Evaluation method for cornering performance of large-span railway suspension bridge

Abstract

The application discloses a kind of large-span railway suspension bridge beam end corner influence driving performance evaluation method, comprising: establishing the three-dimensional finite element model of large-span railway suspension bridge, and coupling suspension bridge beam end, expansion device and track, form suspension bridge beam end-expansion device-track coupling vibration model;Establish the vehicle model of the vehicle operated by large-span railway suspension bridge, with beam end corner or track irregularity as external excitation, form suspension bridge beam end-expansion device-track-train coupling vibration analysis system;Output the dynamic response index of operating vehicle;The dynamic response index of operating vehicle under different beam end corner conditions is calculated, according to the design load of suspension bridge, the amplitude of suspension bridge beam end corner is calculated, to assess whether the beam end corner of suspension bridge meets the requirements. The dynamic response of operating vehicle can be quickly obtained, and the mapping relationship between beam end corner deformation and vehicle dynamic response index is established, so that the rationality of beam end corner can be more accurately evaluated according to vehicle evaluation index.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of railway bridge driving analysis, in particular to a method for evaluating the influence of large-span railway suspension bridge end corner on driving performance. BACKGROUND

[0002] With the progress of bridge construction technology, large-span bridges are continuously adopted in railway lines. The stiffness of large-span bridges is small, and under the action of wind and temperature loads, the bridge will have large deflection and deformation. In particular, the corner displacement at the beam end of the road-bridge transition section has a great threat to the stability and safety of train operation. For small and medium span bridges, the Railway Bridge and Culvert Design Specification stipulates the limit value of the beam end corner. However, for the large-span railway bridge end corner, the existing research takes the damage uplift force of the track fastener as the index limit, but in practical engineering, the stability of train operation is related to the comfort of passengers, and in severe cases, it may endanger the safety of train operation and passenger life. Based on this, it is particularly important to propose a new method for evaluating the influence of large-span railway suspension bridge end corner on driving performance. SUMMARY

[0003] In view of the above shortcomings of the prior art, the present application provides a method for evaluating the influence of large-span railway suspension bridge end corner on driving performance. A large-span suspension bridge end-expansion device-track-train coupled vibration analysis system is established, and the dynamic response of the vehicle is taken as the evaluation index to realize the rationality evaluation of the beam end corner.

[0004] To achieve the above-mentioned application purposes, the technical solutions adopted by the present application are as follows:

[0005] A method for evaluating the influence of large-span railway suspension bridge end corner on driving performance is provided, which comprises the following steps:

[0006] S1: A three-dimensional finite element model of a large-span railway suspension bridge is established, and the suspension bridge beam end, expansion device and track are coupled to obtain a suspension bridge beam end-expansion device-track coupled vibration model. The mass matrix, stiffness matrix and damping matrix of the suspension bridge beam end-expansion device-track coupled vibration model are established;

[0007] S2: A vehicle model of the vehicle operated on the large-span railway suspension bridge is established, and the mass matrix, stiffness matrix and damping matrix of the vehicle model are established. The beam end corner or track irregularity is taken as an external excitation to form a suspension bridge beam end-expansion device-track-train coupled vibration analysis system;

[0008] S3: According to the suspension bridge end-expansion device-track-train coupled vibration analysis system, the position of the operating vehicle, the displacement of the suspension bridge end-expansion device-track, and the time step are initialized; the numerical integration method is used to solve the motion dynamics equation of the operating vehicle and the dynamics equation of the suspension bridge end-expansion device-track, until the convergence condition is met, and the dynamic response index of the operating vehicle is output;

[0009] S4: Calculate the dynamic response index of the operating vehicle under different beam end rotation conditions, and obtain the mapping relationship between the dynamic response index and the beam end rotation at different vehicle speeds; according to the design load of the suspension bridge, the beam end rotation amplitude of the suspension bridge is calculated, and whether the beam end rotation of the suspension bridge meets the requirements is evaluated.

[0010] Further, step S1 comprises:

[0011] S11: Obtain the geometric characteristics, material characteristics and boundary characteristics of the long-span railway suspension bridge, equivalent the bridge deck of the long-span railway suspension bridge to the main truss structure, form a truss structure without bridge deck, and establish a three-dimensional finite element model of the long-span railway suspension bridge;

[0012] S12: Based on the three-dimensional finite element model of the long-span railway suspension bridge, a suspension bridge end-expansion device-track coupled vibration model is established, and a mass matrix, a stiffness matrix and a damping matrix of the suspension bridge end-expansion device-track coupled vibration model are formed.

[0013] Further, step S11 comprises:

[0014] S111: Obtain the geometric characteristics, material characteristics and boundary characteristics of the long-span railway suspension bridge, and establish a full-bridge model of the long-span railway suspension bridge;

[0015] S112: Simulate the main truss structure and the tower, suspender and cable structure, and the bridge deck of the long-span railway suspension bridge, and integrate the main truss structure and the tower, suspender and cable structure, and the bridge deck into a three-dimensional model by using node sharing or degree of freedom coupling;

[0016] S113: Calculate the frequency and mode shape of the long-span railway suspension bridge;

[0017] S114: Remove the bridge deck element in the three-dimensional model, and disperse the bridge deck element into a plurality of concentrated mass points, distribute the bridge deck mass to the main truss according to the area corresponding to the mass points, and adjust the stiffness parameters of the main truss structure, so that the frequency and mode shape of the three-dimensional model without the bridge deck element are consistent with the frequency and mode shape calculated in step S113;

[0018] S115: Output the established three-dimensional finite element model of the long-span railway suspension bridge.

[0019] Further, step S12 comprises:

[0020] S121: Extracting several segments near the beam end from the three-dimensional finite element model of the long-span railway suspension bridge, and simulating the constraints at the node truncation place with spring elements and determining the stiffness of the spring at the node truncation place with unit load to construct the beam end model; and making the beam end model have the same displacement and curvature as the three-dimensional finite element model at the same position;

[0021] The calibration method of the stiffness of the spring at the node truncation place is as follows:

[0022] S1211: Applying force or torque at the node truncation place;

[0023] S1212: Extracting the response values of the local model near the beam end in the same displacement or angle direction as the three-dimensional finite element model;

[0024] S1213: Adjusting the stiffness of the spring at the node truncation place to make the displacement and curvature of the local model at the truncation position consistent with those of the three-dimensional finite element model;

[0025] S122: Adding roadbed segments before and after the beam end model to simulate the fixity of the roadbed by fixed constraints;

[0026] S123: Constructing a three-layer track model composed of steel rails, sleepers and ballast;

[0027] S124: Based on the three-layer track model, establishing a beam end expansion device between the roadbed and the bridge:

[0028] S125: Assembling the suspension bridge beam end-expansion device-track coupling vibration model by the beam end model, the beam end expansion device and the three-layer track model, and assembling the mass matrix, the stiffness matrix and the damping matrix of the suspension bridge beam end-expansion device-track coupling vibration model; specifically including:

[0029] S1251: Inputting the command for modal solution in the command input area of the ANSYS software, and then inputting the command stream for extracting the mass and stiffness matrix, and exporting the TXT format file;

[0030] S1252: Analyzing the TXT format file by using MATLAB, and converting the contents in the TXT format file into a sparse matrix to form the mass and stiffness matrix;

[0031] S1253: Using the mass and stiffness matrix to construct the damping matrix ;

[0032] ;

[0033] wherein, , are the overall mass and stiffness matrixes of the beam end-expansion device-track system, respectively, , respectively are mass, stiffness and damping constant;

[0034] S1254: Obtain the mass matrix, stiffness matrix and damping matrix of the suspension bridge beam end-expansion device-track coupling vibration model.

[0035] Further, step S2 comprises:

[0036] S21: Obtain the geometric characteristics and mechanical characteristics of the operating vehicle of the long-span railway suspension bridge, establish a vehicle model according to the geometric characteristics and mechanical characteristics, and assemble the mass matrix, stiffness matrix and damping matrix of the vehicle model;

[0037] S22: Based on the mass matrix, stiffness matrix and damping matrix of the suspension bridge beam end-expansion device-track coupling vibration model, and the mass matrix, stiffness matrix and damping matrix of the vehicle model, take the beam end rotation angle or track irregularity as the external excitation, form a suspension bridge beam end-expansion device-track-train coupling vibration analysis system.

[0038] Further, step S22 comprises:

[0039] S221: Based on the mass matrix, stiffness matrix and damping matrix of the vehicle model, establish the motion dynamics equation of the operating vehicle:

[0040] ;

[0041] Wherein, v is the train model number in the vehicle model, , , respectively are the mass matrix, damping matrix and stiffness matrix of the train model, is the load vector of the train model, , , respectively are the acceleration, speed and displacement vectors of the train model;

[0042] S222: Based on the suspension bridge beam end-expansion device-track coupling vibration model, establish the dynamics equation of the suspension bridge beam end-expansion device-track:

[0043] ;

[0044] Wherein, , , , respectively are the overall mass matrix, stiffness matrix, damping matrix and node load vector of the suspension bridge beam end-expansion device-track coupling, b is the suspension bridge beam end-expansion device-track system, , , are the acceleration, velocity and displacement vectors of the suspension bridge end-expansion device-track coupling, respectively;

[0045] S223: link the suspension bridge end-expansion device-track coupling vibration model with the vehicle model through the wheel-rail relationship, the load vector of the train model and the node load vector form the wheel-rail contact relationship, and establish the dynamics equation of the suspension bridge end-expansion device-track-vehicle coupling;

[0046] ;

[0047] In the dynamics equation of the suspension bridge end-expansion device-track-vehicle coupling, the load vector of the train model includes:

[0048] the load in the lateral direction of the wheelset;

[0049] ;

[0050] wherein, is the lateral creep force, is the creep coefficient, , are the lateral velocity of the wheelset and the lateral velocity of the track, respectively, w is the wheelset label, r is the track label, k is the wheelset number;

[0051] The interaction forces in the heave and twist directions between the wheel and the rail:

[0052] The interaction forces in the heave and twist directions between the wheel and the rail are determined by the relative motion state in the corresponding direction between the wheel and the rail. The interaction forces between the operating vehicle and the suspension bridge end-expansion device-track include the primary suspension force, the inertia force generated by the wheelset, and the gravity of the wheelset. The displacement of the wheelset in the first bogie direction is defined as , the displacement in the second bogie direction is defined as , and for any wheelset , the force acting on the first bogie direction is , and the force acting on the second bogie direction is

[0053] ;

[0054] ;

[0055] Among them, the force This indicates the forces acting on the suspension bridge end-expansion joint-track in the torsional and buoyancy directions. For the weight of the wheelset, , These are the stiffness and damping of the first series of springs, respectively. , These represent half the lateral span of the primary suspension and half the wheelbase of the operating vehicles, respectively. , These are the wheelset's moment of inertia and mass, respectively. , respectively at the wheelset rails direction, Displacement in direction, , respectively at the wheelset rails direction, velocity in direction, , respectively at the wheelset rails direction, Acceleration in the direction of , , The wheelset is located at the 1st position. bogie direction, direction, velocity in direction, For the sign function, the front wheelset of the bogie of the operating vehicle Take 1, the rear wheelset of the bogie. Take -1, z The direction is the direction of sinking or floating. The direction is the wheelset side-roll direction. The direction is the wheel alignment direction. t For bogies, j Number the bogies;

[0056] S224: Establish a coupled vibration model of the suspension bridge end-expansion device-track-train by using the dynamic equations of the coupling of the suspension bridge end-expansion device-track-train. Take the beam end rotation angle or track irregularity as the external excitation to form a coupled vibration analysis system of the suspension bridge end-expansion device-track-train.

[0057] Further, step S3 includes:

[0058] S31: Based on the coupled vibration analysis system of suspension bridge end-expansion device-track-train, initialize the position of the operating vehicle, the displacement of suspension bridge end-expansion device-track, and determine the time step;

[0059] S32: Taking the beam end rotation angle or track irregularity as an external excitation, the wheel-rail force time history of all wheelsets of the operating vehicle at all time steps is calculated, and the motion dynamics equation of the operating vehicle is solved by using the Newmark-β method to obtain the displacement, velocity and acceleration of the operating vehicle, and the dynamic response index of the operating vehicle is output; specifically including:

[0060] S321: The time history curve of the track irregularity sample or the beam end rotation angle is loaded, and the first-order derivative and the second-order derivative of the track irregularity sample or the beam end rotation angle excitation with respect to time are calculated;

[0061] S322: The position of each wheelset of the operating vehicle at the current time step is calculated, and then the wheel-rail force time history caused by the track irregularity or the beam end rotation angle is calculated;

[0062] S323: The motion dynamics equation of the operating vehicle is solved by using the Newmark-β method to obtain the displacement, velocity and acceleration of the operating vehicle under the condition of the beam end rotation angle or the track irregularity as an external excitation, and the dynamic response index of the operating vehicle is output;

[0063] S33: The wheel-rail force time history is applied to the suspension bridge beam end-expansion device-track, and the suspension bridge beam end-expansion device-track dynamics equation is solved to obtain the displacement, velocity and acceleration of the suspension bridge beam end-expansion device-track; specifically including:

[0064] S331: The position of all wheelsets of the operating vehicle on the track element within each time step is calculated;

[0065] S332: The wheel-rail force is converted into the load of the track element node based on the track element shape function matrix;

[0066] S333: The degrees of freedom of the suspension bridge beam end-expansion device-track are arranged in order, and the load of the track element node is loaded according to the corresponding degrees of freedom to form a node load vector ;

[0067] S334: The suspension bridge beam end-expansion device-track dynamics equation is solved by using the Newmark-β method to obtain the displacement, velocity and acceleration of the suspension bridge beam end-expansion device-track.

[0068] S34: The displacement, velocity and acceleration of the suspension bridge beam end-expansion device-track are superimposed with the beam end rotation angle or the track irregularity as an external excitation, and step S32 is executed to calculate the new wheel-rail force time history of the wheelset of the operating vehicle;

[0069] S35: The wheel-rail force time history error between the new wheel-rail force time history calculated in step S34 and the wheel-rail force time history calculated in step S32 is calculated;

[0070] If the wheel-rail force time history error is less than or equal to the wheel-rail force time history error threshold, it is determined that the convergence condition is met, and the dynamic response index of the operating vehicle is output.

[0071] Otherwise, it is determined that the convergence condition is not met, and step S33 is returned to reapply the wheel-rail force time history on the suspension bridge beam-end expansion device-track to meet the convergence condition, and the dynamic response index of the operating vehicle is output.

[0072] Further, step S4 includes:

[0073] S41: Taking the beam-end rotation angle with gradually increasing gradient as input, the response of the suspension bridge beam-end expansion device-track-train coupling vibration analysis system under different beam-end rotation angle conditions is calculated respectively to obtain the dynamic response index of the operating vehicle under different beam-end rotation angle conditions, and the mapping relationship between the dynamic response index and the beam-end rotation angle under different vehicle speeds is obtained;

[0074] S42: Taking the track irregularity sample of a set length as an excitation source input into the suspension bridge beam-end expansion device-track-train coupling vibration analysis system to obtain the dynamic response index of the operating vehicle under the excitation source condition, and combining the dynamic response index evaluation requirement of the operating vehicle to deduct the influence of random irregularity to obtain the beam-end rotation angle limit value under different vehicle speeds;

[0075] S43: Based on the three-dimensional finite element model of the suspension bridge, the beam-end rotation angle amplitude of the suspension bridge under the design load is calculated, and the beam-end rotation angle of the suspension bridge under the design load is evaluated whether it meets the requirements by comparing with the beam-end rotation angle limit value.

[0076] Further, step S41 includes:

[0077] S411: Inputting the beam-end rotation angle amplitude into the suspension bridge beam-end expansion device-track-train coupling vibration analysis system to determine the beam-end rotation angle value range that makes the dynamic response index of the operating vehicle exceed the limit;

[0078] S412: Taking several beam-end rotation angle gradient values in the beam-end rotation angle value range according to uniform gradient, and calculating the dynamic response index of the operating vehicle under different beam-end rotation angle gradient value conditions to draw a relationship diagram between the dynamic response index and the beam-end rotation angle value, and obtain the mapping relationship between the dynamic response index and the beam-end rotation angle under different vehicle speeds.

[0079] Further, step S42 includes:

[0080] S421: Taking the track irregularity sample of a set length as an excitation source input into the suspension bridge beam-end expansion device-track-train coupling vibration analysis system to obtain the dynamic response index of the operating vehicle under the excitation source condition;

[0081] S422: normality test is performed on the dynamic response index with a normal probability diagram, a normal distribution of data of the dynamic response index is obtained, and a probability density function of the normal distribution is output;

[0082] S423: a probability density fitting is performed on the dynamic response index based on a non-parametric model of Gaussian kernel density estimation, the probability density function of the normal distribution is used as a kernel function of the Gaussian kernel density estimation, and a 97.5% cumulative probability distribution value is calculated;

[0083] S424: according to an evaluation requirement of the dynamic response index of the operating vehicle, and based on the 97.5% cumulative probability distribution value, a dynamic response index deducted from track irregularity excitation is obtained, and the dynamic response index deducted from track irregularity excitation is input into a mapping relationship between the dynamic response index at different speeds and a beam end rotation angle, so that a beam end rotation angle limit value at different speeds is obtained.

[0084] The present application has the following advantages:

[0085] 1. The present application can substantially reduce the calculation of the degrees of freedom of the suspension bridge and realize high-precision simulation, extracts several beam end intervals, establishes a three-layer track model and a telescopic device, and considers an extended roadbed section to reduce the error caused by the "finite length" of the track, constructs a suspension bridge beam end-telescopic device-track model, and uses multi-section marshalling for the operating vehicle, and on this basis, constructs a suspension bridge beam end-telescopic device-train coupling model.

[0086] 2. The rigid gradient beam end rotation angle and the track irregularity are used as external excitation of the coupling model to form an evaluation system of the beam end rotation angle influencing the driving performance, the system is solved based on the separation iteration method, the dynamic response of the operating vehicle can be quickly obtained, the mapping relationship between the beam end rotation angle deformation and the dynamic response index of the vehicle is established, and thus the rationality of the beam end rotation angle can be more accurately evaluated according to the vehicle evaluation index. BRIEF DESCRIPTION OF DRAWINGS

[0087] Figure 1 It is a flow chart of the evaluation method of the beam end rotation angle influencing the driving performance of the long-span railway suspension bridge.

[0088] Figure 2 It is a full-bridge model schematic diagram of the suspension bridge with a bridge deck.

[0089] Figure 3 It is a three-dimensional finite element model schematic diagram of the long-span railway suspension bridge without a bridge deck.

[0090] Figure 4 It is a finite element model diagram of the suspension bridge beam end-telescopic device-track coupling.

[0091] Figure 5 It is a schematic diagram of the suspension bridge beam end-telescopic device-track coupling vibration model.

[0092] Figure 6 is a side view of a single car train model.

[0093] Figure 7 is a rear view of a single car train model.

[0094] Figure 8 is a bottom view of a single car train model.

[0095] Figure 9 is a schematic diagram of track irregularity excitation.

[0096] Figure 10 is a schematic diagram of beam end rotation excitation.

[0097] Figure 11 is a time history comparison diagram of wheel load reduction rate without beam end rotation.

[0098] Figure 12 is a time history comparison diagram of car body vertical acceleration without beam end rotation.

[0099] Figure 13 is a mapping relationship diagram of wheel load reduction rate and vertical droop angle.

[0100] Figure 14 is a mapping relationship diagram of car body vertical acceleration and vertical droop angle.

[0101] Figure 15 is a beam end rotation diagram of a suspension bridge when the wind speed is 40 m / s.

[0102] Figure 16 is a normal probability diagram of wheel load reduction rate.

[0103] Figure 17 is a normal probability diagram of vertical acceleration.

[0104] Figure 18 is a cumulative probability density distribution diagram of vertical acceleration.

[0105] Figure 19 is a cumulative probability density distribution diagram of wheel load reduction rate. DETAILED DESCRIPTION

[0106] The specific embodiments of the present application are described below to facilitate the understanding of the present application for those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all the inventions utilizing the concept of the present application are within the scope of protection.

[0107] As shown in Figure 1 , a method for evaluating the influence of large-span railway suspension bridge beam end rotation on train performance, comprising the following steps:

[0108] S1: a three-dimensional finite element model of the long-span railway suspension bridge is established, and the suspension bridge pier, the expansion device and the track are coupled to obtain a suspension bridge pier-expansion device-track coupling vibration model, and a mass matrix, a stiffness matrix and a damping matrix of the suspension bridge pier-expansion device-track coupling vibration model are established. Step S1 specifically includes:

[0109] S11: the geometric characteristics, material characteristics and boundary characteristics of the long-span railway suspension bridge are obtained, the bridge deck of the long-span railway suspension bridge is equivalent to the main truss structure, the truss structure without the bridge deck is formed, and the three-dimensional finite element model of the long-span railway suspension bridge is established. Step S11 specifically includes:

[0110] S111: the geometric characteristics, material characteristics and boundary characteristics of the long-span railway suspension bridge are obtained, and a full-bridge model of the long-span railway suspension bridge is established. In this embodiment, the APDL parameterized language of the ANSYS software is used to establish the full-bridge model of the suspension bridge, as shown in Figure 2 .

[0111] S112: the main truss structure and the bridge tower of the long-span railway suspension bridge are simulated by using the BEAM4 beam element, the suspender and the cable structure are simulated by using the LINK10 cable element, and the bridge deck is simulated by using the SHELL181 shell element. The main truss structure and the bridge tower, the suspender and the cable structure, and the bridge deck are integrated into a three-dimensional model by using node sharing or degree of freedom coupling;

[0112] S113: the frequency and the mode shape of the long-span railway suspension bridge are calculated. In this embodiment, the ANSYS software is used for calculation;

[0113] S114: the bridge deck element in the three-dimensional model is removed, as shown in Figure 3 , the bridge deck element is discretized into a plurality of concentrated mass points, the bridge deck mass is distributed to the main truss according to the area corresponding to the mass points, and the stiffness parameters of the main truss structure are adjusted so that the frequency and the mode shape of the three-dimensional model after removing the bridge deck element are consistent with the frequency and the mode shape calculated in step S13;

[0114] S115: the established three-dimensional finite element model of the long-span railway suspension bridge is output, as shown in Figure 4 and Figure 5 , Figure 4 the finite element model diagram of the suspension bridge pier-expansion device-track coupling, Figure 5 the schematic diagram of the suspension bridge pier-expansion device-track.

[0115] S12: Based on the three-dimensional finite element model of the long-span railway suspension bridge, a suspension bridge beam end-expansion device-track coupling vibration model is established, and a mass matrix, a stiffness matrix and a damping matrix of the suspension bridge beam end-expansion device-track coupling vibration model are constructed. Step S12 specifically includes:

[0116] S121: Extracting several panel sections near the beam end from the three-dimensional finite element model of the long-span railway suspension bridge, and using a spring element to simulate the constraint at the node truncation and using a unit load to determine the stiffness of the spring at the node truncation, a beam end model is constructed;

[0117] The beam end model and the three-dimensional finite element model have the same displacement and curvature at the same position, and the calibration method of the stiffness of the spring at the node truncation is:

[0118] S1211: Applying a force or a torque at the truncation node;

[0119] S1212: Extracting the response values of the local model near the beam end and the three-dimensional finite element model in the same displacement or angle direction;

[0120] S1213: Adjusting the stiffness of the spring at the node truncation to make the displacement and curvature of the local model and the three-dimensional finite element model consistent at the truncation position.

[0121] S122: Attaching a roadbed section before and after the beam end model to simulate the fixity of the roadbed by fixing constraints and reducing the error caused by the "finite length" of the track;

[0122] S123: For high-precision simulation of the influence of the track on the vehicle, a three-layer track model composed of a steel rail, a sleeper and a ballast is constructed; specifically including:

[0123] S1231: A Beam4 three-dimensional elastic beam element is used to construct a steel rail continuum model, the sleeper and ballast structure are treated as particles, and a Mass21 lumped mass element is used for equivalent simulation;

[0124] S1232: Linear spring damping Combin14 elements are used to simulate the connection between the steel rail-sleeper-ballast-roadbed and the steel rail-sleeper-ballast-longitudinal beam;

[0125] S1233: Taking the stiffness and spacing values of the fastener, sleeper and ballast system, a three-layer track model composed of a steel rail, a sleeper and a ballast is constructed.

[0126] S124: Based on the three-layer track model, a beam end expansion device is established between the roadbed and the bridge to finely simulate the actual situation of the beam end, and the beam end expansion device is established between the roadbed and the bridge, as shown in Figure 5 , specifically including:

[0127] S1241: the longitudinal beam of the expansion device, the movable rail sleeper and the fixed rail sleeper are simulated by BEAM4 beam unit;

[0128] S1242: the longitudinal beam fastener and the rail fastener are simulated by spring-damping COMBINE14 unit;

[0129] S1243: the longitudinal beam of the expansion device spans the roadbed and the bridge, the longitudinal beam is connected with the fixed rail sleeper on the bridge through the fastener, the fastener can move longitudinally with the fixed rail sleeper on the roadbed; the longitudinal beam is transversely connected with the movable rail sleeper and the roadbed side rail sleeper, which is simulated as a fixed constraint, and the longitudinal and vertical directions adopt linear spring constraint.

[0130] S125: the beam end model, the beam end expansion device and the three-layer track model are combined to form a suspension bridge beam end-expansion device-track coupling vibration model, and the mass matrix, the stiffness matrix and the damping matrix of the suspension bridge beam end-expansion device-track coupling vibration model are established; specifically including:

[0131] S1251: the command for modal solution is input in the command input area of the ANSYS software, and the command stream for extracting the mass and stiffness matrix is input, and the TXT format file is exported, which contains the row pointer, column index and numerical value of the non-zero element;

[0132] S1252: the TXT format file is analyzed by MATLAB, and the content in the TXT format file is converted into a sparse matrix, so as to form the mass and stiffness matrix;

[0133] S1253: the damping matrix is constructed by using the mass and stiffness matrix ;

[0134] ;

[0135] wherein, 、 are the overall mass and stiffness matrix of the beam end-expansion device-track system, 、 are the mass, stiffness and damping constants;

[0136] S1254: the mass matrix, the stiffness matrix and the damping matrix of the suspension bridge beam end-expansion device-track coupling vibration model are obtained.

[0137] S2: a vehicle model of the vehicle operated on the long-span railway suspension bridge is established, and the mass matrix, the stiffness matrix and the damping matrix of the vehicle model are established; the beam end rotation angle and the track irregularity are taken as external excitation to form a suspension bridge beam end-expansion device-track-train coupling vibration analysis system. Step S2 specifically includes:

[0138] S21: Obtain the geometric characteristics and mechanical characteristics of the operating vehicle of the long-span railway suspension bridge, establish a vehicle model according to the geometric characteristics and mechanical characteristics, and assemble the mass matrix, stiffness matrix and damping matrix of the vehicle model.

[0139] In this embodiment, the single-section train model, as shown in Figures 6-8 , includes one car body, two bogies and four wheelsets, one bogie and two wheelsets are connected through primary suspension devices, and the bogie is connected with the car body through secondary suspension devices to form a basic model of the vehicle.

[0140] The vehicle subsystem corresponding to the vehicle model is defined as a linear system, the springs of the primary and secondary suspension devices are linear springs, and the dampings are viscous dampings; the car body, the bogie and the wheelset of the operating vehicle are all regarded as rigid bodies without elastic deformation, and only the translation or rotation thereof is considered; the dynamic behaviors of each section of the vehicle do not interfere with each other, and the mechanical connection effects of the coupler and the buffer are ignored; in each section of the vehicle model, the car body and the two bogies are each considered to have five degrees of freedom, i.e. yaw, heave, roll, nod and pitch, and the wheelset is considered to have degrees of freedom in the yaw, heave and roll directions.

[0141] The calculation parameters of the vehicle model are: the wheelbase of the train bogie, the vehicle constant distance, the lateral span of the primary and secondary suspension, and the distance from the car body center to the secondary suspension.

[0142] The mass of the car body, the wheelset and the bogie, the moment of inertia in three directions, and the stiffness and damping of the primary and secondary suspension devices in three directions are obtained; the mass matrix, the stiffness matrix and the damping matrix of the train model are sequentially assembled, and then the mass matrix, the stiffness matrix and the damping matrix of the train model are repeatedly arranged along the main diagonal, so that the mass matrix, the stiffness matrix and the damping matrix of the whole train vehicle model are obtained.

[0143] S22: Based on the mass matrix, the stiffness matrix and the damping matrix of the suspension bridge beam end-expansion device-rail coupling vibration model and the mass matrix, the stiffness matrix and the damping matrix of the vehicle model, the beam end rotation angle and the track irregularity are taken as external excitations, and the suspension bridge beam end-expansion device-rail-train coupling vibration analysis system is formed together with the suspension bridge beam end-expansion device-rail-train coupling vibration model. Specifically, the following steps are included:

[0144] S221: Based on the mass matrix, the stiffness matrix and the damping matrix of the vehicle model, the motion dynamics equation of the operating vehicle is established:

[0145] ;

[0146] Wherein, v is the train model number in the vehicle model, , , respectively are the mass matrix, the damping matrix and the stiffness matrix of the train model, is the load vector of the train model, , , respectively are the acceleration, the velocity and the displacement vector of the train model;

[0147] S222: Based on the suspension bridge end-expansion device-track coupling vibration model, the suspension bridge end-expansion device-track dynamics equation is established:

[0148] ;

[0149] wherein, , , , respectively are the overall mass matrix, the stiffness matrix, the damping matrix and the node load vector of the suspension bridge end-expansion device-track coupling, b is the suspension bridge end-expansion device-track system, , , respectively are the acceleration, the velocity and the displacement vector of the suspension bridge end-expansion device-track coupling;

[0150] S223: The suspension bridge end-expansion device-track coupling vibration model is linked with the vehicle model through the wheel-rail relationship, and the load vector of the train model and the node load vector form the wheel-rail contact relationship, and the dynamics equation of the suspension bridge end-expansion device-track-vehicle coupling is established;

[0151] ;

[0152] In the dynamics equation of the suspension bridge end-expansion device-track-vehicle coupling, the load vector of the train model includes:

[0153] The load in the lateral direction of the wheelset;

[0154] ;

[0155] wherein, is the lateral creep force, is the creep coefficient, , respectively are the lateral velocity of the wheelset and the lateral velocity of the track, w is the wheelset label, r is the track label, k is the wheelset number;

[0156] Wheel-rail interaction forces in the vertical and lateral directions:

[0157] Wheel-rail interaction forces in the vertical and lateral directions can be determined by the corresponding relative motion states between the wheel and the rail, and the interaction forces between the operating vehicle and the suspension bridge end-expansion device-rail include primary suspension forces, inertial forces generated by the wheelset, and the gravity of the wheelset;

[0158] Let the displacement of the wheelset in the th bogie in the direction be , the displacement of the wheelset in the direction be , and the displacement of the wheelset in the direction be , the force in the direction be ,

[0159]

[0160]

[0161] wherein the force represents the force in the lateral and vertical directions of the suspension bridge end-expansion device-rail, is the gravity of the wheelset, , are the stiffness and damping of the primary spring, , are half of the lateral suspension span and half of the wheelbase of the operating vehicle, , are the moment of inertia and mass of the wheelset, , are the displacements of the wheelset in the direction and the direction, , are the velocities of the wheelset in the direction and the direction, , are the accelerations of the wheelset in the direction and the direction, , , are the displacements of the wheelset in the th bogie in the direction, direction, ​​The direction of the velocity of the vehicle, is a symbol function, the front wheel pair of the bogie of the operating vehicle is 1, the rear wheel pair of the bogie is -1, z The direction is the heave direction, The direction is the lateral roll direction of the wheel pair, The direction is the yaw direction of the wheel pair, t is a bogie, j is a bogie number, defining the front bogie j = 1, the rear bogie j = 2;

[0162] S224: A suspension bridge end-expansion device-railway-vehicle coupling vibration model is established by a dynamic equation of the suspension bridge end-expansion device-railway-vehicle coupling, the beam end rotation angle and the track irregularity are taken as external excitations, and a suspension bridge end-expansion device-railway-vehicle coupling vibration analysis system is formed.

[0163] In this embodiment, the track irregularity spectrum adopts a German low interference spectrum with a wavelength of 1-80 m, and a trigonometric series method is used to simulate and generate irregularity samples in three directions of the track as shown in Figure 9 .

[0164] The rigid beam end rotation angle is used for input, in order to alleviate the discontinuity of the beam end rotation angle curvature, a transition section of the road and the bridge described by a smoothing curve considering the rigidity of the rail and the rigidity of the rail support is considered, as shown in Figure 10 . The amplitude of the beam end rotation angle is calculated by the ratio of the vertical displacement of the beam end model truncation to the length of the beam end model.

[0165] S3: According to the suspension bridge end-expansion device-railway-vehicle coupling vibration analysis system, the position of the operating vehicle, the displacement of the suspension bridge end-expansion device-railway, and the time step are initialized; the numerical integration method is used to solve the motion dynamics equation of the operating vehicle and the dynamics equation of the suspension bridge end-expansion device-railway, until the convergence condition is met, and the dynamic response index of the operating vehicle is output. Specifically, the following steps are included:

[0166] S31: According to the suspension bridge end-expansion device-railway-vehicle coupling vibration analysis system, the position of the operating vehicle, the displacement of the suspension bridge end-expansion device-railway, and the time step are initialized;

[0167] S32: Taking the beam end rotation angle or the track irregularity as the external excitation, the wheel-rail force time history of the wheel pair of the operating vehicle at all time steps is calculated, and the Newmark-β method is used to solve the motion dynamics equation of the operating vehicle to obtain the displacement, velocity and acceleration of the operating vehicle, and the dynamic response index of the operating vehicle is output. Specifically, the following steps are included:

[0168] S321: load the track irregularity sample or the time history curve of the beam end rotation angle, and calculate the first derivative and the second derivative of the track irregularity sample or the beam end rotation angle excitation with respect to time;

[0169] S322: calculate the position of each wheel set of the operating vehicle at the current time step, and further calculate the wheel-rail force time history caused by the track irregularity or the beam end rotation angle;

[0170] S323: solve the motion dynamics equation of the operating vehicle by using the Newmark-β method to obtain the displacement, velocity and acceleration of the operating vehicle under the beam end rotation angle or the track irregularity as the external excitation condition, and output the dynamic response index of the operating vehicle.

[0171] S33: apply the wheel-rail force time history to the suspension bridge beam end-expansion device-track to solve the suspension bridge beam end-expansion device-track dynamics equation to obtain the displacement, velocity and acceleration of the suspension bridge beam end-expansion device-track. Specifically, it includes:

[0172] S331: calculate the position of all wheel sets of the operating vehicle on the track unit in each time step;

[0173] S332: convert the wheel-rail force to the load of the track unit node based on the track beam unit shape function matrix;

[0174] S333: arrange the order of the degrees of freedom of the suspension bridge beam end-expansion device-track, load the load of the track unit node according to the corresponding degrees of freedom to form the node load vector ;

[0175] S334: solve the suspension bridge beam end-expansion device-track dynamics equation by using the Newmark-β method to obtain the displacement, velocity and acceleration of the suspension bridge beam end-expansion device-track.

[0176] S34: superimpose the displacement, velocity and acceleration of the suspension bridge beam end-expansion device-track with the beam end rotation angle or the track irregularity as the external excitation, execute step S32 to calculate the new wheel-rail force time history of the wheel set of the operating vehicle;

[0177] S35: calculate the wheel-rail force time history error between the new wheel-rail force time history calculated in step S34 and the wheel-rail force time history calculated in step S32;

[0178] If the wheel-rail force time history error is less than or equal to the wheel-rail force time history error threshold, it is determined that the convergence condition is met, and the dynamic response index of the operating vehicle is output;

[0179] Otherwise, it is determined that the convergence condition is not met, and step S33 is returned to re-apply the wheel-rail force time history to the suspension bridge beam end-expansion device-track until the convergence condition is met, and the dynamic response index of the operating vehicle is output.

[0180] This embodiment takes the lower end corner mode of the middle beam as an example. By inputting the lower end corner of the beam into the suspension bridge beam-end-expansion device-track-train coupled vibration analysis system for analysis and extracting the time history curve of the dynamic response index of the vehicle, the index sensitive to the beam end corner can be obtained, such as Figure 11 and Figure 12 As shown in the figures, each index will have a large fluctuation at the beam end corner, and the dynamic response index includes wheel load reduction rate, vehicle body acceleration, etc.

[0181] S4: Calculate the dynamic response index of the operating vehicle under different beam end corner conditions to obtain the mapping relationship between the dynamic response index and the beam end corner at different vehicle speeds, apply the track irregularity sample as an excitation source, calculate the beam end corner limit value at different vehicle speeds; according to the design load of the suspension bridge, calculate the amplitude of the beam end corner of the suspension bridge, and evaluate whether the beam end corner of the suspension bridge meets the requirements. Step S4 specifically includes:

[0182] S41: Take the beam end corner with gradually increasing gradient as input, respectively calculate the response of the suspension bridge beam-end-expansion device-track-train coupled vibration analysis system under different beam end corner conditions, obtain the dynamic response index of the operating vehicle under different beam end corner conditions, and obtain the mapping relationship between the dynamic response index and the beam end corner at different vehicle speeds. Specifically includes the following steps:

[0183] S411: Input the beam end corner amplitude into the suspension bridge beam-end-expansion device-track-train coupled vibration analysis system to determine the range of beam end corner values that make the dynamic response index of the operating vehicle exceed the limit;

[0184] S412: Take several beam end corner gradient values within the beam end corner value range according to the uniform gradient, calculate the dynamic response index of the operating vehicle under different beam end corner gradient conditions, and draw a relationship diagram between the dynamic response index and the beam end corner value. This embodiment uses ORIGIN drawing software to draw, and obtains the mapping relationship between the dynamic response index and the beam end corner at different vehicle speeds.

[0185] S42: Input the track irregularity sample of a set length as an excitation source into the suspension bridge beam-end-expansion device-track-train coupled vibration analysis system to obtain the dynamic response index of the operating vehicle under the excitation source condition, deduct the influence of random irregularity combined with the dynamic response index evaluation requirements of the operating vehicle to obtain the beam end corner limit value at different vehicle speeds. Specifically includes the following steps:

[0186] S421: In this embodiment, the track irregularity sample of 10 km and wavelength of 1-80 m is input into the suspension bridge beam-end-expansion device-track-train coupled vibration analysis system as an excitation source to obtain the dynamic response index of the operating vehicle under the excitation source condition;

[0187] S422: Perform normality test on the dynamic response index using a normal probability graph to obtain a normal distribution of the data of the dynamic response index, and output a probability density function of the normal distribution; the data points of the dynamic response index are uniformly distributed near the reference line; as shown in Figure 16 and Figure 17 . Figure 16 The normal probability graph of the wheel load reduction rate of the present embodiment is given, Figure 17 The normal probability graph of the vertical acceleration of the present embodiment is given, and the vertical acceleration and the wheel load reduction rate are both dynamic response indexes of the operating vehicle.

[0188] S423: Perform probability density fitting on the dynamic response index based on a non-parametric model of Gaussian kernel density estimation, use the probability density function of the normal distribution as the kernel function of Gaussian kernel density estimation, and calculate the 97.5% cumulative probability distribution value; as shown in Figure 18 and Figure 19 , Figure 18 The cumulative probability density distribution graph of the vertical acceleration of the present embodiment is given, Figure 19 The cumulative probability density distribution graph of the wheel load reduction rate of the present embodiment is given.

[0189] S424: According to the dynamic response index evaluation requirement of the operating vehicle, and based on the 97.5% cumulative probability distribution value, obtain the dynamic response index excluding track irregularity excitation, input the dynamic response index excluding track irregularity excitation into the mapping relationship between the dynamic response index at different vehicle speeds and the beam end rotation angle, and obtain the beam end rotation angle limit value at different vehicle speeds.

[0190] The dynamic response index evaluation requirement of the present embodiment includes:

[0191] 1. The vehicle body acceleration specified in the “Code for Design of High-speed Railway” is: a Standard:

[0192] ;

[0193] 2. The derailment coefficient is a safety index for judging whether the wheel is derailed, and its value is the ratio of the lateral force Q to the vertical force P (dynamic wheel load) of the wheel at a certain moment, i.e. ;

[0194] The standard of the derailment coefficient is:

[0195] ;

[0196] 3. The wheel load reduction rate is a safety index for judging whether the wheel is derailed due to severe load reduction of the wheelset. Its value is the vertical load reduction amount of the wheelset on both sides to the average static wheel load of the wheelset The greater the ratio is, the greater the probability of wheel derailment is.

[0197] The standard of wheel load reduction rate is:

[0198] .

[0199] As Figure 13 and Figure 14 show, Figure 13 the mapping relationship between the beam end downward angle and the dynamic response index (wheel load reduction rate) is shown, and at the same speed, the two are approximately linear. The wheel load reduction rate requirement under the existing specification is 0.6, and considering the influence of track irregularity, the 97.5% cumulative probability distribution value of the wheel load reduction rate under the influence of track irregularity as the excitation source is calculated to be 0.1 (as shown in Figure 18 and Figure 19 , the abscissa of the intersection point of the red dotted line and the blue curve is 0.1), and 0.1 is the error of the dynamic response index. The dynamic response index (wheel load reduction rate) of the operating vehicle is obtained by subtracting the 97.5% cumulative probability distribution value 0.1 under the influence of track irregularity from the specification requirement 0.6 (as shown in Figure 13 the red horizontal dotted line), Figure 13 the abscissa of the intersection point of the horizontal red dotted line and the red oblique straight line (mapping relationship) is 8.04, and 8.04 is the calculated beam end angle limit value at a speed of 200 km / h.

[0200] S43: Based on the three-dimensional finite element model of the suspension bridge, the amplitude of the beam end angle of the suspension bridge under the design load is calculated, and the beam end angle of the suspension bridge under the design load is evaluated by comparing the beam end angle limit value. If the beam end angle of the suspension bridge does not meet the requirements, otherwise, it meets the requirements. As shown in Figure 15 , this embodiment takes a crosswind of 40 m / s as an example to obtain the beam end angle amplitude including the beam end lateral angle and the beam end vertical angle data. If the beam end angle amplitude of the suspension bridge exceeds the beam end angle limit value, it is determined that the beam end angle of the suspension bridge does not meet the requirements, otherwise, it meets the requirements.

Claims

1. A method for evaluating the driving performance influenced by the corner of the large-span railway suspension bridge end, characterized in that, The method comprises the following steps: S1: a three-dimensional finite element model of a long-span railway suspension bridge is established, and a suspension bridge beam end, an expansion device and a track are coupled to obtain a suspension bridge beam end-expansion device-track coupling vibration model, and a mass matrix, a stiffness matrix and a damping matrix of the suspension bridge beam end-expansion device-track coupling vibration model are established; S2: a vehicle model of a vehicle operated on the long-span railway suspension bridge is established, and a mass matrix, a stiffness matrix and a damping matrix of the vehicle model are established; a beam end rotation angle or a track irregularity is taken as an external excitation to form a suspension bridge beam end-expansion device-track-train coupling vibration analysis system; S3: according to the suspension bridge beam end-expansion device-track-train coupling vibration analysis system, the position of the operating vehicle, the displacement of the suspension bridge beam end-expansion device-track are initialized, and the time step is determined; the numerical integration method is used to solve the motion dynamics equation of the operating vehicle and the dynamics equation of the suspension bridge beam end-expansion device-track, until the convergence condition is met, and the dynamic response index of the operating vehicle is output; S4: the dynamic response index of the operating vehicle under different beam end rotation angle conditions is calculated, the mapping relationship between the dynamic response index and the beam end rotation angle under different vehicle speeds is obtained, the track irregularity sample is applied as an excitation source, and the beam end rotation angle limit under different vehicle speeds is calculated; according to the design load of the suspension bridge, the amplitude of the beam end rotation angle of the suspension bridge is calculated, and whether the beam end rotation angle of the suspension bridge meets the requirements is evaluated; The step S4 comprises: S41: the beam end rotation angle with gradually increasing gradient is taken as input, the response of the suspension bridge beam end-expansion device-track-train coupling vibration analysis system under different beam end rotation angle conditions is calculated respectively, the dynamic response index of the operating vehicle under different beam end rotation angle conditions is obtained, and the mapping relationship between the dynamic response index and the beam end rotation angle under different vehicle speeds is obtained; S42: the track irregularity sample with a set length is taken as an excitation source input into the suspension bridge beam end-expansion device-track-train coupling vibration analysis system, the dynamic response index of the operating vehicle under the excitation source is obtained, the influence of random irregularity is deducted combined with the dynamic response index evaluation requirements of the operating vehicle, and the beam end rotation angle limit under different vehicle speeds is obtained; S43: based on the three-dimensional finite element model of the suspension bridge, the amplitude of the beam end rotation angle of the suspension bridge under the design load is calculated, and the beam end rotation angle limit is compared to evaluate whether the beam end rotation angle of the suspension bridge under the design load meets the requirements; The step S41 comprises: S411: the beam end rotation angle amplitude is input into the suspension bridge beam end-expansion device-track-train coupling vibration analysis system, and the beam end rotation angle value range that makes the dynamic response index of the operating vehicle exceed the limit is determined; S412: a plurality of beam end rotation angle gradient values are taken in the beam end rotation angle value range according to a uniform gradient, the dynamic response index of the operating vehicle under different beam end rotation angle gradient value conditions is calculated, a relationship diagram between the dynamic response index and the beam end rotation angle value is drawn, and the mapping relationship between the dynamic response index and the beam end rotation angle under different vehicle speeds is obtained; The step S42 comprises: S421: input the track irregularity sample with a set length as an excitation source into a suspension bridge beam-end expansion device-track-train coupled vibration analysis system to obtain a dynamic response index of the operating vehicle under the excitation source; S422: perform normality test on the dynamic response index using a normal probability graph to obtain a normal distribution of the data of the dynamic response index, and output a probability density function of the normal distribution; S423: perform probability density fitting on the dynamic response index based on a non-parametric model of Gaussian kernel density estimation, use the probability density function of the normal distribution as a kernel function of the Gaussian kernel density estimation, and calculate a 97.5% cumulative probability distribution value; S424: obtain a dynamic response index excluding the track irregularity excitation according to an evaluation requirement of the dynamic response index of the operating vehicle and based on the 97.5% cumulative probability distribution value, input the dynamic response index excluding the track irregularity excitation into a mapping relationship between the dynamic response index and the beam-end rotation angle at different vehicle speeds, and obtain a beam-end rotation angle limit value at different vehicle speeds.

2. The method for evaluating the cornering performance of a long-span railway suspension bridge according to claim 1, characterized in that, The step S1 comprises: S11: obtaining geometric characteristics, material characteristics and boundary characteristics of the long-span railway suspension bridge, equivalently connecting a bridge deck of the long-span railway suspension bridge to a main truss structure to form a truss structure without the bridge deck, and establishing a three-dimensional finite element model of the long-span railway suspension bridge; S12: based on the three-dimensional finite element model of the long-span railway suspension bridge, establishing a suspension bridge beam-end expansion device-track coupled vibration model, and assembling a mass matrix, a stiffness matrix and a damping matrix of the suspension bridge beam-end expansion device-track coupled vibration model.

3. The method of claim 2, wherein the method is characterized by: The step S11 comprises: S111: obtaining geometric characteristics, material characteristics and boundary characteristics of the long-span railway suspension bridge, and establishing a full-bridge model of the long-span railway suspension bridge; S112: simulating a main truss structure and a tower, suspender and cable structure, and a bridge deck of the long-span railway suspension bridge, and integrating the main truss structure and the tower, suspender and cable structure, and the bridge deck into a three-dimensional model by using node sharing or degree of freedom coupling; S113: calculating a frequency and a mode shape of the long-span railway suspension bridge; S114: removing a bridge deck element from the three-dimensional model, discretizing the bridge deck element into a plurality of concentrated mass points, distributing the bridge deck mass to the main truss according to areas corresponding to the mass points, and adjusting a stiffness parameter of the main truss structure so that the frequency and the mode shape of the three-dimensional model without the bridge deck element are consistent with the frequency and the mode shape calculated in the step S113; S115: outputting the established three-dimensional finite element model of the long-span railway suspension bridge.

4. The method of claim 3, wherein the method is characterized by: The step S12 comprises: S121: extracting a plurality of panel points near a beam end from the three-dimensional finite element model of the long-span railway suspension bridge, simulating constraints at node truncations by using spring elements, determining stiffness of the spring at the node truncations by using unit loads, and constructing a beam-end model; and making the beam-end model have the same displacement and curvature as the three-dimensional finite element model at the same position. The calibration method of the spring stiffness at the node truncation is as follows: S1211: applying a force or a moment at the truncation node; S1212: extracting response values of a local model near the beam end and the three-dimensional finite element model in the same displacement or rotation angle direction; S1213: adjust the stiffness of the spring at the cut-off point of the node to make the displacement and curvature of the local model consistent with those of the three-dimensional finite element model at the cut-off position; S122: add a roadbed section before and after the local model to simulate the fixity of the roadbed through fixed constraints; S123: construct a three-layer track model composed of a steel rail, a sleeper, and ballast; S124: based on the three-layer track model, establish a beam end expansion device between the roadbed and the bridge; S125: form a suspension bridge beam end-expansion device-track coupling vibration model by combining the beam end model, the beam end expansion device, and the three-layer track model, and form the mass matrix, the stiffness matrix, and the damping matrix of the suspension bridge beam end-expansion device-track coupling vibration model; specifically including: S1251: input the modal solution command in the command input area of the ANSYS software, and then input the command stream for extracting the mass and stiffness matrix, and export the TXT format file; S1252: analyze the TXT format file using MATLAB, and convert the contents in the TXT format file into a sparse matrix, thereby forming the mass and stiffness matrix; S1253: Constructing the damping matrix using the mass, stiffness matrix ; ； wherein , are the global mass, stiffness matrix of the beam-end-elongation device-rail system, respectively, , are the mass, stiffness and damping constants, respectively; S1254: obtain the mass matrix, the stiffness matrix, and the damping matrix of the suspension bridge beam end-expansion device-track coupling vibration model.

5. The method of claim 1, wherein the method is characterized by: The step S2 includes: S21: obtain the geometric and mechanical characteristics of the vehicles operating on the long-span railway suspension bridge, establish a vehicle model according to the geometric and mechanical characteristics, and form the mass matrix, the stiffness matrix, and the damping matrix of the vehicle model; S22: based on the mass matrix, the stiffness matrix, and the damping matrix of the suspension bridge beam end-expansion device-track coupling vibration model, and the mass matrix, the stiffness matrix, and the damping matrix of the vehicle model, form a suspension bridge beam end-expansion device-track-train coupling vibration analysis system by taking the beam end rotation angle or the track irregularity as an external excitation.

6. The method of claim 5, wherein the method is characterized by: The step S22 includes: S221: based on the mass matrix, the stiffness matrix, and the damping matrix of the vehicle model, establish the motion dynamics equation of the operating vehicle: ； where v is the train model number in the vehicle model, , , are the mass matrix, damping matrix and stiffness matrix of the train model, respectively, is the load vector of the train model, , , are the acceleration, velocity and displacement vectors of the train model, respectively. S222: based on the suspension bridge beam end-expansion device-track coupling vibration model, establish the dynamics equation of the suspension bridge beam end-expansion device-track: ； wherein, , , , are the global mass, stiffness, damping matrices and the nodal load vector of the suspension bridge end- expansion device - track coupling, respectively, b is the suspension bridge end- expansion device - track system, , , are the acceleration, velocity and displacement vectors of the suspension bridge end- expansion device - track coupling, respectively; S223: link the suspension bridge end-expansion device-rail coupling vibration model with the vehicle model through the wheel-rail relationship, the load vector of the train model and the node load vector form the wheel-rail contact relationship, and establish the dynamics equation of the suspension bridge end-expansion device-rail-vehicle coupling; ； In the dynamic equations of a suspension bridge pier-elongation device-track-vehicle coupling, the load vector of the train model comprises: the load in the lateral direction of the wheelset; ； wherein, is the lateral creep force, is the creep coefficient, , are the wheelset lateral and track lateral velocities, respectively, w is the wheelset label, r is the track label, k is the wheelset number; the interaction force between the wheel and the rail in the heave and twist directions: The vertical and torsional interaction forces between the wheel and the rail are determined by the corresponding relative motion states, and the interaction forces between the operating vehicle, the suspension bridge, the end-expansion device and the track include the primary suspension force, the inertia force generated by the wheelset and the gravity of the wheelset; the displacement of the wheelset in the first direction is defined as the displacement of the wheelset in the second direction is defined as the displacement of the wheelset in the third direction is defined as , the displacement of the wheelset in the fourth direction is defined as , the displacement of the wheelset in the fifth direction is defined as , and the action force in the first direction and the action force in the second direction applied to the wheelset are defined as , , , , . ； ； wherein F is the force represents the force of the suspension bridge end-expansion device-track in the twist direction, the sink direction, is the gravity of the wheelset, , are the stiffness and damping of the primary suspension, respectively, , are half of the lateral distance and half of the wheelbase of the primary suspension of the operating vehicle, respectively, , are the moment of inertia and the mass of the wheelset, respectively, , are the displacement of the wheelset track in the direction, direction, respectively, , are the velocity of the wheelset track in the direction, direction, respectively, , are the acceleration of the wheelset track in the direction, direction, respectively, , , are the velocity of the wheelset in the direction, direction, direction of the th bogie, respectively, is a sign function, the front wheelset of the bogie of the operating vehicle takes 1, the rear wheelset of the bogie takes -1, z is the sink direction, is the lateral roll direction of the wheelset, is the nodding direction of the wheelset, t is a bogie, j is the bogie number, the front bogie j = 1, the rear bogie j = 2; S224: establish the suspension bridge beam end-expansion device-track-train coupling vibration model through the dynamics equation of the suspension bridge beam end-expansion device-track-vehicle coupling, and form a suspension bridge beam end-expansion device-track-train coupling vibration analysis system by taking the beam end rotation angle or the track irregularity as an external excitation.

7. The method of claim 1, wherein the method is characterized by: The step S3 includes: S31: initialize the position of the operating vehicle, the displacement of the suspension bridge beam end-expansion device-track, and determine the time step according to the suspension bridge beam end-expansion device-track-train coupling vibration analysis system; S32: calculate the wheel-rail force time history of the wheelset of the operating vehicle under all time steps by taking the beam end rotation angle or the track irregularity as an external excitation, solve the motion dynamics equation of the operating vehicle using the Newmark-β method, obtain the displacement, velocity, and acceleration of the operating vehicle, and output the dynamic response indicators of the operating vehicle; specifically including: S321: load the track irregularity sample or the time history curve of the beam end rotation angle, and calculate the first derivative and the second derivative of the track irregularity sample or the beam end rotation angle excitation with respect to time; S322: calculate the position of each wheel set of the operating vehicle at the current time step, and further calculate the wheel-rail force time history caused by the track irregularity or the beam end rotation angle; S323: solve the motion dynamics equation of the operating vehicle by using the Newmark-β method to obtain the displacement, velocity and acceleration of the operating vehicle under the beam end rotation angle or the track irregularity as the external excitation condition, and output the dynamic response index of the operating vehicle; S33: apply the wheel-rail force time history to the suspension bridge beam end-expansion device-track, solve the suspension bridge beam end-expansion device-track dynamics equation, and obtain the displacement, velocity and acceleration of the suspension bridge beam end-expansion device-track; specifically including: S331: calculate the position of all wheel sets of the operating vehicle on the track unit in each time step; S332: convert the wheel-rail force to the load of the track unit node based on the track unit shape function matrix; S333: arrange the sequence of the degrees of freedom of the cable-stayed bridge end-expansion device-track, load the load of the track unit node according to the corresponding degrees of freedom, and form the node load vector ; S334: solve the suspension bridge beam end-expansion device-track dynamics equation by using the Newmark-β method to obtain the displacement, velocity and acceleration of the suspension bridge beam end-expansion device-track; S34: superimpose the displacement, velocity and acceleration of the suspension bridge beam end-expansion device-track with the beam end rotation angle or the track irregularity as the external excitation, execute step S32, and calculate the new wheel-rail force time history of the operating vehicle wheel set; S35: calculate the wheel-rail force time history error between the new wheel-rail force time history calculated in step S34 and the wheel-rail force time history calculated in step S32; If the wheel-rail force time history error is less than or equal to the wheel-rail force time history error threshold, it is determined that the convergence condition is met, and the dynamic response index of the operating vehicle is output; Otherwise, it is determined that the convergence condition is not met, and step S33 is returned to re-apply the wheel-rail force time history to the suspension bridge beam end-expansion device-track until the convergence condition is met, and the dynamic response index of the operating vehicle is output.

Images