A Study On Random Vibration Analysis Of Coupled Vehicle-bridge Systems By An Explicit Time-domain Method

Random deck or track irregularities may produce a remarkable effect on the dynamic vibration of coupled vehicle-bridge systems during high-speed driving.On the other hand,since bridges account for a larger and larger portion of the total length of high-speed railways than ever before,it is very probable that earthquakes occurr when vehicles pass over bridges.The vibration of coupled vehicle-bridge systems under both random deck or track irregularities and random earthquakes exhibits typical non-stationary stochastic features.The random vibration problem of coupled vehicle-bridge systems has become a hot topic in civil engineering recently.However,there are few accurate and efficient random vibration analysis methods.Based on a newly-developed efficient random vibration method in recent years,namely,the explicit timedomain method,this dissertation is devoted to investigating the efficient method to calculate the random vibration responses of coupled vehicle-bridge systems.The proposed methods are applied to practical large and complex coupled vehicle-bridge systems for demonstrating the high efficiency and accuracy.The major work of this dissertation can be described as follows:(1)The literature review summarizes the research about the random vibration analysis methods for coupled vehicle-bridge systems.Firstly,the existing various types of models of coupled vehicle-bridge systems as well as the deterministic vibration analysis methods are summarized.Secondly,several types of typical track irregularities are presented,and random vibration analysis methods for coupled vehicle-bridge systems are expounded,after which their advantages and disadvantages are discussed thoroughly.Finally,the research progress about random vibration analysis of coupled vehicle-bridge systems under earthquakes is presented.(2)Random vibration analysis method for coupled vehicle-bridge systems under deck irregularities is investigated.Firstly,explicit formulations for the dynamic responses of the vehicle and bridge subsystems with respect to the wheel-track contact forces are established.By using the motion compatibility condition between the vehicle and the bridge,the explicit expression for the vehicle-bridge contact force in terms of deck irregularities is then derived.Consequently,the explicit expression for the critical responses of concerned DOFs of the vehicle and bridge subsystems in terms of deck irregularities are obtained.On that basis,the stochastic dynamic responses of coupled vehicle-bridge systems can be readily obtained by the explicit time-domain direct statistical-moment method or the explicit time-domain Monte-Carlo method.(3)Random vibration analysis method for coupled vehicle-bridge systems under both deck irregularities and earthquakes is investigated.Firstly,explicit formulations for the dynamic responses of the vehicle and bridge subsystems with respect to the wheel-track contact forces and seismic accelerations are established.By using the motion compatibility condition between the vehicle and the bridge,the explicit expression for the vehicle-bridge contact force in terms of deck irregularities and seismic accelerations is then derived.Consequently,the explicit expression for the critical responses of concerned DOFs of the vehicle and bridge subsystems in terms of deck irregularities and seismic accelerations are obtained.On that basis,the stochastic dynamic responses of coupled vehicle-bridge systems can be readily obtained by the explicit time-domain direct statistical-moment method or the explicit time-domain Monte-Carlo method.(4)The above method is applied to a certain suspension bridge,which is a practical and complex bridge with 6602 degrees of freedom to calculate the stochastic dynamic responses of coupled vehicle-bridge systems.Both the stochastic responses under track irregularities with and without seismic excitations are considered.The results of the proposed methods are compared with those by traditional Monte-Carlo method to demonstrate the feasibility and efficiency of the proposed method,as well as its potential of being applied in random vibration analysis of large-scale constructions in practical engineering.The proposed methods can fully cope with physical and probability evolution processes of the coupled problem in a relatively separated manner based on the closed-form explicit formulations of dynamic responses,which is capable of avoiding repeatedly solving the equations of motion for the coupled vehicle-bridge systems.Furthermore,a dimensionreduction scheme is involved for the calculation of the statistical moments of concerned responses as well.Numerical examples indicate that the proposed method yields high accuracy and superior computational efficiency.Such an effective way has a good prospect for random vibration analysis of large and complex coupled vehicle-bridge systems.