基于MATLAB的公路桥梁车桥耦合数值计算方法

应用达朗贝尔原理推导了两自由度车辆和桥梁的振动平衡方程,提出用龙格-库塔法和NEWMARK法来求解车桥耦合振动问题。针对NEWMARK法提出了求解分离的车辆和桥梁运动方程组的分析策略:在每一个时间步长内进行迭代计算并将桥梁的振动平稳状态作为收敛条件。利用MATLAB结合两种数值计算原理分别编制了车桥耦合计算程序。算例分析表明:两种方法的计算精度都较高;采用NEWMARK法求解时,在每个时间步内迭代计算至桥梁振动平稳状态是有意义的。

Numerical Method for Vehicle-Bridge Coupling Vibrations Based on MATLAB

The vibration balance equations for 2-dofs vehicle and bridge were derived with the employment of d'Alembert principle,and the two numerical methods,Runge-Kutta and NEWMARK,were put forward to solve the problem of vehicle-bridge coupling vibration.The analysis strategy was proposed for solving the separated vehicle and bridge motion equations according to NEWMARK method,which conducted iterative computation in each time step and considered the motion equilibrium state of bridge as condition of convergence.In consideration of Runge-Kutta and NEWMARK numerical calculation principals,computational procedures for vehicle-bridge coupling vibration were compiled by use of MATLAB respectively.It is demonstrated through example analysis that the two methods have processed precision.In the process of separated vehicle and bridge motion equations,it is meaningful that the iterative computation was conducted until the bridge reached vibration equilibrium state in each time step.