Stochastic Dynamic Analysis Of Vehicle-(rail)-bridge Coupling System Based On Direct Probability Integral Method

The three subsystems of train,track,and bridge are coupled into a whole large system through the wheel-rail contact force and the bridge-rail interaction relationship,which induces coupled vibration of the system under various excitation.With the continuous increase of train load mass and running speed,the problems of running stability,safety and ride comfort caused by various random excitations become more and more prominent,and the stochastic dynamics analysis of vehicle-(rail)-bridge coupling system has become an important topic in academic and engineering communities.However,the existing analysis methods have shortcomings in the aspects of computational accuracy,efficiency and applicability for solving complex problems.The direct probability integral method is an accurate,efficient and unified new method suitable for linear and nonlinear stochastic vibration analysis and static and dynamic reliability evaluation of large structures.This thesis extends this method to analyze the random vibration of the vehicle-(rail)-bridge coupling system and evaluate the dynamic reliability of the bridge structure.The main research contents are presented as follows:Firstly,starting from the principle of conservation of probability,the probability density integral equation is derived to describe the random propagation of the system,and the key techniques of solving the equation are introduced: probability space subdivision and Dirac function smoothing.The probability density function of stochastic response of the system can be obtained by decoupling the probability density integral equation and the deterministic dynamic equation of the structure.Based on the failure criterion of first excursion,the probability density integral equation of the extreme value response is established by constructing an equivalent extreme value map.Subsequently,the probability density integral equation of the extreme response is integrated in the safety domain to compute the structural dynamic reliability under the framework of probability integral.Then,the dynamic models of the vehicle-bridge coupling system and the three-vehicle vehicle-rail-bridge coupling system are established,and the time-varying motion differential equations are derived in detail.The Newmark algorithm is used to calculate the dynamic response of coupling system.According to inverse Fourier transform method and trigonometric series method,the time-domain samples of the bridge deck and rail random irregularities are generated.Based on direct probability integral method,the probability density functions of acceleration of vehicle,midpoint displacement of rail and mid-span displacement of bridge are achieved under the combined action of vehicle moving load and bridge deck(rail)irregularity excitation,and the corresponding mean value and standard deviation are obtained.The influence of the number of representative points on the smoothness of the probability density function image and the accuracy of the calculation results is analyzed.The propagation regularity of random uncertainty to the stochastic responses in the coupled system is explored,and the impact of random excitation on driving safety and stability and riding comfort according to the vibration of each substructure is examined.The results show that compared to the midpoint displacements of bridge,the random acceleration responses of the vehicle body has greater differences;when multiple vehicles cross the bridge,the vibration of the rear vehicle is more complicated,and the vibration amplitude and frequency of the rear vehicle are sequentially increased compared to the front vehicle.Finally,based on the probability density function of extreme value of mid-span displacement of bridge and Heaviside function,the failure probability and first passage dynamic reliability of the bridge are calculated and verified by comparing with the calculated results of Monte Carlo simulation.The results of numerical examples indicate that direct probability integral method has high computational accuracy and efficiency in random vibration analysis and dynamic reliability evaluation of vehicle-(rail)-bridge coupling system.In addition,it is found that the midpoint displacement response of bridge reaches its maximum when the middle vehicle is about to pass the mid-span position,and the bridge structure is prone to damage.