车路耦合非线性振动高阶Galerkin截断研究

将移动车辆模型化为运动的两自由度质量-弹簧-阻尼系统，道路模型化为立方非线性黏弹性地基上的弹性梁，并将路面不平度设定为简谐函数．通过受力分析，建立车路非线性耦合振动高阶偏微分方程．采用高阶Galerkin截断结合数值方法求解耦合系统的动态响应．首次研究不同截断阶数对车路耦合非线性振动动态响应的影响，确定Galerkin截断研究车路耦合振动的收敛性．研究结果表明，对于软土地基的沥青路面，耦合振动的动态响应，需要150阶以上的截断才能达到收敛效果．并通过高阶收敛的Galerkin截断研究了系统参数对车路耦合非线性振动动态响应的影响.

Nonlinear Vibration of Vehicle-Pavement Coupled System Based on High-Order Galerkin Truncation

The moving vehicle was modeled as a two DOF spring-mass-damper system. The pavement structure was modeled as an elastic beam on a nonlinear viscoelastic foundation. The nonlinear foundation and the road surface roughness were respectively assumed to be cubic and a harmonic function. The nonlinear partial differential governing equations of the vehicle-pavement coupled vibration were developed. The dynamic response of the coupled system was solved with the high-order Galerkin truncation method in conjunction with numerical method. The effects of different truncation orders on the dynamical responses of the vehicle-pavement nonlinear vibration were discussed, and the convergence of the Galerkin truncation to investigate the vehicle-pavement coupled vibration were determined for the first time. The study shows that the numerical investigation into dynamical response of the asphalt pavement on soft soil foundation needs over 150 terms.The influences of system parameters on the dynamical response were numerically studied via the high-order convergent Galerkin truncation method.