Evolutionary Random Response Of Coupled Vehicle-Bridge System Subjected To Multi-vehicle Loads

The coupled vibration between the vehicle and the bridge is caused by the interaction between the vehicle and the bridge when vehicles move on the bridge.The strength and stability of the bridge structure is affected by the vibration of the bridge,while the safety and ride comfort of the vehicle is affected by the vibration of the vehicle,thus the study on the vibration response of the coupled vehicle-bridge system is of great significance.For analysis,the bridge was simplified into a simply supported beam model according to Euler-Bernoulli beam theory,while the vehicle was reduced to a moving mass model,spring-mass model,quarter vehicle model and half vehicle model respectively.The vibration of the coupled vehicle-bridge system is consisted of two parts,one is the deterministic vibration response caused by the vehicle movement,and the other is the random vibration response caused by the bridge surface roughness.The vibration differential equations of the bridge and vehicles were established based on the vibration theory and the D'Alember principle to solve the deterministic vibration responses.Modal analysis method was introduced to transform the partial differential equations into ordinary differential equations with variable coefficients,then the numerical method was used to solve the ordinary differential equations.The vibration response of the coupled vehicle-bridge system excited by the bridge surface roughness can be reduced to the response of the linear time-varying system subjected to the evolutionary random excitation.The evolutionary random response can be obtained through the calculation of the transient response under the deterministic excitation according to the relevant methods of the evolutionary random response.When multiple vehicles pass through the bridge at the same speed and the speed of all vehicles is constant,if the parameters of each vehicle are equal and the distances between any two adjacent vehicles are the same,the vibration response of the coupled vehicle-bridge system is proved to be periodic.Thus the response of the entire process of the vehicles passing through the bridge can be reduced to the response in a single cycle,the amount of computation is largely reduced.