Study On Iterative Convergence Performance Of Vehicle-bridge Coupling Dynamic Analysis Algorithm

In the era of rapid economic development,China has built a huge number of bridges,and the number of vehicles in possession has increased year by year.The research on the coupling vibration between vehicles and bridges has received increasing attention from scholars.Vehicle-bridge coupling vibration has become an important research object for bridge researchers.Many studies have shown that there are many vehicle-bridge coupling analysis models,there are significant differences in solution methods,and numerical divergence problems are prone to occur.In order to improve the stability and convergence of the vehicle-bridge coupling solution process and accurately obtain the response of the vehicle-bridge subsystem,the research on the convergence performance of the vehiclebridge coupling dynamic analysis algorithm is very valuable.The main research contents and conclusions of this article are as follows:(1)Based on the D’Alembert principle,the dynamic analysis models of the 1/4vehicle and 1/2 vehicle close-fitting models are derived.The basic theory of vehicle bridge coupling iterative analysis,the contact relationship between vehicles and bridges,and the convergence and stability of numerical integration algorithms are described.The characteristics of eight different types of progressive integration algorithms are introduced and analyzed.(2)For the types of dynamic solutions for undamped vibration systems,multi degree of freedom forced vibration systems,nonlinear vibration systems,and random vibration systems,eight stepwise integration algorithms are analyzed and compared from the perspectives of stability,convergence,and computational efficiency.The applicability of different stepwise integration algorithms for each vibration system is evaluated.The results show that Newmark-β has the best adaptability to different vibration systems.(3)Based on MATLAB,the VBCA for analyzing and calculating vehicle-bridge coupling vibration is developed.The accuracy of VBCA is verified by moving concentrated forces and moving masses over a simply supported beam,and the phenomenon of divergence in the calculation of vehicle-bridge coupling close fitting model is revealed.Therefore,a simplified model of vehicle-bridge vibration is established(overall vibration model,dense separation iterative model,and non dense separation iterative model).In the dense separation iterative model,if the mass of the wheel set is greater than the mass of the bridge node under the wheel,the calculated dynamic response results will exhibit instability and non convergence.The spectral operators of the iterative operator matrix of the stepwise integration algorithm are calculated for the dense separation iterative model.The results show that the stability and convergence of the stepwise integration algorithm are related to the ratio of the wheel set mass to the bridge node mass under the wheel and the integration step length.When the integration step is too small and the mass of the wheel set is greater than the mass of the bridge node under the wheel,the spectral operator is greater than 1,and the dynamic response of the closely coupled vehicle bridge model will exhibit divergence.(4)Based on the stability influencing factors of the simplified vehicle-bridge model,a new assumption is proposed: when the mass of the wheel set is greater than the mass of the bridge node under the wheel,the acceleration of the wheel set should be related to the acceleration of the bridge node group under the wheel that is equivalent to its mass.At the same time,three iterative relaxation coefficients(static iterative relaxation coefficient,dynamic iterative relaxation coefficient,and adaptive dynamic iterative relaxation coefficient)are proposed to improve the convergence of the vehicle-bridge coupling algorithm.The effectiveness of the iterative relaxation coefficient is verified through the calculation of a simplified vehicle-bridge vibration model and a moving mass bridge model,and their calculation efficiency and accuracy are compared and analyzed.The results show that the dynamic iterative relaxation coefficient has the best effect.Finally,the dynamic iterative relaxation coefficient is applied to model of 1/4 close-fitting vehicle and 1/2 close-fitting vehicle passing through simple supported beam,model of 1/4 closefitting and non-close-fitting vehicle passing through continuous beam,and model of multiple close-fitting vehicles passing through a simply supported beam.The results show that the iterative relaxation coefficient can improve the stability,convergence,and accuracy of the calculation results of the closely coupled vehicle bridge analysis model.