CN104731998A - Computing method of dynamic response under nonuniform excitation of overline overbridge - Google Patents

Abstract

The invention relates to a computing method of dynamic response under nonuniform excitation of an overline overbridge. The computing method of dynamic response under the nonuniform excitation of the overline bridge relates to the computing method of dynamic response of the overline pedestrian overbridge under the action of the nonuniform excitation of a main-line train, the dynamic response of the overline pedestrian overbridge serves as a target value, considering that the nonuniform excitation is generated at the position of a bridge pier of the overline pedestrian overbridge during the high-speed running process of the train, the equation of motion of the overline pedestrian overbridge under the action of the nonuniform excitation is deduced, and the response of the overline pedestrian overbridge under the action of the train can be obtained according to a numerical integration. According to the computing method of dynamic response under the nonuniform excitation of the overline bridge, the analytic method of the nonuniform excitation is brought out creatively to be used for calculating the vibration response under the nonuniform excitation acting on the position of the bridge pier of the overline pedestrian overbridge when the main-line train passing through at a high speed under the overline pedestrian overbridge, the computing method of dynamic response under the nonuniform excitation of the overline bridge is suitable for dynamic response analyses of all overline pedestrian overbridges under the action of the main-line trains and has a comparatively large practical engineering application value and innovativeness.

Description

The computing method of dynamic response under line bridge non-uniform method

Technical field

The present invention relates to transportation civil engineering structure neck, particularly relate to a kind of computing method being applicable to dynamic response under line bridge non-uniform method.

Background technology

The overpass that enters the station is the important infrastructure in railway transport of passengers traffic, when passing through below main track train is at a high speed and continually from it, owing to being subject to the strong effect of train parting load that train high-speed cruising produces and foundation vibration, its vibratory response clearly, have a strong impact on its security, comfortableness and permanance, need for this reason to enter the station overpass main track train at a high speed by time dynamic response study.

The dynamic response of the cross-line overpass structure caused by train parting load is mainly paid close attention in current existing research, does not consider the impact on it of the ambient vibration that Induced by High Speed Trains brings out; And in the ambient vibration of Induced by High Speed Trains, then mainly pay close attention to the vibratory response of train to the buildings closed on, because the buildings closed on is in the side of train, ambient vibration ripple caused by train is almost delivered to this works basis place simultaneously in the same way, therefore can think consistent excitation effect in computational analysis.And in this patent, due to bullet train pass through immediately below cross-line overpass time, ambient vibration effect is delivered to day Bridge Foundation along different directions, therefore, current consistent excitation analytical approach is no longer applicable for cross-line overpass analysis of Environment Vibration, and non-uniform method analytical approach must be adopted reasonably could to calculate the vibratory response of overpass.

Summary of the invention

The technical problem to be solved in the present invention is for defect of the prior art, a kind of computing method about cross-line overpass dynamic response under the effect of main track train non-uniform method are provided, calculate exactly cross-line overpass immediately below bullet train is from it by time the ambient vibration that produces vibratory response, the method has larger practical engineering application and is worth.

The technical solution adopted for the present invention to solve the technical problems is: a kind of computing method about cross-line overpass dynamic response under the effect of main track train non-uniform method, comprise the following steps:

(1) basic parameter of train, track is inputted, auto model, model trajectory is set up respectively according to car track coupling dynamics principle, according to wheel-rail contact relationship, set up train track system Coupled Dynamics two-dimension analysis model, this model is two-dimentional rigid body kinematics model; The basic parameter of described train, track comprises: the quality that train body, bogie and wheel are right and moment of inertia, train body and bogie, bogie and wheel between stiffness coefficient and ratio of damping;

(2) Train Track system, coupled dynamics two-dimension analysis model is utilized, simultaneously according to train, track physical parameter, act on the exciting force time-history curves on rail node when obtaining main track train high-speed cruising, the ambient vibration caused for solving train operation further provides vibration source to encourage;

(3) track-sleeper-the earth three-dimensional finite element TRANSFER MODEL is set up, analyze the attenuation law of the earth vibration on ground caused by bullet train according to this three-dimensional finite element model, thus obtain the ambient vibration ripple time-history curves acting on cross-line overpass bridge pier place;

(4) determine according to the ambient vibration ripple time-history curves acting on cross-line overpass bridge pier place during main track train high-speed cruising the time-histories data curve acting on cross-line overpass bridge pier place, this vibration wave is all not identical on the Time and place variation characteristic at each bridge pier place, obtains the exciting force time-history curves acting on cross-line overpass bridge pier place thus;

(5) input corresponding material parameter and constraint condition, set up cross-line overpass three-dimensional finite element dynamic model according to physical size;

(6) obtain according to Finite Element the equation of motion that the dynamic load time-history curves acted on each node of overpass sets up cross-line overpass, the mass matrix at its body of a bridge and bridge pier place, damping matrix and stiffness matrix are carried out the partitioning of matrix, derive the equation of motion of cross-line overpass under the effect of main track train non-uniform method, and adopt the numerical integration method of unconditional stability, the dynamic response of cross-line overpass under the effect of main track train non-uniform method can be tried to achieve.

By such scheme, step 6) in the equation of motion of cross-line overpass be:

In formula: [M _aa], [C _aa] and [K _aa] represent the mass matrix of the body of a bridge, damping matrix and stiffness matrix respectively; { x _a, with be respectively the displacement of the overpass body of a bridge, speed and vector acceleration; F ' _wexpression other loads suffered by the body of a bridge; { x _bit is the displacement at bridge pier place.

By such scheme, described in step (1), system model only can consider vertical motion, also can consider the vibration of level and vertical both direction simultaneously.

By such scheme, when setting up track-sleeper-the earth three-dimensional finite element TRANSFER MODEL in step (3), based on following theory hypothesis:

A () ignores the impact between structure and soil, think that namely the vibration displacement of effect bridge pier place soil is the displacement acting on bridge pier place;

B () ignores the discreteness of the road soil body, think that the soil body is continuous elastomeric, only consider linear analysis.

The beneficial effect that the present invention produces is: this method innovatively propose non-uniform method analytical approach reasonably calculate cross-line overpass immediately below main track train is from it at a high speed by time act on bridge pier non-uniform method under vibratory response, the method is applicable to the dynamic response analyses of all cross-line overpasses under the effect of main track train, has larger practical engineering application and is worth.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the invention will be further described, in accompanying drawing:

Fig. 1 is the method flow diagram of the embodiment of the present invention;

Ambient vibration wave loops schematic diagram when Fig. 2 is the train operation of the embodiment of the present invention;

Fig. 3 is the overpass non-uniform method that enters the station of embodiment of the present invention partitioning of matrix schematic diagram when calculating;

Fig. 4 is the time-history curves of typical node track dynamical reaction under the 310km/h speed of a motor vehicle of the embodiment of the present invention;

Fig. 5 is the 3d orbit-fastener-sleeper-the earth finite element TRANSFER MODEL of the embodiment of the present invention;

Fig. 6 is the transversal displacement time-history curves of the embodiment of the present invention;

Fig. 7 is the vertical displacement time-history curves of the embodiment of the present invention;

Fig. 8 is certain overpass finite element model that enters the station of the embodiment of the present invention;

Fig. 9 is the vertical motion dynamic response of the cross-line overpass of the embodiment of the present invention;

Figure 10 is the transverse vibration dynamic response of the cross-line overpass of the embodiment of the present invention.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

The invention provides a kind of computing method about cross-line overpass dynamic response under the effect of main track train non-uniform method, it is using cross-line overpass dynamic response as desired value, consider the non-uniform method in train high-speed cruising process, cross-line overpass bridge pier place produced, derive the equation of motion of cross-line overpass under non-uniform method effect, then the response of overpass under train effect can be obtained according to numerical integrating.Specifically: according to train track system Coupled Dynamics two-dimension analysis model, the exciting force time-history curves on rail node is acted on when trying to achieve main track train high-speed cruising, general finite element analysis software is adopted to set up track-sleeper-the earth three-dimensional finite element TRANSFER MODEL again, analyze the attenuation law of the earth vibration on ground caused by bullet train, thus obtain the ambient vibration ripple time-history curves acting on cross-line overpass bridge pier place, then the equation of motion of cross-line overpass under the effect of main track train non-uniform method is derived, utilize the numerical integration method of unconditional stability can obtain the dynamic response of the bridge of cross-line overpass when train high-speed cruising under the non-uniform exciting force of bridge pier place generation.

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further details.

The present invention is to provide the computing method of cross-line overpass dynamic response under the effect of main track train non-uniform method mainly for ground, and selects corresponding computational analysis model to simulate.

Method provided by the invention comprises the following steps:

(1) basic parameter of train, track is inputted, auto model, model trajectory is set up respectively according to vehicle-orbit coupling principle of dynamics, according to wheel-rail contact relationship, set up train track system Coupled Dynamics two-dimension analysis model, this model is two-dimentional rigid body kinematics model;

(2) train-rail system Coupled Dynamics two-dimension analysis model is utilized, simultaneously according to train, track physical parameter, act on the exciting force time-history curves on rail node when obtaining main track train high-speed cruising, the ambient vibration caused for solving train operation further provides vibration source to encourage;

(3) set up track-sleeper-the earth three-dimensional finite element TRANSFER MODEL, this model is three-dimensional finite element model;

(4) the time-histories data curve acting on cross-line overpass bridge pier is determined by above step, this vibration wave is all not identical on the Time and place variation characteristic at each bridge pier place, can obtain the exciting force time-history curves acting on cross-line overpass bridge pier place thus;

(5) input corresponding material parameter and constraint condition, set up cross-line overpass three-dimensional finite element dynamic model according to physical size;

(6) according to the equation of motion of cross-line overpass, the mass matrix at its body of a bridge and bridge pier place, damping matrix and stiffness matrix are carried out the partitioning of matrix, derive the equation of motion of cross-line overpass under the effect of main track train non-uniform method, and adopt the numerical integration method of unconditional stability, the dynamic response of cross-line overpass under the effect of main track train non-uniform method can be tried to achieve.

In order to realize above-mentioned object, the invention provides the computing method of the non-uniform method dynamic response of a kind of cross-line overpass in main track train travelling process.For the buildings of side along the railway, the vibrational excitation of the train load can thought suffered by them is consistent excitation, cross-line overpass is then completely different compared with them: when main track train is at a high speed by cross-line overpass, the bridge pier transmission of the ambient vibration wave direction cross-line overpass both sides produced, in the side of circuit, because distance is very short, the speed of a motor vehicle is very fast, vibration wave is almost delivered to bridge pier simultaneously, the mistiming of vibration wave is negligible, but in the both sides of circuit, the direction that vibration wave is propagated is inconsistent, that is can not the single response analyzing overpass with consistent excitation.In order to conform to actual conditions, the computing method of the non-uniform method that the present invention adopts consider the change in time and space characteristic of vibration wave, vibration wave is produced in train travelling process, vibration wave propagates into and reaches overpass bridge pier in the soil body, pontic is vibrated, the time that the vibration wave that train operation produces passes to basis is roughly the same, but the direction of excitation is inconsistent.

Determine to after the excitation of cross-line overpass in train travelling process, can analyze the dynamic response of cross-line overpass.The equation of motion of structure can not simply apply mechanically the general equation of motion, and the present invention has derived the equation of motion of structure under non-uniform method effect again.Now only analyze some supporting-points under the effect encouraged, the dynamic response of overpass, if overpass is by the effect of the vibration wave produced in train travelling process, its linear system with several degrees of freedom kinetic equation is:

In formula: [M], [C], [K] are respectively the mass matrix of overpass structure, damping matrix and stiffness matrix; { x} is respectively architecture quality and gathers the acceleration in degree of freedom on a node basis direction, speed and motion vector.{ F (t) } is for acting on the dynamic load time-history curves on each node of overpass.

Train is in the process run, and produce vibration wave, vibration wave is delivered to overline bridge bridge pier place, and the ground near bridge pier vibrates, and causes the bridge pier of overline bridge to vibrate with ground vibration.If represent that the overpass body of a bridge is by the relevant item of the node of outer dynamic load with footmark a, footmark b represents the item that node that overpass bridge pier supports is relevant, and as shown in Figure 3, then formula (1) can be expressed as:

$\left[\begin{array}{cc}{M}_{\mathrm{aa}}& M_{\mathrm{ab}}\\ M_{\mathrm{ba}}& M_{\mathrm{bb}}\end{array}\right]\left\{\begin{array}{c}{\stackrel{\·\·}{x}}_a\\ {\stackrel{\·\·}{x}}_b\end{array}\right\}+\left[\begin{array}{cc}{C}_{\mathrm{aa}}& C_{\mathrm{ab}}\\ C_{\mathrm{ba}}& C_{\mathrm{bb}}\end{array}\right]\left\{\begin{array}{c}{\stackrel{\·}{x}}_a\\ {\stackrel{\·}{x}}_b\end{array}\right\}+\left[\begin{array}{cc}{K}_{\mathrm{aa}}& K_{\mathrm{ab}}\\ K_{\mathrm{ba}}& K_{\mathrm{bb}}\end{array}\right]\left[\begin{array}{c}{x}_a\\ x_b\end{array}\right]=\left\{\begin{array}{c}{F}_w^{\′}\\ F_b\end{array}\right\}---\left(2\right)$

Wherein { x _a, with be respectively the displacement of the overpass body of a bridge, speed and vector acceleration; { x _b, with be respectively the displacement of bridge pier supporting, speed and vector acceleration; [M _aa], [C _aa] and [K _aa] represent the mass matrix of the body of a bridge, damping matrix and stiffness matrix respectively; [M _bb], [C _bb] and [K _bb] represent the mass matrix of bridge pier, damping matrix and stiffness matrix respectively; Wherein footmark is the mass matrix of the expression body of a bridge of ab and ba and bridge pier coupling, damping matrix and stiffness matrix; F ' _wrepresent that other loads suffered by the body of a bridge are as wind load, { F _bthe outer dynamic load of expression suffered by bridge pier, be generally 0.

If the displacement at bridge pier place is known, i.e. { x _bknown, then can be obtained by the first formula in formula (2):

$\left[M_{\mathrm{aa}}\right]\left\{{\stackrel{\·\·}{x}}_a\right\}+\left[M_{\mathrm{ab}}\right]\left\{{\stackrel{\·\·}{x}}_b\right\}+\left[C_{\mathrm{aa}}\right]\left\{{\stackrel{\·}{x}}_a\right\}+\left[C_{\mathrm{ab}}\right]\left\{{\stackrel{\·}{x}}_b\right\}+\left[K_{\mathrm{aa}}\right]\left\{x_a\right\}+\left[K_{\mathrm{ab}}\right]\left\{x_b\right\}=\left\{F_w^{\′}\right\}---\left(3\right)$

Following formula can be derived:

$\left[M_{\mathrm{aa}}\right]\left\{{\stackrel{\·\·}{x}}_a\right\}+\left[C_{\mathrm{aa}}\right]\left\{{\stackrel{\·}{x}}_a\right\}+\left[K_{\mathrm{aa}}\right]\left\{x_a\right\}=\left\{F_w^{\′}\right\}-\left[M_{\mathrm{ab}}\right]\left\{{\stackrel{\·\·}{x}}_b\right\}-\left[C_{\mathrm{ab}}\right]\left\{{\stackrel{\·}{x}}_b\right\}-\left[K_{\mathrm{ab}}\right]\left\{x_b\right\}---\left(4\right)$

In most cases, damping is on the impact of the impact of useful load much smaller than inertia effects and elastic restoring force, and therefore, generally can omit the Section 3 on the right of above formula, namely above formula can be written as:

$\left[M_{\mathrm{aa}}\right]\left\{{\stackrel{\·\·}{x}}_a\right\}+\left[C_{\mathrm{aa}}\right]\left\{{\stackrel{\·}{x}}_a\right\}+\left[K_{\mathrm{aa}}\right]\left\{x_a\right\}=\left\{F_w^{\′}\right\}-\left[M_{\mathrm{ab}}\right]\left\{{\stackrel{\·\·}{x}}_b\right\}-\left[K_{\mathrm{ab}}\right]\left\{x_b\right\}---\left(5\right)$

If when adopting lumped mass matrix, i.e. [M _ab]=0, then above formula can be reduced to further:

$\left[M_{\mathrm{aa}}\right]\left\{{\stackrel{\·\·}{x}}_a\right\}+\left[C_{\mathrm{aa}}\right]\left\{{\stackrel{\·}{x}}_a\right\}+\left[K_{\mathrm{aa}}\right]\left\{x_a\right\}=\left\{F_w^{\′}\right\}-\left[K_{\mathrm{ab}}\right]\left\{x_b\right\}---\left(6\right)$

Adopt the dynamic response computing formula of structure under above-mentioned non-uniform method effect herein, calculate in the process of train high-speed cruising, the vibration wave of generation causes bridge pier to be subject to this excitation, creates corresponding displacement, i.e. { x _b, thus obtain the whole dynamic response of overpass.

Below for certain cross-line overpass, the embody rule of this method is described.

(1) basic parameter of train, track is inputted, auto model, model trajectory is set up respectively according to vehicle-orbit coupling principle of dynamics, according to wheel-rail contact relationship, set up train track system Coupled Dynamics two-dimension analysis model, this model is two-dimentional rigid body kinematics model;

The Couple Equations of vehicle and track simultaneous:

$M\stackrel{\·\·}{a}+C\stackrel{\·}{a}+\mathrm{Ka}=Q---\left(7\right)$

Wherein: $M=\left[\begin{array}{cc}{M}_u& 0\\ 0& M_1\end{array}\right],C=\left[\begin{array}{cc}{C}_u& C_{\mathrm{ul}}\\ C_{\mathrm{lu}}& C_1\end{array}\right],K=\left[\begin{array}{cc}{K}_u& K_{\mathrm{ul}}\\ K_{\mathrm{lu}}& K_1\end{array}\right],Q=\left\{\begin{array}{c}{Q}_u^{\′}\\ Q_1^{\′}\end{array}\right\}$

C _uland C _lufor the damping couple item of wheel track; K _uland K _lufor the damping couple item of wheel track; Q ' _uwith Q ' _lbe respectively the wheel load after unknown quantity being moved to system of equations left end and track load force vector.

(2) train-rail system Coupled Dynamics two-dimension analysis model is utilized, simultaneously according to train, track physical parameter, act on the exciting force time-history curves on rail node when obtaining main track train high-speed cruising, the ambient vibration caused for solving train operation further provides vibration source to encourage;

The CRH380a motor-car generally adopted according to China and the relevant physical parameter of trailer, numerical integration method according to the two-dimensional kinematics equation employing unconditional stability taking institute in step (1) to set up solves, can obtain the exciting force time-history curves acted on rail node, Fig. 4 gives the track dynamical reaction time-history curves of the speed of a motor vehicle certain node in 310km/h situation.

(3) set up track-sleeper-the earth three-dimensional finite element TRANSFER MODEL, this model is three-dimensional finite element model;

This patent when setting up track-fastener-sleeper-the earth three-dimensional model, based on following theory hypothesis:

A () ignores the impact between structure and soil, think that namely the vibration displacement of effect bridge pier place soil is the displacement acting on bridge pier place;

B () ignores the discreteness of the road soil body, think that the soil body is continuous elastomeric, only consider linear analysis.

For 3d orbit-fastener-sleeper-the earth finite element TRANSFER MODEL, its middle orbit adopts beam44 beam element to set up simulation I shape rail, fastener adopts combin14 spring unit to be based upon between track and sleeper and arranges, sleeper adopts beam4 rectangular beam unit to set up, Track Pad and the earth soil body adopt solid45 unit to set up, arrange Viscoelastic Three-dimensional power ARTIFICIAL BOUNDARY in the side all around of the soil body and bottom surface, model as shown in Figure 5.

In model, the material properties of each several part is all in the light of actual conditions chosen, as shown in table 1,

Each several part material properties in table 1 model

Soil layer under Practical Project middle orbit changes more complicated and soil layer change is everywhere different, it is very little on the impact on earth's surface when soil depth is more than 30 meters in addition, according to the related data in Practical Project, soil body soil layer is simplified herein, soil layer is reduced to uniform multilayer non-individual body, the soil depth considered in model is 30 meters, and the parameter of each soil layer is as shown in table 2:

Each soil parameters in table 2 model

(4) the time-histories data curve acting on cross-line overpass bridge pier is determined by above step, this vibration wave is all not identical on the Time and place variation characteristic at each bridge pier place, can obtain the exciting force time-history curves acting on cross-line overpass bridge pier place thus;

Have ignored the impact between structure and soil, think that namely the vibration displacement of effect bridge pier place soil is the displacement acting on bridge pier place, therefore think that the impact of vibration on overpass produced due to track irregularity in train operation is exactly that the vibration that produces due to track irregularity is on the impact of the overpass bridge pier bottom position place soil body.According to the structural arrangement of this overpass that enters the station, the transverse direction of corresponding position node at the bottom of extraction distance track 16.75m, 20.75m and 52.8m place overpass post and vertical displacement time-history curves are as shown in Figure 6 and Figure 7.

From Fig. 6 and Fig. 7, at the bottom of track 16.75m place overline bridge post, the trough value of vertical displacement is-2.34mm, distance track 20.75m place's vertical displacement trough value is-1.65mm, distance track 52.8m place's vertical displacement trough value is-0.262mm, the Changing Pattern of vertical displacement is substantially identical with transversal displacement, vertical displacement Amplitude Ration transversal displacement amplitude is large many, and therefore the response of overpass post bottom is based on vertical displacement.

(5) input corresponding material parameter and constraint condition, set up cross-line overpass three-dimensional finite element dynamic model according to physical size;

Certain cross-line overpass model, adopt general finite element analysis software ANSYS to carry out Finite Element Analysis Modeling and Analysis of Dynamic Characteristics to this overpass, the beam in computation model, plate and post are all by physical size modeling.Full-bridge spatial finite element model amounts to 13535 nodes, 12301 unit.The natural frequency of vibration adopts subspace iteration method to solve, and full-bridge finite element model is illustrated in fig. 8 shown below.

(6) according to the equation of motion of cross-line overpass, the mass matrix at its body of a bridge and bridge pier place, damping matrix and stiffness matrix are carried out the partitioning of matrix, derive the equation of motion of cross-line overpass under the effect of main track train non-uniform method, and adopt the numerical integration method of unconditional stability, the dynamic response of cross-line overpass under the effect of main track train non-uniform method can be tried to achieve.

Response under the ambient induced effect of vibration that this patent causes at train certain cross-line overpass is analyzed.Because bullet train seldom at overline bridge place, meeting occurs, when therefore calculating, only consider the operating mode that single line train is current at a high speed herein.Consider that overwhelming majority's vehicle speed that misses the stop is the speed of a motor vehicle of 310km/h, therefore figure below be main track train at a high speed by immediately below cross-line overpass time, the cross-line overpass adopting the non-uniform method computing method of this patent to obtain main track train with the 310km/h speed of a motor vehicle by time footbridge main track span centre place's vertical motion and the displacement of transverse vibration dynamic response and acceleration-time curve

Respectively as shown in Figure 9 and Figure 10.

Through above-mentioned steps, obtain the dynamic response of cross-line overpass under the effect of main track train non-uniform method.

Should be understood that, for those of ordinary skills, can be improved according to the above description or convert, and all these improve and convert the protection domain that all should belong to claims of the present invention.

Claims (4)

1., about computing method for cross-line overpass dynamic response under the effect of main track train non-uniform method, comprise the following steps:

(1) basic parameter of train, track is inputted, auto model, model trajectory is set up respectively according to car track coupling dynamics principle, according to wheel-rail contact relationship, set up train track system Coupled Dynamics two-dimension analysis model, this model is two-dimentional rigid body kinematics model; The basic parameter of described train, track comprises: the quality that train body, bogie and wheel are right and moment of inertia, train body and bogie, bogie and wheel between stiffness coefficient and ratio of damping;

(2) Train Track system, coupled dynamics two-dimension analysis model is utilized, simultaneously according to train, track physical parameter, act on the exciting force time-history curves on rail node when obtaining main track train high-speed cruising, the ambient vibration caused for solving train operation further provides vibration source to encourage;

(3) track-sleeper-the earth three-dimensional finite element TRANSFER MODEL is set up, analyze the attenuation law of the earth vibration on ground caused by bullet train according to this three-dimensional finite element model, thus obtain the ambient vibration ripple time-history curves acting on cross-line overpass bridge pier place;

(4) determine according to the ambient vibration ripple time-history curves acting on cross-line overpass bridge pier place during main track train high-speed cruising the time-histories data curve acting on cross-line overpass bridge pier place, this vibration wave is all not identical on the Time and place variation characteristic at each bridge pier place, obtains the exciting force time-history curves acting on cross-line overpass bridge pier place thus;

(5) input corresponding material parameter and constraint condition, set up cross-line overpass three-dimensional finite element dynamic model according to physical size;

(6) obtain according to Finite Element the equation of motion that the dynamic load time-history curves acted on each node of overpass sets up cross-line overpass, the mass matrix at its body of a bridge and bridge pier place, damping matrix and stiffness matrix are carried out the partitioning of matrix, derive the equation of motion of cross-line overpass under the effect of main track train non-uniform method, and adopt the numerical integration method of unconditional stability, the dynamic response of cross-line overpass under the effect of main track train non-uniform method can be tried to achieve.

2. computing method according to claim 1, is characterized in that, step 6) in the equation of motion of cross-line overpass be:

In formula: [M _aa], [C _aa] and [K _aa] represent the mass matrix of the body of a bridge, damping matrix and stiffness matrix respectively; { x _a, with be respectively the displacement of the overpass body of a bridge, speed and vector acceleration; F ' _wexpression other loads suffered by the body of a bridge; { x _bit is the displacement at bridge pier place.

3. computing method according to claim 1, is characterized in that, described in step (1), system model only can consider vertical motion, also can consider the vibration of level and vertical both direction simultaneously.

4. computing method according to claim 1, is characterized in that, when setting up track-sleeper-the earth three-dimensional finite element TRANSFER MODEL in step (3), based on following theory hypothesis:

A () ignores the impact between structure and soil, think that namely the vibration displacement of effect bridge pier place soil is the displacement acting on bridge pier place;

B () ignores the discreteness of the road soil body, think that the soil body is continuous elastomeric, only consider linear analysis.