Analysis Of Dynamic Characteristics And Response Of Bridge Based On Vehicle-bridge Coupling

With the continuous improvement of China’s comprehensive national strength,highway and bridge construction has been rapid development.The progress of science and technology and the use of new materials have improved the level of bridge construction,making the span of bridge structure larger,lighter weight,stiffness greater.The number of vehicles running on the bridge increases with each passing day,and the speed of the vehicles is getting faster and faster.Under such a background,the coupled vibration of the vehicle and bridge becomes more and more serious.Based on vehicle-bridge coupling vibration,the dynamic characteristics of bridge are analyzed in detail in this paper.The vibration differential equation of the system is written in the form of matrix,and the solution is programmed by Wolfram Mathematica software.In this paper,starting with the analysis of the free vibration and forced vibration of the bridge,the natural vibration characteristics of the bridge are studied,the vibration of the Euler-Bernoulli beam is discussed in detail,and the analytical solution of the dynamic response of the simple supported beam with constant cross section is given by using the Duhame integral.Several discrete approximations for continuous systems are discussed in this paper,and a method for calculating the natural frequencies and modes of simply supported beams with variable cross-section based on the transfer matrix method is presented.Then,three kinds of multi-degree of freedom analysis methods are introduced:the finite element method,the modal superposition method and the synthetic modal method,and the numerical methods of the differential equation:the central difference method,the Wilson-θ method and the Newmark-β method.Then,the vehicle-bridge coupling vibration problems of three classical vehicle models are studied in detail.Based on the modal superposition method,the vehicle-bridge coupling equilibrium equations of uniform moving load,concentrated mass and mass spring systems are established respectively.According to the relation between the continuous system and the multi-degree-of-freedom system,the differential equation is transformed into a matrix.In this paper,Newmark-β method and Wolfram Mathematica software are used to calculate the dynamic response of the bridge when studying the vibration of the vehicle-bridge coupling problem of the mass spring model,that is,the quarter-vehicle model.The influence of vibration mode number,vehicle speed,bridge span and bending stiffness on the displacement,bending moment and shear force of the bridge is discussed under three vehicle models respectively.Finally,the dynamic response analysis of the bridge under the action of multiple vehicles is discussed,and the effects of vehicle spacing,vehicle mass ratio and vehicle velocity ratio on the internal force and deformation of the bridge are discussed.