Stochastic Vibration Analysis Method, Terminal, Medium and Program Product for Vehicle-Track-Bridge System Based on Interlayer Debonding Damage

Abstract

The present invention discloses a random vibration analysis method, terminal, medium, and program product for a train-track-bridge system based on interlayer delamination damage. The method comprises: constructing a random parameter vector comprising a random parameter vector for interlayer delamination damage and a random parameter vector for track irregularity; wherein the random parameter vector for interlayer delamination damage comprises a random vector for the transverse delamination lengths of the plate ends and plate edges; selecting points for the random parameter vector based on a multi-distribution point selection method to obtain a random parameter point set; constructing a spatial random vibration analysis model for the train-track-bridge system; substituting the random parameter point set into the spatial random vibration analysis model for simulation, and solving the vibration response of the train-track-bridge system under random interlayer delamination damage using a combination of a numerical integration method and a probability density evolution method. Simultaneously considering multiple random factors, including interlayer delamination damage and random track irregularity, can significantly improve the accuracy and reliability of the response analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed railways, and in particular to a random vibration analysis method, terminal, medium and program product of a vehicle-track-bridge system based on interlayer void damage. Background Art

[0002] As a force-transmitting structure for the interaction between trains and bridges, ballastless track offers advantages such as smoothness, high stability, and minimal maintenance. The main components of a slab track structure include rails, fasteners, track slabs, CA mortar layers, and base plates. As a key component of the structure, the CA mortar layer provides support for the track slabs, transfers loads, cushions vehicle-induced loads on the structure, and reduces vibration. Therefore, the performance of the CA mortar layer determines the safety, durability, smoothness, and comfort of the ballastless track structure and significantly impacts subsequent maintenance costs.

[0003] Bridges provide smooth and stable overpasses for high-speed trains and account for 50% of all high-speed railway lines. Current research on train-track-bridge dynamic interactions primarily focuses on deterministic structures and excitations. However, this is not the case in reality. Most structures have been in operation for a long time and have already developed deterioration phenomena such as interlaminar debonding (deterioration of the CA mortar layer leads to debonding between the track slab and the base plate). Interlaminar debonding is a deterioration damage phenomenon that severely disrupts the force transmission system of the track's interlaminar structure. Furthermore, both structural damage and excitation are stochastic, making it difficult to guarantee the reliability of the system's vibration response using existing vibration analysis methods. Therefore, studying the coupled vibration response of the train-track-bridge system incorporating interlaminar debonding damage states can facilitate a rational assessment of the bridge's dynamic performance and the safety and stability of trains operating on the bridge. This research can also determine the operational reliability of each system structure under damaged conditions, fulfilling an engineering requirement for the operation and maintenance of modern high-speed railway track-bridge systems. This research is of great theoretical significance and has significant engineering application value. Summary of the Invention

[0004] The present invention provides a random vibration analysis method, terminal, medium and program product for a vehicle-track-bridge system based on interlayer void damage, so as to solve the problem that the existing technology mainly takes deterministic structures and excitations as research objects, fails to consider the randomness of interlayer void damage and excitation, and thus leads to poor reliability of the system vibration response analysis results.

[0005] In a first aspect, a random vibration analysis method for a vehicle-track-bridge system based on interlayer delamination damage is provided, comprising the following steps:

[0006] S1: Construct a random parameter vector including an interlayer void damage random parameter vector and a track irregularity random parameter vector; the interlayer void damage random parameter vector includes a random vector of the transverse void length at the plate end and a random vector of the transverse void length at the plate edge;

[0007] S2: Random parameter vector points are selected based on the multi-distribution point selection method to obtain a random parameter point set;

[0008] S3: Construct a spatial random vibration analysis model for the train-track-bridge system;

[0009] S4: The random parameter point set is substituted into the spatial random vibration analysis model of the train-track-bridge system for simulation. The numerical integration method is combined with the probability density evolution method to obtain the vibration response of the train-track-bridge system under random interlayer delamination damage.

[0010] Furthermore, the interlayer void damage random parameter vector is constructed by the following method:

[0011] The CA mortar layer area corresponding to the track plate is discretized longitudinally, and the void units on the left and right sides of the track plate have indivual;

[0012] The void cells within a preset distance close to both ends of the track plate are classified as plate end void cells, and the remaining void cells are plate edge void cells;

[0013] Random vector of horizontal gap length at the plate end It is composed of the transverse void lengths of all plate end void units and is expressed as follows:

[0014] ;

[0015] Where, represents the horizontal void length of the i-th plate end void unit, Indicates the number of plate end emptying units;

[0016] Random vector of horizontal gap length of plate edge It is composed of the transverse void lengths of all plate edge void units and is expressed as follows:

[0017] ;

[0018] Where, represents the horizontal void length of the jth plate edge void unit, Indicates the number of plate edge hollow units, ;

[0019] The random vector of transverse void length at the plate end and the random vector of transverse void length at the plate edge are combined to form the random parameter vector of interlayer void damage.

[0020] Furthermore, the track irregularity random parameter vector is constructed by the following method:

[0021] Considering four types of track irregularities, namely directional irregularity, gauge irregularity, height irregularity and horizontal irregularity, the spatial frequency and phase angle of the power spectrum of each type of track irregularity are used as independent track irregularity random parameters.

[0022] The power spectrum density functions of various track irregularities are divided into P segments according to the spatial frequency, and the two track irregularity random parameters, spatial frequency and phase angle, are divided into Q-dimensional random vectors.

[0023] The track irregularity random parameters corresponding to the four types of track irregularities are combined to form a track irregularity random parameter vector.

[0024] Furthermore, step S2 specifically includes:

[0025] Assumptions 、 、 and are the dimensions of the random parameter vector, the random vector of the lateral gap length at the plate end, the random vector of the lateral gap length at the plate edge, and the random parameter vector of the track irregularity, respectively. ;

[0026] And assume that the horizontal gap length in the random vector of the horizontal gap length at the plate end obeys the normal distribution The horizontal gap length in the random vector of the plate edge horizontal gap length all obeys the normal distribution ; are the mean and standard deviation of the horizontal gap length in the random vector of the horizontal gap length at the plate end, are the mean and standard deviation of the random vector of transverse gap lengths of the plate edge, and satisfy ;

[0027] First, the good grid point method is used to select points on the random parameter vector to obtain the first random parameter point set;

[0028] The first random parameter point is concentrated on the random vector of the horizontal gap length of the plate end and the random vector of the horizontal gap length of the plate edge. dimensional random parameter vector point set to perform Rosenblatt transformation so that the The dimensional random parameter vector point set obeys the normal distribution, and the second random parameter point set is obtained;

[0029] Combined with the normal distribution of the lateral gap length random vectors of the slab end and the slab edge, the second random parameter point set is subjected to a linear affine transformation, and finally a random parameter point set that satisfies the probability space distribution of the train-track-bridge system is obtained.

[0030] Furthermore, in step S3, in the spatial random vibration analysis model of the train-track-bridge system, the various components of the vehicle body in the vehicle system are simulated using a multi-rigid body model, and the suspension components connecting the rigid bodies are simulated using a spring damper; the rails of the track system are simulated using a three-dimensional Euler beam model, the track plate and the base plate are simulated using a plate-shell model, the rail fasteners are simulated using a linear spring damper, and the CA mortar layer between the track plate and the base plate is simulated using a spring damper after considering interlayer delamination damage; the beam body of the bridge system is simulated using a three-dimensional Euler beam model.

[0031] Furthermore, in step S4, when the random parameter point set is substituted into the train-track-bridge system spatial random vibration analysis model for simulation, the stiffness of each grid unit is calculated based on the random parameter vector of interlayer void damage in the random parameter point set combined with the grid unit area after discretization of the CA mortar layer. If a grid unit is a non-voided grid unit, the stiffness of the grid unit is calculated based on its area and the set stress level and the ratio of the number of cyclic loadings; if a grid unit is a voided grid unit, the stiffness of the grid unit satisfies: when the contact point of the voided grid unit is relatively displaced vertically When it is not greater than the threshold, its stiffness is 0. When it is greater than the threshold, its stiffness is a preset value; then the stiffness of each grid unit of the CA mortar layer is substituted into the spatial random vibration analysis model of the train-track-bridge system;

[0032] The track irregularity excitation values of the left and right tracks are calculated based on the track irregularity random parameters in the random parameter point set, and then substituted into the spatial random vibration analysis model of the train-track-bridge system.

[0033] Furthermore, in step S4, the vibration response of the train-track-bridge system under random interlayer void damage is obtained by combining the numerical integration method with the probability density evolution method, specifically including:

[0034] The Newmark-β method and the Newton-Raphson iterative method are used to jointly solve the system vibration response value corresponding to each random sample point in the random parameter point set;

[0035] Based on the system vibration response value corresponding to each random sample point, the probability density evolution method is used to obtain the probability density distribution of the system vibration response under interlayer void damage that depends on time.

[0036] In a second aspect, an electronic terminal is provided, comprising:

[0037] Memory on which computer programs or instructions are stored;

[0038] The processor is used to load and execute the computer program or instructions to implement the above-mentioned random vibration analysis method of the vehicle-track-bridge system based on interlayer delamination damage.

[0039] In a third aspect, a computer-readable storage medium is provided, on which a computer program or instruction is stored. When the computer program or instruction is executed by a processor, the random vibration analysis method of the vehicle-track-bridge system based on interlayer delamination damage as described above is implemented.

[0040] In a fourth aspect, a computer program product is provided, wherein a computer program or instruction is stored in the computer program product, and when the computer program or instruction is executed by a processor, the random vibration analysis method of the vehicle-track-bridge system based on interlayer delamination damage as described above is implemented.

[0041] The present invention proposes a random vibration analysis method, terminal, medium and program product for a vehicle-track-bridge system based on interlayer void damage. Compared with the existing technology, the present invention has the following beneficial effects:

[0042] (1) Taking into account the multiple random factors of interlayer gap damage and track random irregularities, the interlayer lateral gap length is discretized into a random parameter that obeys the normal distribution based on the multi-distribution point selection method, which can realize the description of different gap conditions at the plate end and plate edge. The dynamic response of the vehicle-track-bridge system is calculated and verified through simulation and probability density evolution method, which can significantly improve the accuracy and reliability of the vehicle-track-bridge vibration response analysis;

[0043] (2) The probability density evolution method is used to directly solve the random vibration response of the system, avoiding a large number of random sample simulations and greatly improving the computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0045] Figure 1 This is a flow chart of a random vibration analysis method for a vehicle-track-bridge system based on interlayer void damage provided by an embodiment of the present invention;

[0046] Figure 2This is a schematic diagram of the transverse clearance length between the plate end and the plate edge provided by an embodiment of the present invention;

[0047] Figure 3 Schematic diagram of interlayer degassing provided by an embodiment of the present invention, wherein (a) is a schematic diagram of a separation state, and (b) is a schematic diagram of a contact state;

[0048] Figure 4 The random vibration characteristics of the vehicle body lateral acceleration provided by an embodiment of the present invention, wherein (a), (b), (c), and (d) are the probability density function evolution surface of the vehicle body lateral acceleration, the probability density function contour lines of the vertical displacement, the mean curve of the vertical displacement, and the standard deviation curve of the vertical displacement, respectively;

[0049] Figure 5 These are the random vibration characteristics of the vertical acceleration of the mid-span track slab provided by an embodiment of the present invention, where (a), (b), (c), and (d) are the probability density function evolution surface of the vertical acceleration of the mid-span track slab, the probability density function contour lines of the vertical displacement, the mean curve of the vertical displacement, and the standard deviation curve of the vertical displacement, respectively. DETAILED DESCRIPTION

[0050] To make the objectives, technical solutions, and advantages of the present invention more apparent, the technical solutions of the present invention will be described in detail below. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other implementations obtained by those of ordinary skill in the art without inventive effort are within the scope of protection of the present invention.

[0051] like Figure 1 As shown, an embodiment of the present invention provides a random vibration analysis method for a vehicle-track-bridge system based on interlayer void damage, comprising the following steps:

[0052] S1: Construct a random parameter vector including an interlayer void damage random parameter vector and a track irregularity random parameter vector; the interlayer void damage random parameter vector includes a random vector of the transverse void length at the plate end and a random vector of the transverse void length at the plate edge;

[0053] S2: Random parameter vector points are selected based on the multi-distribution point selection method to obtain a random parameter point set;

[0054] S3: Construct a spatial random vibration analysis model for the train-track-bridge system;

[0055] S4: The random parameter point set is substituted into the spatial random vibration analysis model of the train-track-bridge system for simulation. The numerical integration method is combined with the probability density evolution method to obtain the vibration response of the train-track-bridge system under random interlayer delamination damage.

[0056] This embodiment provides a random vibration analysis method for a vehicle-track-bridge system based on interlayer delamination damage, which has the following advantages: it simultaneously considers multiple random factors such as interlayer delamination damage and random track irregularities; based on a multi-distribution point selection method, it discretizes the interlayer lateral delamination length into a random parameter that obeys a normal distribution, thereby enabling the description of different delamination conditions at the plate ends and plate edges; and calculates and verifies the dynamic response of the vehicle-track-bridge system through simulation and probability density evolution methods, which can significantly improve the accuracy and reliability of the vehicle-track-bridge dynamic response analysis; and adopts a probability density evolution method to directly solve the random vibration response of the system, thus avoiding the simulation of a large number of random samples and greatly improving the computational efficiency.

[0057] For the convenience of understanding and the same expression, let the random parameter vector It is expressed as follows:

[0058] ;

[0059] Where, is the random vector of the horizontal gap length at the plate end, is the random vector of the horizontal gap length of the plate edge, is the track irregularity random parameter vector. In this embodiment, the vector and The random parameters in the equation follow a normal distribution, and the track irregularity random parameter vector It is usually assumed to be a uniform distribution parameter with uniform distribution characteristics.

[0060] Interlayer voids mainly occur at the ends and edges of the track slabs. In the lateral distribution of the track slabs, the areas close to the edges are prone to voids, while the areas close to the middle are not prone to voids. However, how to simulate the probability distribution of the lateral void areas is a key issue in the coupled random vibration analysis of the train-track-bridge system under random void conditions. In this embodiment, the CA mortar layer area corresponding to the interlayer void track slab under study is discretized longitudinally, as shown in Figure 2. Figure 2 As shown, assuming that the left and right sides of a track plate have There are vertically discrete void units, where the void units on the left and right sides each have and meet the following requirements:

[0061] ;

[0062] Where, The longitudinal length of each hollow unit (the longitudinal lengths of hollow units are set to be equal), The length of a track plate.

[0063] The void units within a preset distance from both ends of the track plate are classified as plate end void units, and the remaining void units are plate edge void units. Assuming that the transverse void length of each void unit obeys a normal distribution, the transverse void lengths of the plate end void units constitute a random vector of plate end transverse void lengths. It can be expressed as:

[0064] ;

[0065] Where, represents the horizontal void length of the i-th plate end void unit, Indicates the number of plate end emptying units;

[0066] The random vector of the horizontal void length of the plate edge void unit is composed of the horizontal void length of the plate edge. It can be expressed as:

[0067] ;

[0068] Where, represents the horizontal void length of the jth plate edge void unit, Indicates the number of plate edge hollow units, .

[0069] Generally speaking, the transverse void length of the plate end void unit is larger than that of the plate edge void unit, so the plate end void unit and the plate edge void unit adopt different normal distributions, and the transverse void length of the plate end void unit is set to All obey normal distribution , the horizontal void length of the plate edge void unit All obey normal distribution ,in, are the mean and standard deviation of the horizontal gap length in the random vector of the horizontal gap length at the plate end, are the mean and standard deviation of the random vector of transverse gap lengths of the plate edge, and satisfy .

[0070] Assumptions 、 、 and are the dimensions of the random parameter vector, the random vector of the lateral gap length at the plate end, the random vector of the lateral gap length at the plate edge, and the random parameter vector of the track irregularity, respectively. ; Among them The random vector follows the normal distribution. The random parameter follows a uniform distribution.

[0071] First, we use the good grid point method to get the s-dimensional hypercube vector space The representative point set selected from the random parameter point set is used as the first random parameter point set , which is expressed as follows:

[0072] ;

[0073] Where, is the qth representative point, is the number of representative point sets selected, which is also the number of deterministic samples calculated subsequently.

[0074] Because the first random parameter point set selected by the good grid point method is a uniformly distributed point set, it is necessary to perform Rosenblatt transformation to convert the first random parameter point set corresponding to the random vector of the horizontal gap length of the plate end and the random vector of the horizontal gap length of the plate edge into the first random parameter point set. dimensional random parameter vector point set to perform Rosenblatt transformation so that the The dimensional random parameter vector point set obeys the normal distribution, and the second random parameter point set is obtained;

[0075] Among them, the former After the Rosenblatt transformation of the dimensional random parameter vector point set, the random parameter point set obeys the normal distribution It can be expressed as:

[0076] ;

[0077] Where, represents the random parameter point set of the transverse gap length at the plate end, Represents the random parameter point set of the lateral void length of the plate edge. is the Rosenblatt transformation operator (inverse transformation function); therefore, the second set of random parameter points can be expressed as follows:

[0078] ;

[0079] Where, represents the second random parameter point set.

[0080] Combined with the normal distribution of the lateral gap length random vectors of the slab end and the slab edge, the second random parameter point set is subjected to a linear affine transformation, and finally a random parameter point set that satisfies the probability space distribution of the train-track-bridge system is obtained.

[0081] According to the previously set horizontal gap length random vector, the horizontal gap length obeys the normal distribution The horizontal gap length in the random vector of the horizontal gap length of the plate edge obeys the normal distribution , then we have:

[0082] ;

[0083] In this way, a representative sample point set of the random vector of the transverse void length at the plate end and a representative sample point set of the random vector of the transverse void length at the plate edge can be obtained.

[0084] Since the voided area and the non-voided area of the CA mortar layer are two different working conditions, the stiffness of the non-voided area of the CA mortar layer is linear stiffness, and the voided area of the CA mortar layer needs to consider the nonlinear contact effect when the train passes, and its stiffness is nonlinear stiffness. Figure 3 As shown in (a) and (b), when the CA mortar layer 2 between the track slab 1 and the base plate 3 is partially debonded, it appears to be in a gap-separated state when no train is running. When a train passes, rigid contact occurs between the track slab 1 and the base plate 3. Therefore, the nonlinear contact effect of the debonded area must be considered in system modeling.

[0085] Therefore, when the random parameter point set is substituted into the spatial random vibration analysis model of the train-track-bridge system for simulation, the stiffness of each grid unit is calculated based on the random parameter vector of interlayer void damage in the random parameter point set combined with the grid unit area after discretization of the CA mortar layer. If a grid unit is a non-void grid unit, the stiffness of the grid unit is calculated based on its area and the set stress level and the ratio of the number of cyclic loadings; if a grid unit is a void grid unit, the stiffness of the grid unit satisfies: when the contact point of the void grid unit is relatively displaced vertically, When it is not greater than the threshold, its stiffness is 0. When it is greater than the threshold, its stiffness is a preset value; then the stiffness of each grid unit of the CA mortar layer is substituted into the spatial random vibration analysis model of the train-track-bridge system.

[0086] In order to facilitate calculation, when the CA mortar layer is discretized into grid units, the length of the grid corresponding to the longitudinal division of the track plate and the longitudinal length of the aforementioned void unit are and the horizontal length of the void unit is an integer multiple of the length of the grid for horizontally dividing the track plate, so as to ensure that each grid unit after discretization is void or non-void.

[0087] For non-empty mesh elements, the stiffness is calculated as follows:

[0088] Set the stress level of the mesh elements and the number of cyclic loading times is the fatigue damage parameter, and the damage variable of the CA mortar layer loaded n times is It can be written as:

[0089] ;

[0090] Where, 、 and It is a series of parameters related to the damage state of CA mortar layer; is the number of loads, is the fatigue life of CA mortar layer;

[0091] and Dynamic elastic modulus of secondary loading It can be expressed as:

[0092] ;

[0093] ;

[0094] Where, is the initial dynamic elastic modulus; and Load once and The total fatigue strain, is the residual strain after loading once;

[0095] Total fatigue strain after 1 loading It can be expressed as:

[0096] ;

[0097] Total fatigue strain after N loadings (fatigue failure) It can be expressed as:

[0098] ;

[0099] load Total fatigue strain It can be expressed as:

[0100] ;

[0101] Fatigue life of CA mortar layer satisfy:

[0102] ;

[0103] Where, is the stress level, i.e. the ratio of the maximum compressive stress to the compressive strength;

[0104] No. The residual strain after the first fatigue loading is: .

[0105] The stress level of the mesh element will be set and the number of cyclic loading times Substituting into the above formula, we can get the corresponding stress level, loading Fatigue dynamic elastic modulus , mainly considering the vertical influence of the plate unit, then the stiffness of the CA mortar layer grid unit can be expressed as:

[0106] ;

[0107] Where, The coordinates are The equivalent linear spring stiffness of the mesh element; is the effective bonding area of the CA mortar layer grid unit (area of discrete grid units); is the thickness of CA mortar layer.

[0108] For the voided mesh elements, the stiffness is expressed as follows:

[0109] ;

[0110] in, represents the relative vertical displacement of the contact point, Indicates the contact stiffness of the contact point. When the relative vertical displacement of the contact point Less than or equal to When the upper and lower contact points are in the gap state, the contact point stiffness is 0, when Greater than When the upper and lower contact points are in contact, the contact stiffness is set to a constant value for ease of calculation. .

[0111] The track irregularities in this embodiment include four types of track irregularities: directional irregularity, gauge irregularity, height irregularity, and horizontal irregularity. The spatial frequency and phase angle of the power spectrum of each type of track irregularity are used as independent track irregularity random parameters. The power spectrum density function of each type of track irregularity is divided into P segments according to the spatial frequency, and the two track irregularity random parameters, spatial frequency and phase angle, are divided into Q-dimensional random vectors; the track irregularity random parameters corresponding to the four types of track irregularities are combined to form a 4×2×P×Q-dimensional track irregularity random parameter vector. Track irregularity random parameter point set The components in can be expressed as:

[0112] ;

[0113] ;

[0114] Where, are the random parameters of height irregularity, direction irregularity, horizontal irregularity and gauge irregularity respectively; and denote the spatial frequency and phase angle, respectively.

[0115] The random spatial frequency and phase angle can be expressed as and ,in, They represent height unevenness, direction unevenness, level unevenness and gauge unevenness respectively. , Assuming random spatial frequencies for Inside, remember , , and satisfies ,in is the upper cutoff frequency, is the lower cutoff frequency.

[0116] The second random parameter point set When performing linear affine transformation, The linear radiation transformation for random parameters can be expressed as follows:

[0117] ;

[0118] Where, is a 4×2×P-dimensional vector, which can be expressed as: , ; equal ; express in , express in .

[0119] Use random harmonic function to simulate random track irregularity, then the amplitude of random harmonic function is Expressed as:

[0120] ;

[0121] Where, is the track irregularity power spectral density function, is the equally divided spatial frequency range of each segment;

[0122] The four representative samples of track irregularity can be expressed as:

[0123] ;

[0124] Where, 、 、 and Representative samples of height irregularity, direction irregularity, horizontal irregularity and gauge irregularity, respectively. x represents the time coordinate axis (rail ordinate);

[0125] Based on the four representative samples of track irregularity, the height and horizontal irregularity sample points of the left and right tracks can be obtained, which are expressed as follows:

[0126] ;

[0127] ;

[0128] Where, and They represent the sample points of height irregularity and horizontal irregularity of the left track respectively; and They represent the sample points of height unevenness and horizontal unevenness of the right track respectively. Indicates half of the rail gauge.

[0129] According to the above formula, the track irregularity sample values of the left and right tracks can be generated. The random track irregularity excitation value, including the track irregularity displacement and acceleration, can be further calculated. Then, it can be substituted into the spatial random vibration analysis model of the train-track-bridge system for simulation.

[0130] In the spatial random vibration analysis model of the train-track-bridge system, the various components of the vehicle body in the vehicle system are simulated using a multi-rigid body model, and the suspension components connecting the rigid bodies are simulated using spring dampers; the rails of the track system are simulated using a three-dimensional Euler beam model, the track slab and base plate are simulated using a plate-shell model, the rail fasteners are simulated using a linear spring damper, and the CA mortar layer between the track slab and base plate is simulated using a spring damper after considering interlayer delamination damage; the beams of the bridge system are simulated using a three-dimensional Euler beam model.

[0131] Among them, the dynamic equation of the train system can be expressed as:

[0132] ;

[0133] Where, 、 and are the mass matrix, damping matrix and stiffness matrix of the vehicle respectively; 、 and represent the acceleration, velocity and displacement of the vehicle respectively; represents the vehicle load matrix considering the influence of random parameters of track irregularities.

[0134] The track-bridge system serves as the basic structure, and the dynamic equation of the track-bridge system is:

[0135] ;

[0136] Where, is the mass matrix of the track-bridge system; and The random parameters of interlayer delamination damage are considered separately and The damping matrix and stiffness matrix of the track-bridge system are affected by the transverse gap length at the slab ends and the transverse gap length at the slab edges. The damping matrix is closely related to the stiffness matrix and the mass matrix. When the stiffness matrix is affected by the random parameters of the interlayer gap damage, the damping matrix will also be affected. The calculation of the damping matrix is an existing technology and will not be elaborated on here. is the random load matrix of the track-bridge system, which includes the vehicle axle load and the wheel-rail interaction force caused by random track irregularities. It will vary with the contact state of the gap area, so the train-track-bridge system including the gap is a high-dimensional nonlinear dynamic system that requires an iterative method to solve.

[0137] In this embodiment, the Newmark-β method and the Newton-Raphson iterative method are first used to jointly solve the system vibration response value corresponding to each random sample point in the random parameter point set; then, based on the system vibration response value corresponding to each random sample point, the probability density evolution method is used to solve the probability density distribution of the system vibration response under interlayer void damage depending on time.

[0138] The following is an explanation of the principle of joint solution of Newmark-β method and Newton-Raphson iterative method. The specific process includes:

[0139] The dynamic equation of the high-speed railway train-track-bridge system can be expressed as:

[0140] (1);

[0141] in, is the mass matrix of the system, are the damping matrix and stiffness matrix of the system considering the random parameters of interlayer delamination damage, is the random load matrix of the system; 、 and represent the acceleration, velocity and displacement of the system respectively.

[0142] Combining the last two terms on the left side of formula (1), formula (1) can be re-expressed as:

[0143] (2);

[0144] in, Represents operators related to velocity and displacement at the corresponding moment.

[0145] By shifting the terms in equation (2), we can obtain:

[0146] (3);

[0147] in, is the residual force vector. For a multi-degree-of-freedom system, the basic expression of the final velocity and displacement at each time step of the Newmark-β method is:

[0148] (4);

[0149] (5);

[0150] Where, represents the time step, 、 are all fixed parameters. In this embodiment, Take 0.25, Take 0.5;

[0151] According to the prediction relationship between formula (4) and formula (5), we can get:

[0152] (6);

[0153] (7);

[0154] Where, 、 、 They represent the predicted values of displacement, velocity, and acceleration at the i+1th time step respectively;

[0155] By setting Equation (4) and Equation (5) The prediction formula can be obtained:

[0156] (8);

[0157] (9);

[0158] Substituting Equations (6) and (7) into Equation (3), the residual force equation can be obtained simply by express:

[0159] (10);

[0160] At this time, the linearization method can be used to solve the nonlinear equation (10). According to the basic principle of the Newton-Raphson iterative method, the nonlinear equation (10) can be expressed in a linear way as follows:

[0161] (11);

[0162] Among them, the Jacobian matrix (also called iteration matrix) is:

[0163] (12);

[0164] The above formula can be expanded into:

[0165] (13);

[0166] in: is the influence matrix of internal force changing with displacement, i.e. tangent stiffness matrix ; is the influence matrix of internal force changing with velocity, i.e. tangent damping matrix ; It is the dependence of external load on system displacement. For the model established by the present invention, this value is 0.

[0167] Noting equations (6) and (7), it is easy to deduce:

[0168] (14);

[0169] in, is the identity matrix.

[0170] Therefore, the iterative matrix can be finally expressed as:

[0171] (15);

[0172] The nonlinear equation (10) can be solved by the Newton-Raphson iterative method. The time step Step iteration results Corrected to .

[0173] Correction of the displacement vector calculated by the linear equation satisfy:

[0174] (16);

[0175] According to equations (6) and (7), the corrections of velocity and acceleration vectors can be obtained:

[0176] ;

[0177] in, and They represent the correction of velocity vector and acceleration vector respectively.

[0178] The probability density evolution method is an existing technology, and its specific principles will not be described in detail here.

[0179] Of course, there are many factors that affect the random vibration response of the train-track-bridge system. In addition to the above-mentioned interlayer void damage random parameters and track irregularity random parameters, they also include the random parameters of the vehicle structure itself and the mechanical parameters of the track-bridge structure itself, such as the variability of parameters such as the elastic modulus, damping ratio, mass density and vehicle body mass of the reinforced concrete structure, and the stiffness and damping of the vehicle body connectors. Therefore, in some other embodiments, the random parameters of the vehicle structure itself and the mechanical parameters of the track-bridge structure itself can also be taken into account. Of course, the research on the influence of the random parameters of the vehicle structure itself and the mechanical parameters of the track-bridge structure itself on the system response is relatively mature. The introduction of the random parameters of the vehicle structure itself and the mechanical parameters of the track-bridge structure itself belongs to the existing technology, and the present invention will not go into details here.

[0180] To verify the accuracy of the established random vibration analysis model for a system with random interlayer void damage, a three-span high-speed railway ballastless track-simply supported beam bridge model was established in this example. 400 sets of random vehicle-track-bridge response samples were calculated based on the numerical integration method jointly solved by the probability density evolution method and the Newmark-β method and the Newton-Raphson iterative method.

[0181] In one of the air-out conditions, the random response information of the lateral acceleration of the vehicle center of gravity is as follows: Figure 4 As shown, Figure 4 (a) shows the three-dimensional probability density evolution time surface of acceleration. It can be seen that as the train enters the bridge, the probability density function of the lateral vibration acceleration of the vehicle body is concentrated in a range of smaller values. This indicates that after the train enters the bridge, the track smoothness of the bridge will be better and the lateral acceleration of the vehicle body will also be smaller. Figure 4 The probability density contour lines shown in (b) are wide at both ends and narrow in the middle, which also confirms this conclusion. Figure 4 (c) and (d) are the mean curve and standard deviation curve of the vehicle body lateral vibration acceleration, respectively.

[0182] By performing 9999 calculations using the Monte Carlo method (MCM) and comparing the results with the probability density evolution method (PDEM), the maximum deviations of the acceleration mean and standard deviation were found to be 1.1% and 0.9%, respectively, proving that the established random model is correct and reliable. This also verifies that the use of the probability density evolution method can ensure the efficiency of the calculation process and the high accuracy of the calculation results when performing spatial random vibration analysis on the train-track-bridge dynamic system containing derailment.

[0183] Similarly, the three-dimensional probability density evolution surface, probability density contour lines, and mean and standard deviation curves of the vertical acceleration of the track slab at the mid-span position are shown in Figure 2. Figure 5 As shown in Figures (a), (b), (c), and (d), the variations in the mean and standard deviation curves indicate that the vehicle-track-bridge coupling effect when a train passes through the track-bridge system causes the vertical random dynamic response of the track plate to experience violent up-and-down oscillations. Furthermore, compared to deterministic dynamic time history analysis of a vehicle-track-bridge coupled system, which only outputs a few deterministic time history samples and fails to capture the random response of the vehicle body and structure, the probability density evolution method efficiently and accurately describes the time-dependent random vibration characteristics of the system when a train passes over a bridge.

[0184] An embodiment of the present invention further provides an electronic terminal, including:

[0185] Memory on which computer programs or instructions are stored;

[0186] The processor is used to load and execute the computer program or instructions to implement the above-mentioned random vibration analysis method of the vehicle-track-bridge system based on interlayer delamination damage.

[0187] An embodiment of the present invention further provides a computer-readable storage medium having a computer program or instruction stored thereon, which, when executed by a processor, implements the aforementioned method for random vibration analysis of a vehicle-track-bridge system based on interlayer delamination damage.

[0188] An embodiment of the present invention further provides a computer program product, which stores a computer program or instructions. When the computer program or instructions are executed by a processor, the random vibration analysis method of the vehicle-track-bridge system based on interlayer delamination damage as described above is implemented.

[0189] It can be understood that the same or similar parts of the above embodiments can be referenced to each other, and the contents not described in detail in some embodiments can refer to the same or similar contents in other embodiments.

[0190] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0191] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0192] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0193] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0194] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A random vibration analysis method for a vehicle-track-bridge system based on interlayer void damage, characterized in that: The steps include: S1: Construct a random parameter vector including an interlayer void damage random parameter vector and a track irregularity random parameter vector; the interlayer void damage random parameter vector includes a random vector of the transverse void length at the plate end and a random vector of the transverse void length at the plate edge; S2: Random parameter vector points are selected based on the multi-distribution point selection method to obtain a random parameter point set; S3: Construct a spatial random vibration analysis model for the train-track-bridge system; S4: Substitute the random parameter point set into the spatial random vibration analysis model of the train-track-bridge system for simulation, and use the numerical integration method combined with the probability density evolution method to solve the vibration response of the train-track-bridge system under random interlayer delamination damage; In step S3, in the spatial random vibration analysis model of the train-track-bridge system, the various components of the vehicle body in the vehicle system are simulated using a multi-rigid body model, and the suspension components connecting the rigid bodies are simulated using a spring-damper model; the rails of the track system are simulated using a three-dimensional Euler beam model, the track plate and base plate are simulated using a plate-shell model, the rail fasteners are simulated using a linear spring-damper model, and the CA mortar layer between the track plate and base plate is simulated using a spring-damper model after considering interlayer delamination damage; the beams of the bridge system are simulated using a three-dimensional Euler beam model; In step S4, when the random parameter point set is substituted into the train-track-bridge system spatial random vibration analysis model for simulation, the stiffness of each grid unit is calculated based on the random parameter vector of interlayer void damage in the random parameter point set combined with the grid unit area after discretization of the CA mortar layer. If a grid unit is a non-voided grid unit, the stiffness of the grid unit is calculated based on its area and the set stress level and the ratio of the number of cyclic loadings; if a grid unit is a voided grid unit, the stiffness of the grid unit satisfies: when the contact point of the voided grid unit is relatively displaced vertically, When it is not greater than the threshold, its stiffness is 0. When it is greater than the threshold, its stiffness is a preset value; then the stiffness of each grid unit of the CA mortar layer is substituted into the spatial random vibration analysis model of the train-track-bridge system; The track irregularity excitation values of the left and right tracks are calculated based on the track irregularity random parameters in the random parameter point set, and then substituted into the spatial random vibration analysis model of the train-track-bridge system.

2. The random vibration analysis method of the vehicle-track-bridge system based on interlayer void damage according to claim 1 is characterized in that: The interlayer void damage random parameter vector is constructed by the following method: The CA mortar layer area corresponding to the track plate is discretized longitudinally, and the void units on the left and right sides of the track plate have indivual; The void cells within a preset distance close to both ends of the track plate are classified as plate end void cells, and the remaining void cells are plate edge void cells; Random vector of horizontal gap length at the plate end It is composed of the transverse void lengths of all plate end void units and is expressed as follows: ； Where, represents the horizontal void length of the i-th plate end void unit, Indicates the number of plate end emptying units; Random vector of horizontal gap length of plate edge It is composed of the transverse void lengths of all plate edge void units and is expressed as follows: ； Where, represents the horizontal void length of the jth plate edge void unit, Indicates the number of plate edge hollow units, ; The random vector of transverse void length at the plate end and the random vector of transverse void length at the plate edge are combined to form the random parameter vector of interlayer void damage.

3. The random vibration analysis method of the vehicle-track-bridge system based on interlayer void damage according to claim 1 is characterized in that: The track irregularity random parameter vector is constructed by the following method: Considering four types of track irregularities, namely directional irregularity, gauge irregularity, height irregularity and horizontal irregularity, the spatial frequency and phase angle of the power spectrum of each type of track irregularity are used as independent track irregularity random parameters. The power spectrum density functions of various track irregularities are divided into P segments according to the spatial frequency, and the two track irregularity random parameters, spatial frequency and phase angle, are divided into Q-dimensional random vectors. The track irregularity random parameters corresponding to the four types of track irregularities are combined to form a track irregularity random parameter vector.

4. The random vibration analysis method of the vehicle-track-bridge system based on interlayer void damage according to claim 1 is characterized in that: Step S2 specifically includes: Assumptions 、 、 and are the dimensions of the random parameter vector, the random vector of the lateral gap length at the plate end, the random vector of the lateral gap length at the plate edge, and the random parameter vector of the track irregularity, respectively. ; And assume that the horizontal gap length in the random vector of the horizontal gap length at the plate end obeys the normal distribution The horizontal gap length in the random vector of the plate edge horizontal gap length all obeys the normal distribution ; are the mean and standard deviation of the horizontal gap length in the random vector of the horizontal gap length at the plate end, are the mean and standard deviation of the random vector of transverse gap lengths of the plate edge, and satisfy ; First, the good grid point method is used to select points on the random parameter vector to obtain the first random parameter point set; The first random parameter point is concentrated on the random vector of the horizontal gap length of the plate end and the random vector of the horizontal gap length of the plate edge. dimensional random parameter vector point set to perform Rosenblatt transformation so that the The dimensional random parameter vector point set obeys the normal distribution, and the second random parameter point set is obtained; Combined with the normal distribution of the lateral gap length in the random vector of the lateral gap length at the plate end and the random vector of the lateral gap length at the plate edge, the second random parameter point set is subjected to a linear affine transformation, and finally a random parameter point set that satisfies the probability space distribution of the train-track-bridge system is obtained.

5. The random vibration analysis method of the vehicle-track-bridge system based on interlayer void damage according to claim 1 is characterized in that: In step S4, the numerical integration method is combined with the probability density evolution method to obtain the vibration response of the train-track-bridge system under random interlayer void damage, which specifically includes: The Newmark-β method and the Newton-Raphson iterative method are used to jointly solve the system vibration response value corresponding to each random sample point in the random parameter point set; Based on the system vibration response value corresponding to each random sample point, the probability density evolution method is used to obtain the probability density distribution of the system vibration response under interlayer void damage that depends on time.

6. An electronic terminal, characterized in that: include: Memory on which computer programs or instructions are stored; A processor is used to load and execute the computer program or instructions to implement the random vibration analysis method of the vehicle-track-bridge system based on interlayer delamination damage according to any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program or instruction stored thereon, characterized in that: The computer program or instruction stored therein, when executed by a processor, implements the random vibration analysis method of a vehicle-track-bridge system based on interlayer delamination damage as described in any one of claims 1 to 5.

8. A computer program product, characterized in that The computer program product stores a computer program or instructions, which, when executed by a processor, implements the random vibration analysis method for a vehicle-track-bridge system based on interlayer delamination damage as described in any one of claims 1 to 5.

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