Vehicle-bridge deck pavement-bridge coupled vibration analysis method

Abstract

The application discloses a kind of car-bridge pavement-bridge coupling vibration analysis methods, comprising the following steps: establishing car-bridge pavement-bridge system model, using spring damper to simulate bridge pavement layer;Establish the motion equation of rigid plate-asphalt bridge pavement layer system and export the calculation formula of stiffness coefficient K and damping coefficient C;Dynamic mechanical analysis test is carried out to asphalt mixture, its storage modulus is determined and is expressed by Prony series, the finite element simulation of rigid plate-asphalt bridge pavement layer system is carried out, and stiffness coefficient K and damping coefficient C are obtained, and the motion equation of vehicle and bridge is obtained, and the dynamic response of car-bridge pavement-bridge coupling system is obtained.The application perfects the modeling method of car-bridge coupling system in highway traffic, obtains more accurate tire road contact force and the dynamic response of car-bridge pavement-bridge coupling system, provides basis for accurately analyzing bridge pavement layer damage evolution mechanism, vehicle driving safety when passing bridge, bridge structure health monitoring and the like.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge engineering test, and particularly relates to a vehicle-bridge deck pavement-bridge coupling vibration analysis method. BACKGROUND

[0002] With the rapid development of highway transportation, the proportion of bridges in highways and urban expressways is increasing, and the length and load of heavy vehicles are also increasing. When heavy vehicles pass through the bridge, the coupling dynamic system composed of the vehicle, the bridge deck pavement and the bridge has strong time-varying characteristics. In the current research on the analysis of the vehicle-bridge coupling vibration, the bridge deck pavement layer is usually only considered as self-weight, and the influence of the pavement layer is not considered in the structural dynamic analysis, and only the dynamic interaction between the vehicle and the bridge is analyzed. However, the bridge deck pavement layer is the first part to appear diseases in the bridge structure, and the early damage will deteriorate the smoothness of the bridge deck, causing the vibration of the vehicle and the bridge to intensify, and in turn the intensified dynamic response of the vehicle and the bridge will cause the diseases of the bridge deck pavement layer, thus forming a vicious cycle, which further deteriorates the diseases of the bridge deck pavement layer and seriously affects the safe operation of the vehicle and the bridge. Therefore, it is necessary to establish a more actual vehicle-bridge deck pavement-bridge coupling vibration system. SUMMARY

[0003] The application aims to provide a vehicle-bridge deck pavement-bridge coupling vibration analysis method, and aims to solve the technical problem that the existing vehicle-bridge coupling vibration system in the prior art does not consider the influence of the bridge deck pavement layer and only analyzes the dynamic interaction between the vehicle and the bridge, which is inconsistent with the actual situation.

[0004] To solve the above technical problem, the technical scheme adopted by the application is as follows:

[0005] A vehicle-bridge deck pavement-bridge coupling vibration analysis method, comprising the following steps:

[0006] A, establishing a vehicle-bridge deck pavement-bridge system model, including a vehicle model, a bridge deck pavement layer model and a bridge model, the vehicle model comprising a vehicle body, a suspension, a tire and a spring damper connected between the three, the bridge deck pavement layer model comprising a plurality of spring dampers for simulating the bridge deck pavement layer, the spring dampers being continuously and uniformly distributed on the upper surface of the bridge model to form a vehicle-bridge deck pavement-bridge system model;

[0007] B, calculation of the stiffness coefficient K and the damping coefficient C of the asphalt bridge deck pavement layer: a rigid plate-asphalt bridge deck pavement layer system is constructed by the spring damper and the rigid plate, a motion equation of the rigid plate-asphalt bridge deck pavement layer system is established, and a calculation formula of the stiffness coefficient K and the damping coefficient C representing the stiffness and damping characteristics of the asphalt bridge deck pavement layer is obtained;

[0008] C. Dynamic mechanical analysis test is carried out on the asphalt mixture of the asphalt bridge pavement layer material to determine the storage modulus of the asphalt mixture and express the storage modulus by Prony series;

[0009] D. The Prony series obtained in the test of step C is input into the finite element model of the rigid plate-asphalt bridge pavement layer system to calculate the response of the rigid plate-asphalt bridge pavement layer system, and the response of the system is substituted into the calculation formula of the stiffness coefficient K and the damping coefficient C in step B to obtain the values of the stiffness coefficient and the damping coefficient;

[0010] E. According to the motion equations of the vehicle model and the bridge model and the stiffness coefficient and the damping coefficient of the asphalt bridge pavement layer obtained in step D, the response of the vehicle-bridge pavement-bridge coupling system is calculated.

[0011] Preferably, the motion equations of the vehicle model and the bridge model are established as follows,

[0012] Vehicle motion equation:

[0013]

[0014] wherein,

[0015]

[0016] Q2=0, Q3=0

[0017] y i (i=1, 2, 3) are the generalized displacements of the tire, the suspension and the vehicle body of the vehicle respectively;

[0018] represent the generalized velocities of the tire, the suspension and the vehicle body respectively;

[0019] represent the generalized accelerations of the tire, the suspension and the vehicle body respectively;

[0020] Q i (i=1, 2, 3) represent the generalized forces;

[0021] M i (i=1, 2, 3) represent the masses of the tire, the suspension and the vehicle body respectively;

[0022] K1 and C1 represent the stiffness and the damping of the tire;

[0023] K2 and C2 represent the stiffness and the damping of the suspension;

[0024] A c represents the area of the tire of the vehicle contacting the ground;

[0025] Bridge motion equation:

[0026]

[0027] wherein,

[0028] p and A represent the density and cross-sectional area of the bridge, respectively;

[0029] E and I represent the elastic modulus and cross-sectional moment of inertia of the bridge, respectively;

[0030] y b (x, t) represents the vertical displacement of the bridge;

[0031] b represents the tire contact ground width of the vehicle;

[0032] l represents the length of the bridge;

[0033] v represents the vehicle travel speed;

[0034] x represents the position coordinate of the vehicle on the bridge;

[0035] t represents time;

[0036] H(Δ) represents the Heaviside function;

[0037] F b (t) represents the force acting on the bridge generated by the vehicle and bridge deck pavement movement;

[0038]

[0039] wherein,

[0040] g is the acceleration of gravity;

[0041] K is the stiffness coefficient of the bridge deck pavement;

[0042] C is the damping coefficient of the bridge deck pavement.

[0043] Combined with the vehicle motion equation and the bridge motion equation, the motion equation of the vehicle-bridge deck pavement-bridge coupling system is derived in matrix form by modal superposition method:

[0044]

[0045] wherein,

[0046] d and represent the generalized acceleration vector, the generalized displacement vector and the generalized velocity vector of the vehicle-bridge deck pavement-bridge coupling system, respectively;

[0047] M s , K s and C sThe mass matrix, the stiffness matrix and the damping matrix of the vehicle-bridge pavement-bridge coupling system are respectively expressed as follows:

[0048] F s The generalized load vector is expressed as follows.

[0049] Preferably, in step B, the Lagrange equation is applied to the rigid plate-asphalt pavement layer system to establish the motion equation of the rigid plate-asphalt pavement layer system:

[0050]

[0051] wherein,

[0052] w represents the deflection of the rigid plate, which depends on time only and is irrelevant to coordinates because the rigid plate cannot be deformed;

[0053] v represents the velocity of the rigid plate;

[0054] a represents the acceleration of the rigid plate;

[0055] K and C represent the stiffness coefficient and the damping coefficient of the asphalt pavement layer;

[0056] m represents the concentrated mass of the rigid plate, m represents the mass per unit area of the rigid plate;

[0057] P represents the concentrated exciting force acting on the center of the upper surface of the rigid plate;

[0058] a and b represent the length and the width of the rigid plate respectively;

[0059] It is assumed that the concentrated exciting force P acts on the rigid plate for a short time, and after the P is unloaded, the motion of the rigid plate-asphalt pavement layer system is free damping vibration, and the calculation formulae of the stiffness coefficient K and the damping coefficient C of the asphalt pavement layer are derived as follows:

[0060]

[0061] wherein,

[0062] m represents the concentrated mass of the rigid plate;

[0063] τ d represents the period of the free damping vibration of the rigid plate;

[0064] X i represents the amplitude of the rigid plate;

[0065] X i+n represents the amplitude of the rigid plate after n periods from the X i ; and

[0066] a, b represent the length and width of the rigid plate, respectively;

[0067] n represents the number of cycles.

[0068] Preferably, in step C, the storage modulus of the asphalt pavement layer material asphalt mixture is measured at a reference temperature of 20°C, and the experimental data is fitted with Prony series.

[0069] Preferably, in step D, the relevant parameters in the following formula are input when simulating the finite element model of the rigid plate-asphalt pavement layer system,

[0070] For the shear relaxation kernel function of the asphalt pavement layer material asphalt mixture, it can be expressed by Prony series as follows:

[0071]

[0072] wherein,

[0073] G0represents the instantaneous shear modulus, and its expression is:

[0074]

[0075] When time t is equal to 0, there is,

[0076]

[0077] That is: Then

[0078] wherein,

[0079] G ∞ represents the equilibrium modulus;

[0080] G i represents the shear modulus;

[0081] n G represents the logarithm of Prony series.

[0082] represents the relative modulus;

[0083] represents the relaxation time.

[0084] Preferably, in step D, the finite element model of the rigid plate-asphalt pavement layer system is modeled by solid 185 elements.

[0085] Preferably, in the finite element model of the rigid plate-asphalt bridge deck pavement layer system, two nodes are selected from the top surface of the rigid plate, and the average vertical displacement of the two nodes is used to describe the dynamic response of the rigid plate-asphalt bridge deck pavement layer system.

[0086] Preferably, the bridge model is a simply supported Euler-Bernoulli beam; a 1 / 4 vehicle model is used to move on the simply supported Euler-Bernoulli beam at a constant speed, and the 1 / 4 vehicle model has three degrees of freedom, which are the vertical displacements of the tire, the suspension and the vehicle body, respectively.

[0087] The beneficial effects produced by the above technical solutions are that, compared with the prior art, the spring damper is used to simulate the bridge deck pavement layer in the present application, the asphalt pavement material performance is linked to the equivalent mechanical parameters by using the test and numerical simulation method, the stiffness coefficient and the damping coefficient of the bridge deck pavement layer are obtained by using the dynamic response of the rigid plate-asphalt bridge deck pavement layer system; the dynamic response of the vehicle-bridge deck-pavement-bridge coupling system is calculated through the change law of the vehicle and bridge dynamic response. The present application can perfect the modeling method of the vehicle-bridge coupling system in the highway traffic, obtain more accurate tire-road contact force and dynamic response of the vehicle-bridge deck-pavement-bridge coupling vibration system, and provide reliable basis for accurately analyzing the damage evolution mechanism of the bridge deck pavement layer, the driving safety of the vehicle passing through the bridge, and the health monitoring of the bridge structure. BRIEF DESCRIPTION OF DRAWINGS

[0088] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0089] Figure 1 is a flow chart of a vehicle-bridge deck-pavement-bridge coupling vibration analysis method provided by an embodiment of the present application;

[0090] Figure 2 is a structural schematic diagram of a vehicle-bridge deck-pavement-bridge system model in an embodiment of the present application;

[0091] Figure 3 is a structural schematic diagram of a rigid plate-asphalt bridge deck pavement layer system in an embodiment of the present application;

[0092] Figure 4 is Figure 3 a stress schematic diagram of a rigid plate-asphalt bridge deck pavement layer system in an embodiment of the present application;

[0093] Figure 5 is a rut test specimen schematic diagram after the vehicle wheel tire travels in an embodiment of the present application; Figure 6 is a finite element model of a rigid plate-asphalt bridge deck pavement layer system;

[0094] In the figure: 1-vehicle model, 11-vehicle body, 12-suspension, 13-tire; 2-bridge deck pavement layer model; 3-bridge model; 4-spring damper, 5-rigid plate. Detailed Implementation

[0095] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0096] Currently, scholars both domestically and internationally have conducted extensive research on the mechanical properties, types of defects, and mechanisms of bridge deck pavement. The common research approaches generally fall into two categories: First, using finite element method (FEM) software, a full-bridge model is established for overall calculations. The internal forces and deformations at the nodes of the local model's calculation sections under the load of interest are extracted and applied to the local model. For example, one end of the boundary section of the local model is fixed, and all nodes and mass elements at the other end are connected by rigid arms to form a rigid surface. Finally, force or displacement boundary conditions are applied to the mass elements to analyze the mechanical properties of the bridge deck pavement. However, this approach does not consider the vibration of the vehicle-bridge coupled system and its dynamic effects on the bridge deck pavement. Second, the asphalt pavement layer and bridge deck are treated as a double-layered continuous elastic thin plate, with a point-contact model between the vehicle and the pavement layer. A vehicle-asphalt pavement-bridge coupled dynamic model is established. However, this method typically treats the asphalt pavement layer as a linear elastic material, which differs somewhat from the actual structure. Therefore, establishing an efficient computational model that can consider both the viscoelastic properties of the asphalt pavement layer on the bridge deck and perform coupled vibration analysis of the vehicle-bridge deck pavement-bridge is of great scientific significance and engineering application value.

[0097] This invention provides a method for analyzing vehicle-bridge deck pavement-bridge coupled vibration, comprising the following steps:

[0098] A. Establish a vehicle-bridge deck pavement-bridge system model, such as Figure 2 As shown, the vehicle-bridge pavement-bridge system model includes a vehicle model 1, a bridge pavement layer model 2, and a bridge model 3. The vehicle model 1 includes a body 11, suspension 12, tires 13, and spring dampers 4 connecting the three components. The bridge pavement layer model 2 includes several spring dampers 4 simulating the asphalt mixture pavement material. These spring dampers 4 are continuously and evenly distributed on the upper surface of the bridge model 3. The bridge model is a simply supported Euler-Bernoulli beam. The vehicle model 1 and the bridge pavement layer model 2 are coupled through tire forces and the displacement of the tire-road contact surface (the contact surface between the tire and the pavement layer). The equations of motion for the vehicle model and the bridge model are established as follows.

[0099] Vehicle motion equations:

[0100]

[0101] where,

[0102]

[0103] Q2= 0, Q3= 0

[0104] y i (i = 1, 2, 3) are the generalized displacements of the tire, suspension and body of the vehicle, respectively;

[0105] are the generalized velocities of the tire, suspension and body, respectively;

[0106] are the generalized accelerations of the tire, suspension and body, respectively;

[0107] Q i (i = 1, 2, 3) are the generalized forces;

[0108] M i (i = 1, 2, 3) are the masses of the tire, suspension and body, respectively;

[0109] K1and C1are the stiffness and damping of the tire;

[0110] K2and C2are the stiffness and damping of the suspension;

[0111] A c is the area of the tire of the vehicle in contact with the ground;

[0112] Bridge motion equation:

[0113]

[0114] where,

[0115] p and A are the density and cross-sectional area of the bridge, respectively;

[0116] e and I are the modulus of elasticity and the moment of inertia of the cross-section of the bridge, respectively;

[0117] y b (x, t) is the vertical displacement of the bridge;

[0118] b is the width of the tire of the vehicle in contact with the ground;

[0119] l is the length of the bridge;

[0120] v is the speed of the vehicle;

[0121] x is the position coordinate of the vehicle on the bridge;

[0122] t is time;

[0123] H(Δ) represents the Heaviside function;

[0124] F b (t) represents the force acting on the bridge caused by the movement of the vehicle and the bridge deck pavement layer;

[0125]

[0126] wherein,

[0127] g is the acceleration of gravity;

[0128] K is the stiffness coefficient of the bridge deck pavement layer;

[0129] C is the damping coefficient of the bridge deck pavement layer.

[0130] Combined with the vehicle motion equation and the bridge motion equation, the motion equation of the vehicle-bridge deck pavement-bridge coupling system is derived by modal superposition method in matrix form:

[0131]

[0132] wherein,

[0133] d and respectively represent the generalized acceleration vector, the generalized displacement vector and the generalized velocity vector of the vehicle-bridge deck pavement-bridge coupling system;

[0134] M s , K s and C s respectively represent the mass matrix, the stiffness matrix and the damping matrix of the vehicle-bridge deck pavement-bridge coupling system;

[0135] F s represents the generalized load vector.

[0136] The response of the vehicle-bridge deck pavement-bridge coupling system is calculated by solving the above system control equation, since the stiffness matrix K S and the damping matrix C S of the vehicle-bridge deck pavement-bridge coupling system contain the stiffness coefficient K and the damping coefficient C of the asphalt bridge deck pavement layer, it is necessary to further establish the rigid plate-asphalt bridge deck pavement layer system to determine K and C.

[0137] B, the rigid plate-asphalt bridge deck pavement layer system is composed of the spring damper 4 and the rigid plate 5, as shown in Figure 3 , the stress of the rigid plate-asphalt bridge deck pavement layer system is shown in Figure 4 , the motion equation of the rigid plate-asphalt bridge deck pavement layer system is established, and the calculation formula of the stiffness coefficient K and the damping coefficient C representing the stiffness and damping characteristics of the asphalt bridge deck pavement layer is obtained through formula derivation.

[0138] The Lagrange equation is applied to the rigid plate-asphalt bridge deck pavement system to establish the motion equation of the rigid plate-asphalt bridge deck pavement system:

[0139]

[0140] wherein,

[0141] w represents the deflection of the rigid plate, which only depends on time and is irrelevant to coordinates because the rigid plate cannot be deformed;

[0142] represents the velocity of the rigid plate;

[0143] represents the acceleration of the rigid plate;

[0144] K and C represent the stiffness coefficient and the damping coefficient of the asphalt pavement;

[0145] m represents the concentrated mass of the rigid plate, represents the mass per unit area of the rigid plate;

[0146] P represents the concentrated exciting force acting on the center of the upper surface of the rigid plate;

[0147] a and b represent the length and the width of the rigid plate, respectively;

[0148] It is assumed that the concentrated exciting force P acts on the rigid plate for a short time, and after the P is unloaded, the motion of the rigid plate-asphalt bridge deck pavement system is free damping vibration. The calculation formulae of the stiffness coefficient K and the damping coefficient C are further derived as follows:

[0149]

[0150] wherein,

[0151] m represents the concentrated mass of the rigid plate;

[0152] τ d represents the period of the free damping vibration of the rigid plate;

[0153] X i represents the amplitude of the rigid plate;

[0154] X i+n represents the amplitude of the rigid plate after n periods from the X i ;

[0155] a and b represent the length and the width of the rigid plate, respectively;

[0156] n represents the number of periods.

[0157] C. Dynamic mechanical analysis (DMA) test is conducted on the rigid plate-asphalt bridge deck pavement system, which can measure the mechanical properties of viscoelastic materials in relation to time, temperature or frequency; the storage modulus of the asphalt mixture of the asphalt pavement material is determined and expressed by Prony series.

[0158] D. The Prony series obtained in the test of step C is input into the finite element model of the rigid plate-asphalt bridge deck pavement system, and the response of the system is calculated. The response of the system is substituted into the calculation formula (9) of the stiffness coefficient K and the damping coefficient C of the asphalt bridge deck pavement to obtain the values of the stiffness coefficient and the damping coefficient.

[0159] E. According to the equations of motion of the vehicle model and the bridge model, and the stiffness coefficient and the damping coefficient of the asphalt bridge deck pavement obtained in step D, the response of the vehicle-bridge deck-pavement-bridge coupling system is calculated. When the finite element model of the rigid plate-asphalt bridge deck pavement system is simulated by using solid 185 elements, the upper layer is the rigid plate, the lower layer is the asphalt bridge deck pavement, the UY degree of freedom of the bottom surface and the UZ, UX degrees of freedom of the side surface are constrained, and the viscoelasticity of the asphalt mixture of the asphalt bridge deck pavement material is defined by the TB command family in the ANSYS software. In the finite element model of the rigid plate-asphalt bridge deck pavement system, two nodes are selected from the top surface of the rigid plate, and the average vertical displacement of the two nodes is used to describe the dynamic response of the rigid plate-asphalt pavement system. According to the calculation formula (9) of the stiffness coefficient K and the damping coefficient C in step B, the stiffness coefficient and the damping coefficient of the asphalt pavement are calculated.

[0160] When the finite element model of the rigid plate-asphalt bridge deck pavement system is simulated by using ANSYS software, the related parameters in the following formula are input to characterize the viscoelastic properties of the asphalt bridge deck pavement. For the shear relaxation kernel function, it can be expressed by Prony series as follows:

[0161]

[0162] wherein,

[0163] G0 represents the instantaneous shear modulus, and its expression is:

[0164]

[0165] When the time t is equal to 0, it has,

[0166]

[0167] That is: Then

[0168] wherein,

[0169] G∞ represents the equilibrium modulus;

[0170] G i represents the shear modulus;

[0171] n G represents the logarithm of Prony series.

[0172] represents the relative modulus;

[0173] represents the relaxation time.

[0174] In Figure 2 In the embodiment shown, the vehicle model 1 adopts a 1 / 4 vehicle model moving on a simply supported Euler-Bernoulli beam at a constant speed, and the bridge deck pavement model 2 is modeled as a continuous and uniformly distributed spring damper with spring constant and damping coefficient. Without considering the damping characteristics of the bridge, the cross-section type of the bridge model 3 is equal cross-section or variable cross-section; the bridge model 3 can also be extended from a simply supported beam to a continuous beam and other complex highway bridges which can be simplified as equivalent simply supported beams and continuous beams.

[0175] The three degrees of freedom of the 1 / 4 vehicle model are the vertical displacements of the tire 13, the suspension 12 and the vehicle body 11 respectively, and the contact between the tire 13 and the bridge deck pavement is modeled as a mass block with a width of b. The tire is in contact with the bridge deck pavement at all times, and the spring damper of the bridge deck pavement is only compressed within the contact width. Of course, the vehicle model can be extended to a six-degree-of-freedom model and a vehicle platoon model, etc.

[0176] In the rigid plate-asphalt bridge deck pavement system, the bridge deck pavement model 2 is an asphalt bridge deck pavement which is uniformly distributed under the rigid plate, with one end fixed to the ground and the other end connected to the rigid plate. The length, width and thickness of the rigid plate are denoted as a, b and h respectively. The length and width of the asphalt bridge deck pavement are the same as those of the rigid plate.

[0177] In one specific embodiment of the present application, the DMA test device is used in step C to measure the storage modulus of the asphalt bridge deck pavement material asphalt mixture at a reference temperature of 20°C, and the experimental data is fitted with Prony series. Table 1 is a table of material parameters of the asphalt mixture used in this embodiment, and Table 2 is a table of parameters of Prony series used in this embodiment.

[0178] Table 1 Material parameters of asphalt mixture

[0179] Transient modulus E0 (MPa) Poisson's ratio μ Density p a (kg / m 3 )]]> 10346.8778 0.25 2470

[0180] Table 2 Parameters of Prony series

[0181]

[0182] In one embodiment of the present application, the finite element model of the rigid plate- asphalt pavement layer system in step D is modeled by using SOLID 185 element, as shown in FIG. 2. SOLID 185 is a 3D 8-node solid element for modeling 3D solid structures. The element is defined by 8 nodes, each with 3 degrees of freedom, i.e. translational displacement along the x, y and z directions of the nodal coordinate system. The element has the features of hyperelastic, viscoelastic, viscoplastic and automatic selection of element technology, and can simulate the elastic-plastic behavior of almost incompressible materials and the hyperelastic behavior of fully incompressible materials by using a hybrid formulation. The model contains 1183 nodes and 864 elements. Figure 6 A rut specimen composed of asphalt mixture is used to represent the asphalt pavement layer (a schematic view of the wheel rut specimen is shown in FIG. 3), which has a size of 30 x 30 x 5 cm. The rigid plate has a size of 30 x 30 x 10 cm. Table 3 shows the material parameters of the rigid plate used in this embodiment.

[0183] Figure 5 Table 3 Material parameters of the rigid plate

[0184] Table 3 Material parameters of the rigid plate

[0185] Modulus of elasticity (MPa) Possion s ratio Density (kg / m 3 )]]> 3 x 10 7 ]] 0.2 2500

[0186] The loading process is from 0.1 s to 0.11 s. After 0.11 s, the rigid plate- asphalt pavement layer system is free to vibrate. Since the value of the excitation force is small, the rigid plate model is considered to be a sufficiently rigid plate. In the above finite element model, two nodes A and B (as shown in FIG. 4) with coordinates (0.15, 0.1, 0.2) and (0.15, 0.1, 0.1) are selected from the top surface of the rigid plate, and the average vertical displacement of the two nodes is used to describe the dynamic response of the rigid plate- asphalt pavement layer system. The parameters, vibration period and amplitude of the system are substituted into the calculation formula (9) to calculate the stiffness coefficient K and the damping coefficient C of the asphalt pavement layer, and then the dynamic response of the vehicle-pavement layer-bridge coupling system is calculated. Figure 6

[0187] ​​In summary, the present application uses test and numerical simulation methods to link the material properties of the asphalt bridge deck pavement layer to equivalent mechanical parameters; by changing the vehicle speed, bridge span, stiffness coefficient of the bridge deck pavement layer, damping coefficient and tire contact width, the change law of the vehicle, bridge deck pavement and bridge dynamic response is analyzed; by increasing the degrees of freedom of the vehicle model, a three-degree-of-freedom, six-degree-of-freedom vehicle model and a vehicle fleet model are established, and the dynamic response of the system is calculated. The present application can improve the modeling method of the vehicle-bridge coupling system in highway traffic, obtain more accurate tire-road contact force and dynamic response of the vehicle-bridge deck pavement-bridge coupling vibration system, and provide a reliable basis for accurately analyzing the damage evolution mechanism of the bridge deck pavement layer, the driving safety of the vehicle passing through the bridge, and the health monitoring of the bridge structure.

[0188] In the above description, many specific details are set forth in order to provide a thorough understanding of the present application, but the present application can also be practiced without other different ways from those described herein, and those skilled in the art can make similar extensions without departing from the concept of the present application, therefore the present application is not limited by the specific embodiments disclosed above.

Claims

1. A vehicle-bridge deck pavement-bridge coupled vibration analysis method, characterized by, The method comprises the following steps: A. Establishing a vehicle-pavement-bridge system model, including a vehicle model, a pavement layer model, and a bridge model, wherein the vehicle model comprises a vehicle body, a suspension, a tire, and a spring damper connected between the three, the pavement layer model comprises a plurality of spring dampers for simulating an asphalt pavement layer, and the spring dampers are uniformly distributed on the upper surface of the bridge model to form the vehicle-pavement-bridge system model; The motion equations of the vehicle model and the bridge model are as follows, Vehicle motion equation: （1） （2） （3） wherein, ， ， ； are respectively the generalized displacements of the tire, suspension and body of the vehicle; Vx, Vy, Vz respectively denote the generalized velocities of the tire, suspension and body; respectively denote the generalized accelerations of the tire, suspension and body; represents a generalized force; respectively denote the mass of the tire, suspension and body; and represent the stiffness and damping of the tire; and denote the stiffness and damping of the suspension; represents the area of the vehicle tire in contact with the ground; Bridge motion equation: （4） wherein, and and respectively denote the density and cross-sectional area of the bridge; and E and I represent the elastic modulus and the cross-sectional moment of inertia of the bridge, respectively; represents the vertical displacement of the bridge; b represents the width of the tire of the vehicle in contact with the ground; denotes the length of the bridge; denotes the vehicle travel speed; representing the position coordinates of the vehicle on the bridge; representing time; denotes the Heaviside function; represent the forces acting on the bridge resulting from the motion of the vehicle and the bridge deck pavement; In combination with the vehicle motion equation and the bridge motion equation, the motion equation of the vehicle-pavement-bridge coupling system is derived by using the modal superposition method in the form of a matrix: （7） wherein, , and represent the generalized acceleration vector, the generalized displacement vector and the generalized velocity vector of the vehicle-bridge pavement-bridge coupled system, respectively; , and denote the mass matrix, the stiffness matrix and the damping matrix of the vehicle- deck pavement-bridge coupled system, respectively; represents the generalized load vector; B. Calculation of the stiffness coefficient K and the damping coefficient C of the asphalt pavement layer: a rigid plate-asphalt pavement layer system is constructed by using spring dampers and rigid plates, the motion equation of the rigid plate-asphalt pavement layer system is established, and the calculation formula of the stiffness coefficient K and the damping coefficient C representing the stiffness and damping characteristics of the asphalt pavement layer is obtained; C. Dynamic thermal mechanical analysis test is performed on the asphalt mixture of the asphalt pavement layer material to determine the storage modulus of the asphalt mixture and express the storage modulus by using Prony series; D. The Prony series obtained in the test of step C is input into the finite element model of the rigid plate-asphalt pavement layer system, the response of the rigid plate-asphalt pavement layer system is calculated, the response of the system is substituted into the calculation formula of the stiffness coefficient K and the damping coefficient C in step B, and the values of the stiffness coefficient and the damping coefficient are obtained; E. According to the motion equations of the vehicle model and the bridge model and the stiffness coefficient and the damping coefficient of the asphalt pavement layer obtained in step D, the response of the vehicle-pavement-bridge coupling system is calculated.

2. The vehicle-pavement-bridge coupling vibration analysis method according to claim 1, wherein, （5） （6） wherein, g is the gravitational acceleration; K is the stiffness coefficient of the pavement layer; C is the damping coefficient of the pavement layer.

3. The car-bridge deck-pavement-bridge coupled vibration analysis method according to claim 2, characterized by, In step B, the Lagrange equation is applied to the rigid plate-asphalt pavement layer system, the motion equation of the rigid plate-asphalt pavement layer system is established, and the calculation formula of the stiffness coefficient K and the damping coefficient C of the asphalt pavement layer is derived: （9） wherein, represents the lumped mass of the rigid plate; denotes the period of the free damped vibration of the rigid plate; represents the amplitude of the rigid plate; represents the amplitude of the rigid plate after n cycles from start a and b represent the length and the width of the rigid plate, respectively; n represents the number of cycles.

4. The car-bridge deck pavement-bridge coupled vibration analysis method according to claim 1, characterized by, In step C, the storage modulus of the asphalt mixture of the asphalt pavement layer material is measured at a reference temperature of 20 ℃, and the experimental data are fitted by using Prony series.

5. The car-bridge pavement-bridge coupled vibration analysis method according to claim 4, characterized by, In step D, when simulating by using the finite element model of the rigid plate-asphalt pavement layer system, the related parameters in the following formula are input, and the shear relaxation kernel function representing the asphalt mixture of the asphalt pavement layer material is expressed by using Prony series as follows: （10） wherein, represents the instantaneous shear modulus, whose expression is: （11） when the time t is equal to 0, （12） That is, Then ; wherein, represents the equilibrium modulus; G represents the shear modulus; logarithm of the Prony series; represents the relative modulus; represents the relaxation time.

6. The car- deck-paving-bridge coupled vibration analysis method according to claim 1, characterized by, In step D, the finite element model of the rigid plate-asphalt pavement layer system is modeled by using solid 185 elements.

7. The car-bridge pavement-bridge coupled vibration analysis method according to claim 6, characterized by, In the finite element model of rigid plate-asphalt bridge deck pavement system, two nodes are selected from the top surface of the rigid plate, and the average vertical displacement of the two nodes is used to describe the dynamic response of the rigid plate-asphalt bridge deck pavement system.

8. The car-bridge deck pavement-bridge coupled vibration analysis method according to any one of claims 1 to 7, characterized by: The bridge model is a simply supported Euler-Bernoulli beam; a 1 / 4 vehicle model moves on the simply supported Euler-Bernoulli beam at a constant speed, and the 1 / 4 vehicle model has three degrees of freedom, which are the vertical displacements of the tire, suspension and vehicle body, respectively.

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