.

[0096] In the formula, The expression is as follows:

[0097]

[0098] In the formula, The expression is as follows:

[0099]

[0100] Note that except for G2, which needs to change with the window, G1, H1, and H2 are invariants and have been prepared in step one.

[0101] Step 3.4: Solve for matrices G1, G2, H1, and H2 based on the interface, as well as the velocity increments of the vehicle subsystem, track subsystem, and bridge subsystem under external forces. , and Obtain the incremental connection force at interface 1 (vehicle-track interface). Incremental connection force with Interface 2 (track and bridge interface) .

[0102]

[0103]

[0104] in, The velocity increment of the vehicle subsystem and track subsystem at interface 1 under the action of external force. This represents the velocity increment of the track subsystem and the bridge subsystem at interface 2 under the action of external forces.

[0105]

[0106]

[0107] Step 3.5: Based on the increase in connection force at interface 1 (vehicle-track interface) Incremental connection force with Interface 2 (track and bridge interface) Determine the interface force , and .

[0108] The expression is as follows:

[0109]

[0110] in, A Boolean matrix representing the degrees of freedom of the vehicle subsystem and the track subsystem at interface 1. For a moment Boolean matrix of the degrees of freedom of the vehicle subsystem and track subsystem corresponding to train position a+1 within the sliding window at interface interface 1. To represent the Boolean matrix of the interface degrees of freedom of the track subsystem and the bridge subsystem at interface 2, For window The Boolean matrix of the interface degrees of freedom of the bridge subsystem at interface 2. Display window of Time interface 2 (track and bridge interface) connects the force increment, T represents the transpose matrix.

[0111] Step 3.6: [The sentence is incomplete and requires more context to be translated accurately.] , and Substituting back into the incremental kinematic equations in the equivalent stiffness form, we obtain the kinematic increments. , , as well as , , , , , As the dynamic response of the track subsystem within the window.

[0112] Furthermore, symbols and These represent the displacements of the track and the bridge, respectively, without a window segment. To improve computational efficiency, the degrees of freedom of the track subsystem are compressed into a window; therefore, the displacement of the track without a window segment is... The displacement of the corresponding degree of freedom of the windowless bridge section was not calculated here. Assigning values ​​to the orbital path improves calculation accuracy. For example... Figure 3 As shown, the red line obtained by the above approximation method after the window is removed fits well with the reference solution—the blue line of the domain decomposition model without using a sliding window.

[0113] Example 2:

[0114] This embodiment describes a computer-readable storage medium storing a computer program that, when executed by a processor, implements a rapid vehicle-rail-bridge coupled vibration simulation method based on the sliding window domain decomposition method as described in any of Embodiment 1.

[0115] Example 3:

[0116] This embodiment describes a computer device, including:

[0117] Memory is used to store instructions.

[0118] A processor is configured to execute the instructions, causing the computer device to perform operations as described in any of Embodiment 1 of a rapid vehicle-rail-bridge coupled vibration simulation method based on the sliding window domain decomposition method.

[0119] Example 4:

[0120] This embodiment demonstrates the computational efficiency of the method of the present invention through an example of a four-span bridge, using a computational window length of 50 meters. The vehicle-local track-bridge vertical system is as follows: Figure 4 As shown, for ease of explanation, the vehicle subsystem simulates only a single train; in reality, if multiple trains are included, it will only increase the total train length. The vehicle runs at a constant speed v0 = 100 m / s, using a time step Δh = 0.001 s. The track subsystem consists of three layers: rails, sleepers, and ballast. Its total length is determined by the length of the calculation window. The longitudinal spacing between the sleeper layer and the ballast layer is 0.5 m, while the rail layer is discretized more finely with a spacing of 0.1 m to improve computational stability. The bridge subsystem consists of a multi-span simply supported bridge, with each span being 32 meters long.

[0121] like Figure 5 As shown: For the same window length (50 meters), the computation time of the NECP method (partitioning method without window), the traditional overall method (neither window nor partitioning) and the NP-SW method (the present invention uses both window and partitioning) are compared under different bridge span conditions.

[0122] Figure 5The computation time ratios of the NECP method relative to the NP-SW method and the traditional method were compared for different bridge spans: When the number of bridge spans was 2, the computation time ratio of NECP / NP-SW was 1.3, and that of NECP / Traditional was 19.6; when the number of bridge spans increased to 4, the ratios increased to 15.0 and 392.9, respectively; in the case of 6 spans, the computation time ratios further increased to 37.9 and 947.4, respectively; when the number of bridge spans reached 8, the computation time ratio of NECP / NP-SW increased significantly to 277.8, and that of NECP / Traditional reached 2617.4. Overall, with the increase in the number of bridge spans, both sets of computation time ratios showed a significant and rapid growth trend, indicating that the computational time differences between the NECP method, the NP-SW method, and traditional methods widened as the bridge structure scale increased. Specifically, the time ratio of NECP relative to traditional methods was consistently much higher than that relative to the NP-SW method, indicating that the computational cost of traditional methods increased more dramatically in multi-span bridge problems. While the NP-SW method already had some efficiency advantages over traditional methods, the gap with the NECP method gradually widened as the number of spans increased. Especially in the 8-span case, the two time ratios reached 277.8 and 2617.4 respectively, reflecting that with the increase in computational degrees of freedom and the scale of contact analysis, the advantages of efficient algorithms in the dynamic calculation of large-scale multi-span bridges were further amplified.

[0123] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A rapid vehicle-track-bridge coupled vibration simulation method based on the sliding window domain decomposition method, characterized in that: Includes the following steps: Step 1: Divide the vehicle-track-bridge coupled system into vehicle subsystem, track subsystem, and bridge subsystem, and obtain the corresponding matrices and state variables for each subsystem; Step 2: Construct the initial window position based on the window position parameters, and determine the values ​​of the variable mapping operation matrix and the windowed orbit matrix under the initial window based on the matrices corresponding to each subsystem. Step 3: Based on the matrices and state variables corresponding to each subsystem, as well as the values ​​of the variable mapping operation matrix under the initial window and the windowed orbital matrix, solve the incremental dynamic equations of each subsystem within the window to obtain the dynamic response of each subsystem within the window. Step 4: Take the track response without window segment as the dynamic response of the bridge subsystem without window segment, and combine the dynamic response of the bridge subsystem without window segment with the dynamic response of each subsystem within the window to obtain the dynamic response of the entire track. Step 5: Update the window position parameters, and simultaneously advance the window's start and end points by one track unit; Step 6: Compare the current window endpoint index with the bridge preset endpoint index to determine whether the window has completely passed the bridge segment. If the current window endpoint index is less than the bridge preset endpoint index, the window is still on the bridge, and the process proceeds to the next window, repeating steps 3 to 6. Otherwise, the algorithm ends.

2. The rapid vehicle-track-bridge coupled vibration simulation method based on the sliding window domain decomposition method according to claim 1, characterized in that: Step three specifically includes: Step 3.1: Construct the incremental dynamic equation, the expression of which is as follows: ； In the formula, For the mass matrix of the vehicle subsystem, For vehicle subsystem The incremental acceleration of power response at all times For the damping matrix of the vehicle subsystem, For vehicle subsystem Increment of velocity dynamic response at any moment For the stiffness matrix of the vehicle subsystem, For vehicle subsystem Increment of displacement dynamic response at time intervals For vehicle subsystem The increment of interface force at any moment For vehicle subsystem The increment of external force at all times This represents the portion of the compensation term that acts on the vehicle as the system transitions from a time-varying to a time-invariant state. For the windowed orbital subsystem mass matrix, For window orbital subsystem The incremental acceleration of power response at all times For the damping matrix of the windowed orbital subsystem, For window orbital subsystem Increment of velocity dynamic response at any moment For the stiffness matrix of the windowed orbital subsystem, For window orbital subsystem Increment of displacement dynamic response at time intervals For window orbital subsystem The increment of interface force at any moment For window orbital subsystem The increment of external force at all times This represents the portion of the compensation term that acts on the track after the system transitions from time-varying to time-invariant. For the mass matrix of the bridge subsystem, For bridge subsystem The incremental acceleration of power response at all times For the damping matrix of the bridge subsystem, For bridge subsystem Increment of velocity dynamic response at any moment For the stiffness matrix of the bridge subsystem, For bridge subsystem Increment of displacement dynamic response at time intervals For bridge subsystem The increment of interface force at any moment For bridge subsystem The increment of external force at any given moment; Step 3.2: Transform the incremental dynamic equations into incremental kinematic equations in equivalent stiffness form, the expression of which is as follows: ； in: The equivalent stiffness matrix of the vehicle subsystem, For vehicle subsystem Increment of velocity dynamic response at any moment For vehicle subsystem Real-time speed and dynamic response For vehicle subsystem Constant acceleration and power response; The equivalent stiffness matrix of the windowed orbital subsystem, For window orbital subsystem Increment of velocity dynamic response at any moment For window orbital subsystem Real-time speed and dynamic response For window orbital subsystem Real-time speed and dynamic response; The equivalent stiffness matrix of the bridge subsystem, For bridge subsystem Increment of velocity dynamic response at any moment For bridge subsystem Real-time speed and dynamic response For bridge subsystem Constant acceleration dynamic response, β and γ are integral constants, This is the integration time step; Step 3.3: Obtain the velocity increments of the vehicle subsystem, track subsystem, and bridge subsystem under the action of external forces. , as well as And the interface solution matrices G1, G2, H1 and H2; The expression is as follows: ； ； ； ； ； ； ； in, For vehicle subsystem The increment of external force at all times For the corrected equivalent stiffness matrix of the vehicle subsystem, The compensation term resulting from the system's transition from time-varying to time-invariant applies to the vehicle's portion. The equivalent stiffness matrix of the vehicle subsystem, For vehicle subsystem Real-time speed and dynamic response For vehicle subsystem Constant acceleration and power response; For window orbital subsystem The increment of external force at all times The compensation term resulting from the transformation from time-varying to time-invariant applies to the portion of the orbit. What is the corrected equivalent stiffness matrix of the orbital subsystem for windowing? For window orbital subsystem The incremental acceleration of power response at all times For window orbital subsystem Increment of velocity dynamic response at any moment The equivalent stiffness matrix of the windowed orbital subsystem, The stiffness matrix of the windowed orbital subsystem; For bridge subsystem The increment of external force at all times For the corrected equivalent stiffness matrix of the bridge subsystem, The equivalent stiffness matrix of the bridge subsystem, For the stiffness matrix of the bridge subsystem, For bridge subsystem Always accelerate power response, For bridge subsystem Real-time speed and dynamic response; For a moment Boolean matrix of the degrees of freedom of the vehicle subsystem and track subsystem corresponding to train position a+1 within the sliding window at interface interface 1. To represent the Boolean matrix of the interface degrees of freedom of the track subsystem and the bridge subsystem at interface 2, A Boolean matrix representing the degrees of freedom of the vehicle subsystem and the track subsystem at interface 1. Let T be the Boolean matrix of the degrees of freedom of the track subsystem and bridge subsystem of window w(e,s) at interface interface 2, and let T represent the transpose matrix. Step 3.4: Solve for matrices G1, G2, H1, and H2 based on the interface, as well as the velocity increments of the vehicle subsystem, track subsystem, and bridge subsystem under external forces. , and Get the connection force increment of interface 1 Incremental connection force with interface 2 Its expression is as follows: ； ； in, The velocity increment of the vehicle subsystem and track subsystem at interface 1 under the action of external force. This represents the velocity increment of the track subsystem and the bridge subsystem at interface 2 under the action of external forces; Step 3.5: Based on the increase in connection force in Interface 1 Incremental connection force with interface 2 Determine the interface force , and Its expression is as follows: ； in, A Boolean matrix representing the degrees of freedom of the vehicle subsystem and the track subsystem at interface 1. For a moment Boolean matrix of the degrees of freedom of the vehicle subsystem and track subsystem corresponding to train position a+1 within the sliding window at interface interface 1. To represent the Boolean matrix of the interface degrees of freedom of the track subsystem and the bridge subsystem at interface 2, For window The Boolean matrix of the interface degrees of freedom of the bridge subsystem at interface 2. Display window of In the time interface 2, the force increment is connected, and T represents the transpose matrix; Step 3.6: [The sentence is incomplete and requires more context to be translated accurately.] , and Substituting back into the incremental kinematic equations in the equivalent stiffness form, we obtain the kinematic increments. , , as well as , , , , , As the dynamic response of the orbital subsystem within the window.

3. The rapid vehicle-track-bridge coupled vibration simulation method based on the sliding window domain decomposition method according to claim 2, characterized in that: The The expression is as follows: ； The Is to take Corresponding window In The time row and all columns are composed of, where, The expression is as follows: ； In the formula: The Boolean matrix of the interface degrees of freedom of the vehicle subsystem and the track subsystem at interface 1. For a moment Boolean matrix of the degrees of freedom of the vehicle subsystem and track subsystem corresponding to train position a+1 within the sliding window at interface interface 1. For a moment Boolean matrix of the degrees of freedom of the vehicle subsystem and track subsystem corresponding to train position a within the sliding window at interface interface 1. For window orbital subsystem Momentary displacement dynamic response Represents the contact stiffness constant between the wheel and the track. This represents the contact damping constant between the wheel and the track. T is the transpose matrix. The Boolean matrix representing the degrees of freedom of the interface between the vehicle subsystem and the track subsystem at interface 0. For vehicle subsystem Momentary displacement dynamic response.

4. The rapid vehicle-track-bridge coupled vibration simulation method based on the sliding window domain decomposition method according to claim 2, characterized in that: The , , The expression is as follows: ； The , , The expression is as follows: ； In the formula: For the kth subsystem The increment of the displacement dynamic response at any given moment. For the kth subsystem Real-time speed and dynamic response, The kth subsystem Constant acceleration dynamic response; For the kth subsystem Constantly accelerating the incremental change in power response, For the kth subsystem The increment of velocity dynamic response at any moment β and γ are integration constants. This represents the integration time step.

5. The rapid vehicle-track-bridge coupled vibration simulation method based on the sliding window domain decomposition method according to claim 2, characterized in that: The , The expression is as follows: ； The The expression is as follows: 。 6. The rapid vehicle-track-bridge coupled vibration simulation method based on the sliding window domain decomposition method according to claim 1, characterized in that: The , The expression is as follows: ； The The expression is as follows: 。 7. The rapid vehicle-track-bridge coupled vibration simulation method based on the sliding window domain decomposition method according to claim 2, characterized in that: The , The expression is as follows: ； 。 8. The rapid vehicle-track-bridge coupled vibration simulation method based on the sliding window domain decomposition method according to claim 2, characterized in that: The values ​​for β and γ are 0.25 and 0.5, respectively.

9. A computer-readable storage medium, characterized in that: It stores a computer program, which, when executed by a processor, implements a rapid vehicle-rail-bridge coupled vibration simulation method based on the sliding window domain decomposition method as described in any one of claims 1-8.

10. A computer device, characterized in that: include: Memory, used to store instructions; A processor is configured to execute the instructions, causing the computer device to perform the operation of a rapid vehicle-rail-bridge coupled vibration simulation method based on the sliding window domain decomposition method as described in any one of claims 1-8.

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