Vehicle-rail-bridge system random vibration analysis method based on interlayer void damage, terminal, medium and program product

Abstract

The invention discloses a vehicle-rail-bridge system random vibration analysis method based on interlayer void damage, a terminal, a medium and a program product. The method comprises the following steps: constructing a random parameter vector comprising an interlayer void damage random parameter vector and a rail irregularity random parameter vector; wherein the interlayer void damage random parameter vector comprises a plate end and plate edge transverse void length random vector; performing random parameter vector point selection based on a multi-distribution point selection method to obtain a random parameter point set; constructing a train-rail-bridge system space random vibration analysis model; and substituting the random parameter point set into the train-track-bridge system space random vibration analysis model for simulation, and solving by combining a numerical integration method and a probability density evolution method to obtain train-track-bridge system vibration response under random interlayer void damage. And meanwhile, multiple random factors such as interlayer void damage and track random irregularity are considered, so that the accuracy and reliability of response analysis can be remarkably improved.

Description

Technical Field

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

[0002] As a force - transmitting structure for the interaction between trains and bridges, the ballastless track has the advantages of good smoothness, high stability and less maintenance. The main components of the slab ballastless track structure include rails, fasteners, track slabs, CA mortar layers and base plates, etc. As a key part of its structure, the CA mortar layer has functions such as providing support for the track slab, transmitting loads to buffer the loads generated by vehicles on the structure and reducing vibration effects. Therefore, the performance of the CA mortar layer determines the driving safety, durability, smoothness and comfort of the ballastless track structure, and is seriously related to the level of later maintenance costs.

[0003] Bridges can provide a smooth and stable on - bridge line for high - speed trains, and the proportion of bridges in the high - speed railway line generally reaches 50%. At present, most of the research on the dynamic interaction of train - track - bridge takes deterministic structures and excitations as the research objects. However, this is not the case in reality. Most structures have been in operation for a long time, and there is already an interlayer delamination degradation phenomenon (delamination between the track slab and the base plate caused by the degradation of the CA mortar layer). Interlayer delamination is a relatively serious degradation damage phenomenon in the force - transmitting system of the track interlayer structure, and both structural damage and excitation are random. Therefore, it is difficult to guarantee the reliability of the analysis results of the system vibration response in the existing vibration analysis methods. Therefore, studying the coupled vibration response of the train - track - bridge system in combination with the interlayer delamination damage state is beneficial to reasonably evaluate the dynamic performance of bridges and the safety and stability of trains running on bridges, determine the operation reliability of each structure of the system in the damaged state, and is also an engineering requirement for the operation and maintenance of the modern high - speed railway track - bridge system. This research is of great theoretical significance and also of great value in engineering applications. Summary of the Invention

[0004] The present invention provides a random vibration analysis method, a terminal, a medium and a program product for a vehicle - track - bridge system based on interlayer delamination damage, so as to solve the problem that the existing technology mainly takes deterministic structures and excitations as the research objects, without considering the randomness of both interlayer delamination damage and excitation, resulting in poor reliability of the analysis results of the system vibration response.

[0005] In the first aspect, a random vibration analysis method for a vehicle - track - bridge system based on interlayer delamination damage is provided, including the following steps: S1: Construct a random parameter vector including the random parameter vector of interlayer void damage and the random parameter vector of track irregularity; where the random parameter vector of interlayer void damage includes the random vector of transverse void length at the slab end and the random vector of transverse void length at the slab edge. S2: Select points for the random parameter vector based on the multi-distribution point selection method to obtain a set of random parameter points. S3: Construct a spatial random vibration analysis model of the train-track-bridge system. S4: Substitute the set of random parameter points into the spatial random vibration analysis model of the train-track-bridge system for simulation, and use a combination of numerical integration method and probability density evolution method to solve for the vibration response of the train-track-bridge system under random interlayer void damage.

[0006] Further, the random parameter vector of interlayer void damage is constructed by the following method: Discretize the CA mortar layer area corresponding to the track slab longitudinally, and there are void units corresponding to the left and right sides of the track slab respectively. Group the void units within a preset distance near both ends of the track slab as void units at the slab end, and the remaining void units as void units at the slab edge. The random vector of transverse void length at the slab end is composed of the transverse void lengths of all void units at the slab end, and is expressed as follows: ; where represents the transverse void length of the i-th void unit at the slab end, represents the number of void units at the slab end; The random vector of transverse void length at the slab edge is composed of the transverse void lengths of all void units at the slab edge, and is expressed as follows: ; where represents the transverse void length of the j-th void unit at the slab edge, represents the number of void units at the slab edge, ; The random vector of transverse void length at the slab end and the random vector of transverse void length at the slab edge are combined to form the random parameter vector of interlayer void damage.

[0007] Further, the random parameter vector of track irregularity is constructed by the following method: Considering four types of track irregularities, namely direction irregularity, gauge irregularity, vertical irregularity, and horizontal irregularity, regard the spatial frequency and phase angle of the power spectrum of each type of track irregularity as independent random parameters of track irregularity. The power spectral density functions of various types of track irregularities are evenly divided into P segments according to the spatial frequency, and the two track irregularity random parameters, i.e., the spatial frequency and the phase angle, are both segmented into Q-dimensional random vectors; The track irregularity random parameter vectors are formed by combining the track irregularity random parameters corresponding to the four types of track irregularities.

[0008] Furthermore, step S2 specifically includes: Assume that 、 、 and are the dimensions of the random parameter vector, the random vector of the lateral void length at the slab end, the random vector of the lateral void length at the slab edge, and the track irregularity random parameter vector respectively, ; and it is set that the lateral void lengths in the random vector of the lateral void length at the slab end all follow a normal distribution , and the lateral void lengths in the random vector of the lateral void length at the slab edge all follow a normal distribution ; are the mean and standard deviation of the lateral void length in the random vector of the lateral void length at the slab end respectively, are the mean and standard deviation of the lateral void length in the random vector of the lateral void length at the slab edge respectively, and satisfy ; First, the good lattice point method is used to select points for the random parameter vector to obtain the first random parameter point set; The -dimensional random parameter vector point sets corresponding to the random vector of the lateral void length at the slab end and the random vector of the lateral void length at the slab edge in the first random parameter point set are subjected to the Rosenblatt transformation to make the -dimensional random parameter vector point set follow a normal distribution, obtaining the second random parameter point set; Combined with the normal distributions that the lateral void lengths in the random vector of the lateral void length at the slab end and the random vector of the lateral void length at the slab edge all follow, the second random parameter point set is subjected to a linear affine transformation to finally obtain a random parameter point set that satisfies the probability space distribution of the vehicle-track-bridge system.

[0009] Furthermore, in step S3, in the spatial random vibration analysis model of the vehicle-track-bridge system, each component of the car body in the vehicle system is simulated by a multi-rigid body model, and the suspension components connecting the rigid bodies are simulated by spring dampers; the rail in the track system is simulated by a three-dimensional Euler beam model, the track slab and the base slab are simulated by a plate shell model, the rail fasteners are simulated by linear spring dampers, and the CA mortar layer between the track slab and the base slab is simulated by a spring damper considering interlayer void damage; the beam body of the bridge system is simulated by a three-dimensional Euler beam model.

[0010] Further, in step S4, when substituting the random parameter point set into the spatial random vibration analysis model of the train-track-bridge system for simulation, the stiffness of each grid element is calculated according to the interlayer delamination damage random parameter vector in the random parameter point set and the area of the grid element after discretization of the CA mortar layer. If a grid element is a non-delaminated grid element, the stiffness of the grid element is calculated based on its area, the set stress level, and the cyclic loading ratio. If a grid element is a delaminated grid element, the stiffness of the grid element satisfies: when the relative vertical displacement of the contact point of the delaminated grid element is not greater than the threshold value, its stiffness is 0, and when is greater than the threshold value, its stiffness is a preset value; then the stiffness of each grid element of the CA mortar layer is substituted into the spatial random vibration analysis model of the train-track-bridge system; And the track irregularity excitation values of the left and right tracks are calculated according to 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.

[0011] Further, in step S4, a numerical integration method and a probability density evolution method are combined to solve for the vibration response of the train-track-bridge system under random interlayer delamination damage, specifically including: The Newmark-β method and the Newton-Raphson iteration method are jointly used to solve for the system vibration response values corresponding to each random sample point in the random parameter point set; Based on the system vibration response values corresponding to each random sample point, the probability density evolution method is used to solve for the time-dependent probability density distribution of the system vibration response under interlayer delamination damage.

[0012] In a second aspect, an electronic terminal is provided, including: A memory storing a computer program or instruction thereon; A processor for loading and executing the computer program or instruction to implement the method for random vibration analysis of the vehicle-track-bridge system based on interlayer delamination damage as described above.

[0013] In a third aspect, a computer-readable storage medium is provided, storing a computer program or instruction thereon, and when the stored computer program or instruction is executed by a processor, the method for random vibration analysis of the vehicle-track-bridge system based on interlayer delamination damage as described above is implemented.

[0014] In a fourth aspect, a computer program product is provided, storing a computer program or instruction therein, and when the computer program or instruction is executed by a processor, the method for random vibration analysis of the vehicle-track-bridge system based on interlayer delamination damage as described above is implemented.

[0015] The present invention provides a method, a terminal, a medium, and a program product for analyzing the random vibration of a vehicle-track-bridge system based on interlayer delamination damage. Compared with the prior art, the present invention has the following beneficial effects: (1) By simultaneously considering multiple random factors such as interlayer delamination damage and track random unevenness, and based on the multi-distribution point selection method, the lateral interlayer delamination length is discretized into random parameters that follow a normal distribution, enabling the description of different delamination conditions at the plate ends and plate edges. Through simulation and the probability density evolution method, the dynamic response of the vehicle-track-bridge system is calculated and verified, which can significantly improve the accuracy and reliability of the vibration response analysis of the vehicle-track-bridge system; (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 calculation efficiency. Description of the Drawings

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0017] Figure 1 is a flowchart of a method for analyzing the random vibration of a vehicle-track-bridge system based on interlayer delamination damage provided by an embodiment of the present invention; Figure 2 is a schematic diagram of the lateral delamination length at the plate end and plate edge provided by an embodiment of the present invention; Figure 3 is a schematic diagram of interlayer delamination provided by an embodiment of the present invention, where (a) is a schematic diagram of the separated state and (b) is a schematic diagram of the contact state; Figure 4 is the random vibration characteristic of the lateral acceleration of the vehicle body provided by an embodiment of the present invention, where (a), (b), (c), and (d) are, in sequence, the probability density function evolution surface of the lateral acceleration of the vehicle body, the contour line of the probability density function of the vertical displacement, the mean curve of the vertical displacement, and the standard deviation curve of the vertical displacement; Figure 5 is the random vibration characteristic of the vertical acceleration of the track slab at the mid-span provided by an embodiment of the present invention, where (a), (b), (c), and (d) are, in sequence, the probability density function evolution surface of the vertical acceleration of the track slab at the mid-span, the contour line of the probability density function of the vertical displacement, the mean curve of the vertical displacement, and the standard deviation curve of the vertical displacement. Detailed Embodiments

[0018] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be described in detail below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without any creative work fall within the scope of protection of the present invention.

[0019] As Figure 1 shown, an embodiment of the present invention provides a method for random vibration analysis of a vehicle-track-bridge system based on interlayer delamination damage, including the following steps: S1: Construct a random parameter vector including a random parameter vector of interlayer delamination damage and a random parameter vector of track irregularity; wherein the random parameter vector of interlayer delamination damage includes a random vector of the transverse delamination length at the plate end and a random vector of the transverse delamination length at the plate edge; S2: Select points for the random parameter vector based on the multi-distribution point selection method to obtain a set of random parameter points; S3: Construct a spatial random vibration analysis model of the train-track-bridge system; S4: Substitute the set of random parameter points into the spatial random vibration analysis model of the train-track-bridge system for simulation, and use a combination of the numerical integration method and the probability density evolution method to solve for the vibration response of the train-track-bridge system under random interlayer delamination damage.

[0020] The method for random vibration analysis of a vehicle-track-bridge system based on interlayer delamination damage provided in this embodiment has the following advantages: simultaneously considering multiple random factors such as interlayer delamination damage and random track irregularity, based on the multi-distribution point selection method, discretizing the transverse interlayer delamination length into random parameters subject to a normal distribution, realizing the description of different delamination conditions at the plate end and the plate edge, calculating and verifying the dynamic response of the vehicle-track-bridge system through simulation and the probability density evolution method, which can significantly improve the accuracy and reliability of the dynamic response analysis of the vehicle-track-bridge; directly solving the random vibration response of the system using the probability density evolution method, avoiding a large number of random sample simulations, and greatly improving the calculation efficiency.

[0021] For the convenience of understanding and unified expression, let the random parameter vector be expressed as follows: ; wherein, is the random vector of the transverse delamination length at the plate end, is the random vector of the transverse delamination length at the plate edge, is the random parameter vector of track irregularity. In this embodiment, each random parameter in the vectors and obeys a normal distribution, while the random parameter vector of track irregularity It is usually assumed to be a uniformly distributed parameter with the characteristics of a uniform distribution.

[0022] Interlayer voids mainly occur at the ends and edges of the track slab. In the transverse distribution of the track slab, the positions near the edges are areas prone to voids, while the positions near the middle of the slab are areas less prone to voids. However, how to simulate the probability distribution of the transverse void area is a key issue in the coupled stochastic vibration analysis of the train-track-bridge system considering random voids. In this embodiment, the CA mortar layer area corresponding to the interlayer void track slab under study is discretized longitudinally, as Figure 2 shown. Assume that there are longitudinally discrete void units on both the left and right sides of a track slab, with void units on each of the left and right sides, and satisfying: ; In the formula, is the longitudinal length of each void unit (assuming that the longitudinal lengths of the void units are all equal), is the length of a track slab.

[0023] The void units within a preset distance near both ends of the track slab are classified as end void units, and the remaining void units are edge void units; assume that the transverse void lengths of each void unit follow a normal distribution. The random vector of the transverse void lengths of the end void units can be expressed as: ; In the formula, represents the transverse void length of the i-th end void unit, represents the number of end void units; The random vector of the transverse void lengths of the edge void units can be expressed as: ; In the formula, represents the transverse void length of the j-th edge void unit, represents the number of edge void units, .

[0024] Generally speaking, the transverse void lengths of the end void units are larger than those of the edge void units. Therefore, different normal distributions are adopted for the end void units and the edge void units. It is set that the transverse void lengths of the end void units all follow the normal distribution , and the transverse void lengths of the edge void units all follow the normal distribution , where, are the mean and standard deviation of the lateral void length in the random vector of the lateral void length at the slab end, respectively, are the mean and standard deviation of the lateral void length in the random vector of the lateral void length at the slab edge, respectively, and satisfy .

[0025] Suppose , , and are the dimensions of the random parameter vector, the random vector of the lateral void length at the slab end, the random vector of the lateral void length at the slab edge, and the random parameter vector of the track irregularity, respectively, ; among which, the first -dimensional random vector follows a normal distribution, and the last -dimensional random parameter follows a uniform distribution.

[0026] First, the good lattice point method is used to select a representative point set from the s-dimensional hypercube vector space as the first random parameter point set , which is expressed as follows: ; In the formula, is the q-th representative point, is the number of the selected representative point set, that is, the number of the subsequent calculated deterministic samples.

[0027] Because the first random parameter point set selected by the good lattice point method is a uniformly distributed point set, the Rosenblatt transformation is still required to perform the Rosenblatt transformation on the first -dimensional random parameter vector point set corresponding to the random vector of the lateral void length at the slab end and the random vector of the lateral void length at the slab edge, so that this -dimensional random parameter vector point set follows a normal distribution to obtain the second random parameter point set; Among them, after the first -dimensional random parameter vector point set undergoes the Rosenblatt transformation, the random parameter point set that follows a normal distribution can be expressed as: ; In the formula, represents the random parameter point set of the lateral void length at the slab end, represents the random parameter point set of the lateral void length at the slab edge. is the Rosenblatt transformation operator (inverse transformation function); therefore, the second random parameter point set can be expressed as follows: ; In the formula, represents the second random parameter point set.

[0028] Combined with the normal distributions that the lateral void lengths in the random vectors of the plate end lateral void length and the plate edge lateral void length both follow, a linear affine transformation is performed on the second set of random parameter points, and finally a set of random parameter points that satisfies the probability space distribution of the train-track-bridge system is obtained.

[0029] According to the normal distribution that the lateral void length in the random vector of the plate end lateral void length follows as set previously and the normal distribution that the lateral void length in the random vector of the plate edge lateral void length follows , then there is: ; Thus, a representative sample point set of the random vector of the plate end lateral void length and a representative sample point set of the random vector of the plate edge lateral void length can be obtained.

[0030] Since the void area and the non-void area of the CA mortar layer are two working conditions, the stiffness of the non-void area of the CA mortar layer is the linear stiffness, and for the void area of the CA mortar layer, the nonlinear contact effect when the train passes needs to be considered, and its stiffness is the nonlinear stiffness. As shown in (a) and (b) of Figure 3 , after local voids occur in the CA mortar layer 2 between the track slab 1 and the base slab 3, it shows a separated state when there is no train running, and rigid contact occurs between the track slab 1 and the base slab 3 when the train passes. Therefore, the nonlinear contact effect in the void area needs to be considered in the system modeling.

[0031] Therefore, when substituting the set of random parameter points into the spatial random vibration analysis model of the train-track-bridge system for simulation, the stiffness of each grid element is calculated according to the random parameter vector of the interlayer void damage in the set of random parameter points and the area of the grid elements after the CA mortar layer is discretized. If a certain grid element is a non-void grid element, the stiffness of this grid element is calculated according to its area and the set stress level and cyclic loading ratio; if a certain grid element is a void grid element, the stiffness of this grid element satisfies: when the relative vertical displacement of the contact point of the void grid element is not greater than the threshold value, its stiffness is 0, and when is greater than the threshold value, its stiffness is the preset value; then the stiffness of each grid element of the CA mortar layer is substituted into the spatial random vibration analysis model of the train-track-bridge system.

[0032] For the convenience of calculation, when discretizing the CA mortar layer into grid elements, the grid length corresponding to the longitudinal division of the track slab is equal to the longitudinal length of the aforementioned void element , and moreover, the lateral length of the void element is an integer multiple of the grid length of the transverse division of the track slab, so as to ensure that each discretized grid element is either void or non-void.

[0033] For non - void grid cells, their stiffness is calculated by the following method: Set the stress level of the grid cell and the cyclic loading ratio as fatigue damage parameters, and the damage variable of the CA mortar layer under n - times loading can be written as: ; In the formula, , and are a series of parameters related to the damage state of the CA mortar layer; is the number of loadings, is the fatigue life of the CA mortar layer; while the dynamic elastic modulus under the -th loading ; ; In the formula, is the initial dynamic elastic modulus; and are the total fatigue strains under 1 - time loading and -th loading respectively, is the residual strain under 1 - time loading; The total fatigue strain under 1 - time loading can be expressed as: ; The total fatigue strain under N - times (at fatigue failure) loading can be expressed as: ; The total fatigue strain under -th loading can be expressed as: ; The fatigue life of the CA mortar layer satisfies: ; In the formula, is the stress level, that is, the ratio of the maximum compressive stress to the compressive strength; The residual strain of the -th fatigue loading is: .

[0034] Set the stress level of the set grid cell Substituting into the above formula, the fatigue dynamic elastic modulus after loading times can be obtained. Considering mainly the vertical influence of the plate element, the stiffness of the CA mortar layer grid element can be expressed as: ; In the formula, is the equivalent linear spring stiffness of the grid element with coordinates ; is the effective bonding area (discrete grid element area) of the CA mortar layer grid element; is the thickness of the CA mortar layer.

[0035] For the delaminated grid element, its stiffness is expressed as follows: ; Among them, represents the relative vertical displacement of the contact point, represents the contact stiffness of the contact point. When the relative vertical displacement of the contact point is less than or equal to , the upper and lower contact points are in a separated state, and the contact point stiffness is 0. When is greater than , the upper and lower contact points are in a contact state. For the convenience of calculation, the contact stiffness is set as a fixed value .

[0036] The track irregularities in this embodiment include four types of track irregularities: direction irregularity, gauge irregularity, vertical irregularity, and level irregularity. The spatial frequencies and phase angles of the power spectra of various track irregularities are used as independent track irregularity random parameters. The power spectral density functions of various track irregularities are evenly divided into P segments according to the spatial frequency, and both the spatial frequency and the phase angle, the two track irregularity random parameters, are segmented into Q-dimensional random vectors; the track irregularity random parameter vectors corresponding to the four types of track irregularities are combined to form a 4×2×P×Q-dimensional track irregularity random parameter vector. Each component in the track irregularity random parameter point set can be expressed as: ; ; In the formula, respectively represent the random parameters of vertical irregularity, direction irregularity, level irregularity, and gauge irregularity; and respectively represent the spatial frequency and the phase angle.

[0037] The random spatial frequency and phase angle can be respectively expressed as and , where represent unevenness in height, unevenness in direction, unevenness in level, and gauge unevenness respectively, , . Assume the random spatial frequency is a point within, denoted as , , and satisfies , where is the upper cut-off frequency, is the lower cut-off frequency.

[0038] When performing a linear affine transformation on the second set of random parameter points , where the subsequent the linear affine transformation of the random parameter can be expressed as follows: ; In the formula, is a vector of dimension 4×2×P and can be expressed as: , ; equals ; represents in , represents in .

[0039] Using a random harmonic function to simulate random track unevenness, then the amplitude of the random harmonic function can be expressed as: ; In the formula, is the power spectral density function of the track unevenness, is the evenly divided spatial frequency range for each segment; Then the representative samples of the four types of track unevenness can be expressed as: ; In the formula, , , and are the representative samples of unevenness in height, unevenness in direction, unevenness in level, and gauge unevenness respectively, and x represents the time axis (vertical coordinate of the rail); Based on the representative samples of the four types of track unevenness, the sample points of unevenness in height and unevenness in level of the left and right rails can be obtained and expressed as follows: ; ; In the formula, and respectively represent the vertical irregularity and horizontal irregularity sample points of the left rail; and respectively represent the vertical irregularity and horizontal irregularity sample points of the right rail, represents half of the rail gauge.

[0040] According to the above formula, the track irregularity sample values of the left and right rails can be generated. Further, the random track irregularity excitation values, including track irregularity displacement and acceleration, can be calculated. Then, they can be substituted into the spatial random vibration analysis model of the train-track-bridge system for simulation.

[0041] In the spatial random vibration analysis model of the train-track-bridge system, each component of the vehicle body in the vehicle system is simulated by a multi-rigid body model, and the suspension components connecting the rigid bodies are simulated by spring dampers; the rails in the track system are simulated by a three-dimensional Euler beam model, the track slab and the base slab are simulated by a plate-shell model, the rail fasteners are simulated by linear spring dampers, and the CA mortar layer between the track slab and the base slab is simulated by a spring damper considering the interlayer delamination damage; the beam body of the bridge system is simulated by a three-dimensional Euler beam model.

[0042] Among them, the dynamic equation of the train system can be expressed as: ; In the formula, , 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 track irregularity random parameters.

[0043] As the basic structure, the dynamic equation of the track-bridge system is: ; In the formula, is the mass matrix of the track-bridge system; and respectively consider the damping matrix and stiffness matrix of the track-bridge system affected by the interlayer delamination damage random parameters and (the transverse delamination length at the plate end and the transverse delamination length at the plate edge). The damping matrix is closely related to the stiffness matrix and the mass matrix. When the stiffness matrix is affected by the interlayer delamination damage random parameters, the damping matrix will also be affected accordingly. The calculation of the damping matrix is prior art and will not be elaborated here; is the random load matrix of the track-bridge system, which includes the axle load of the vehicle and the wheel-rail interaction force caused by random track irregularities. Since varies with the contact state of the void region, the train-track-bridge system with voids is a high-dimensional nonlinear dynamic system and an iterative method needs to be used to solve it.

[0044] In this embodiment, the Newmark-β method and the Newton-Raphson iteration method are first used jointly to solve the system vibration response values corresponding to each random sample point in the random parameter point set; then, based on the system vibration response values corresponding to each random sample point, the probability density evolution method is used to solve the time-dependent probability density distribution of the system vibration response under interlayer void damage.

[0045] The principle of the joint solution of the Newmark-β method and the Newton-Raphson iteration method is described below, and the specific process includes: The overall dynamic equation of the train-track-bridge system of high-speed railways can be expressed as: (1); Among them, is the mass matrix of the system, are respectively the damping matrix and the stiffness matrix of the system considering the influence of random parameters of interlayer void damage, is the random load matrix of the system; , and respectively represent the acceleration, velocity and displacement of the system.

[0046] By combining the last two terms on the left side of Equation (1), Equation (1) can be rewritten as: (2); Among them, represents the operator related to the velocity and displacement at the corresponding moment.

[0047] By transposing Equation (2), we can get: (3); Among them, is the residual force vector. For a multi-degree-of-freedom system, the basic expressions of the final velocity and displacement at each time step of the Newmark-β method are: (4); (5); In the formula, represents the time step, , are all fixed parameters. In this embodiment, Take 0.25, take 0.5; According to the prediction relationships in Equations (4) and (5), we can obtain: (6); (7); In the formula, and and respectively represent the predicted values of displacement, velocity, and acceleration at the (i + 1)-th time step; By setting in Equations (4) and (5), we can obtain the prediction formula: (8); (9); Substituting Equations (6) and (7) into Equation (3), the residual force equation can be expressed only through as: (10); At this time, the nonlinear Equation (10) can be solved using a linearization approach. According to the basic principle of the Newton - Raphson iteration method, the nonlinear Equation (10) is expressed linearly as: (11); where the Jacobian matrix (also called the iteration matrix) is: (12); The above equation can be expanded as: (13); where: is the influence matrix of internal force with respect to displacement, i.e., the tangent stiffness matrix ; is the influence matrix of internal force with respect to velocity, i.e., the tangent damping matrix ; is the dependence of the external load on the displacement of the system. For the model established in the present invention, this value is 0.

[0048] Noticing Equations (6) and (7), it is relatively easy to deduce: (14); where is the identity matrix.

[0049] Thus, the iteration matrix can finally be expressed as: (15); The non-linear equation (10) can be solved by the Newton-Raphson iterative method. At the th time step and the th iteration result is corrected to .

[0050] The correction of the displacement vector calculated by the linear equation satisfies: (16); According to Eqs. (6) and (7), the corrections of the velocity and acceleration vectors can be obtained: ; where and represent the correction of the velocity vector and the correction of the acceleration vector, respectively.

[0051] The probability density evolution method is a prior art, and its specific principle will not be elaborated here.

[0052] Of course, there are many factors affecting the random vibration response of the train-track-bridge system. In addition to the above-mentioned random parameters of the interlayer delamination damage and the random parameters of the track irregularity, it also includes the random parameters of the vehicle structure itself and the mechanical parameters of the track-bridge structure itself, such as the variability of the elastic modulus, damping ratio, mass density of the reinforced concrete structure and the mass of the car body, the stiffness and damping of the car body connectors, etc. 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 selected to be considered. 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 has been relatively mature, and the introduction of the random parameters of the vehicle structure itself and the mechanical parameters of the track-bridge structure itself belongs to the prior art, and the present invention will not elaborate here.

[0053] To verify the accuracy of the established system random vibration analysis model with random interlayer delamination damage, a three-span high-speed railway ballastless track-simply supported beam bridge model is established in this embodiment. Based on the combination of the probability density evolution method and the Newmark-β method and the Newton-Raphson iterative method to solve the numerical integration method, 400 groups of random vehicle-track-bridge response samples are calculated.

[0054] In the case of one delamination condition, the random response information of the lateral acceleration of the car body center of gravity is as Figure 4 shown, Figure 4In (a), it shows the three-dimensional probability density evolution time history 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 car body concentrates in a relatively small range. This indicates that after the train gets on the bridge, the track smoothness of the bridge will be better, and the lateral acceleration of the car body will also be relatively small. Figure 4 The probability density contour lines shown in (b) are wide at both ends and narrow in the middle, which also verifies this conclusion. Figure 4 In (c) and (d), they are respectively the mean value curve and the standard deviation curve of the lateral vibration acceleration of the car body.

[0055] By using the Monte Carlo method (MCM) to perform 9999 calculations and comparing the results with the Probability Density Evolution Method (PDEM), the maximum deviations of the acceleration mean value and the standard deviation are 1.1% and 0.9% respectively, which proves that the established stochastic model is correct and reliable. This also verifies that when performing spatial stochastic vibration analysis on the train-track-bridge dynamic system with voids, the Probability Density Evolution Method can ensure the high efficiency of the calculation process and the high precision of the calculation results.

[0056] Similarly, the three-dimensional probability density evolution surface, probability density contour lines, and mean value and standard deviation curves of the vertical acceleration of the track slab at the mid-span position are as shown in Figure 5 (a), (b), (c) and (d). From the variation laws of their mean value curves and standard deviation curves, it can be known that the vehicle-track-bridge coupling effect when the train passes through the track-bridge system causes the vertical stochastic dynamic response of the track slab to have severe up and down oscillations. And compared with the deterministic vehicle-track-bridge coupling system dynamic time history analysis which can only output several deterministic time history samples and the stochastic response information of the car body and the structure cannot be shown, the Probability Density Evolution Method can efficiently and accurately describe the time-dependent stochastic vibration characteristics of the system when the train passes through the bridge.

[0057] The embodiment of the present invention also provides an electronic terminal, including: A memory, on which computer programs or instructions are stored; A processor, configured to load and execute the computer programs or instructions to implement the stochastic vibration analysis method of the vehicle-track-bridge system based on interlayer void damage as described above.

[0058] The embodiment of the present invention also provides a computer-readable storage medium, on which computer programs or instructions are stored, and when the stored computer programs or instructions are executed by a processor, the stochastic vibration analysis method of the vehicle-track-bridge system based on interlayer void damage as described above is implemented.

[0059] An embodiment of the present invention also provides a computer program product. A computer program or instruction is stored in the computer program product. When the computer program or instruction is executed by a processor, the random vibration analysis method of the vehicle-rail-bridge system based on the interlayer void damage as described above is implemented.

[0060] It can be understood that the same or similar parts in the above embodiments can be referred to each other. For the content not detailed in some embodiments, reference can be made to the same or similar content in other embodiments.

[0061] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0062] The present application is described with reference to the flowcharts and / or block diagrams of 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 can be implemented by computer program instructions, and the combination of processes and / or blocks in the flowchart and / or block diagram can also be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in one Figure 1 process or multiple processes and / or blocks Figure 1 or multiple blocks.

[0063] These computer program instructions can 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 generate a manufactured article including an instruction device, and the instruction device implements the functions specified in one Figure 1 process or multiple processes and / or blocks Figure 1 or multiple blocks.

[0064] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one Figure 1 process or multiple processes and / or blocks Figure 1 or multiple blocks.

[0065] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A random vibration analysis method for vehicle-track-bridge system based on interlayer delamination damage, characterized in that It includes the following steps: S1: Construct a random parameter vector including the random parameter vector of interlayer debonding damage and the random parameter vector of track irregularity; among them, the random parameter vector of interlayer debonding damage includes the random vector of the transverse debonding length at the plate end and the random vector of the transverse debonding length at the plate edge; S2: Select points for the random parameter vector based on the multi-distribution point selection method to obtain a set of random parameter points; S3: Construct a spatial random vibration analysis model of the train-track-bridge system; S4: Substitute the set of random parameter points into the spatial random vibration analysis model of the train-track-bridge system for simulation, and use the combination of the numerical integration method and the probability density evolution method to solve and obtain the vibration response of the train-track-bridge system under random interlayer debonding damage.

2. The random vibration analysis method of vehicle-rail-bridge system based on interlayer debonding damage according to claim 1, characterized in that The random parameter vector of the interlayer debonding damage is constructed by the following method: The longitudinal discretization is carried out for the CA mortar layer area corresponding to the track slab, and there are void units corresponding to the left and right sides of the track slab respectively; The debonding units within a preset distance near both ends of the track slab are classified as the debonding units at the plate end, and the remaining debonding units are the debonding units at the plate edge; Random vector of transverse debonding length at slab ends Composed of the transverse debonding lengths of all debonding elements at slab ends, expressed as follows: ； In the formula, represents the transverse void length of the i-th slab-end void unit, represents the number of slab-end void units; Random vector of transverse void length at slab edge It is composed of the transverse void lengths of all void units at slab edges and is expressed as follows: ； In the formula, represents the lateral void length of the j-th edge void unit of the slab, represents the number of edge void units of the slab, ; The random vector of the transverse debonding length at the plate end and the random vector of the transverse debonding length at the plate edge are combined to form the random parameter vector of the interlayer debonding damage.

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

4. The random vibration analysis method of vehicle-track-bridge system based on interlayer debonding damage according to claim 1, characterized in that, Step S2 specifically includes: Hypothesis , , and are the dimensions of the random parameter vector, the random vector of the transverse void length at the slab end, the random vector of the transverse void length at the slab edge, and the random parameter vector of the track irregularity, respectively, ; And it is set that the lateral void lengths in the random vectors of the lateral void lengths at the plate ends all follow a normal distribution , and the lateral void lengths in the random vectors of the lateral void lengths at the plate edges all follow a normal distribution ; are the mean and standard deviation of the lateral void lengths in the random vector of the lateral void lengths at the plate ends respectively, are the mean and standard deviation of the lateral void lengths in the random vector of the lateral void lengths at the plate edges respectively, and satisfy ; First, use the good lattice point method to select points for the random parameter vector to obtain the first set of random parameter points; Perform Rosenblatt transformation on the random parameter vector point sets corresponding to the random vectors of the transverse void length at the plate end and the transverse void length at the plate edge in the first random parameter point set, so that the dimensional random parameter vector point set follows a normal distribution to obtain a second random parameter point set; ​ Combined with the normal distribution followed by the transverse debonding length in the random vector of the transverse debonding length at the plate end and the random vector of the transverse debonding length at the plate edge, perform a linear affine transformation on the second set of random parameter points to finally obtain a set of random parameter points that satisfy the probability space distribution of the train-track-bridge system.

5. The random vibration analysis method of vehicle-rail-bridge system based on interlayer delamination damage according to claim 1, characterized in that, In step S3, in the spatial random vibration analysis model of the train-track-bridge system, each component of the car body in the vehicle system is simulated by a multi-rigid body model, and the suspension components connecting the rigid bodies are simulated by spring dampers; the rail in the track system is simulated by a three-dimensional Euler beam model, the track slab and the base slab are simulated by a plate shell model, the rail fasteners are simulated by linear spring dampers, and the CA mortar layer between the track slab and the base slab is simulated by a spring damper considering interlayer debonding damage; the beam body of the bridge system is simulated by a three-dimensional Euler beam model.

6. The random vibration analysis method of vehicle-track-bridge system based on interlayer debonding damage according to claim 1, characterized in that In step S4, when substituting the random parameter point set into the spatial random vibration analysis model of the train-track-bridge system for simulation, the stiffness of each grid element is calculated according to the interlayer void damage random parameter vector in the random parameter point set and the area of the grid element after discretization of the CA mortar layer. If a grid element is a non-void grid element, the stiffness of the grid element is calculated based on its area, the set stress level, and the cyclic loading ratio. If a grid element is a void grid element, the stiffness of the grid element satisfies: when the relative vertical displacement of the contact point of the void grid element is not greater than the threshold value, its stiffness is 0, and when is greater than the threshold value, its stiffness is a preset value; then the stiffness of each grid element of the CA mortar layer is substituted into the spatial random vibration analysis model of the train-track-bridge system; And calculate the track irregularity excitation values of the left and right rails according to the random parameters of the track irregularity in the set of random parameter points, and then substitute them into the spatial random vibration analysis model of the train-track-bridge system.

7. The random vibration analysis method of vehicle-rail-bridge system based on interlayer debonding damage according to claim 1, characterized in that In step S4, the combination of the numerical integration method and the probability density evolution method is used to solve and obtain the vibration response of the train-track-bridge system under random interlayer debonding damage, which specifically includes: The Newmark-β method and the Newton-Raphson iteration method are jointly used to solve for the system vibration response values corresponding to each random sample point in the random parameter point set; Based on the system vibration response values corresponding to each random sample point, the probability density evolution method is used to solve for the time-dependent probability density distribution of the system vibration response under interlayer delamination damage.

8. An electronic terminal, characterized in that, Including: A memory on which computer programs or instructions are stored; A processor for loading and executing the computer programs 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 7.

9. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer programs or instructions stored are executed by the processor, the random vibration analysis method of the vehicle-track-bridge system based on interlayer delamination damage according to any one of claims 1 to 7 is implemented.

10. A computer program product, characterized in that, A computer program or instructions are stored in the computer program product, and when the computer programs or instructions are executed by the processor, the random vibration analysis method of the vehicle-track-bridge system based on interlayer delamination damage according to any one of claims 1 to 7 is implemented.

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