车路耦合振动中Galerkin截断收敛阶数的研究

Analysis of the Galerkin Tuncation Convergence Term in the Vehicle-pavement System

Galerkin截断法是研究车路耦合系统动力学响应的常用方法。将路面假设为非线性黏弹性地基夹层梁模型,车辆假设为匀速运动的弹簧振子,建立车路耦合系统的振动方程。基于路面线性固有频率,提出两种确定Galerkin截断收敛项的有效方案,并分析系统耦合振动响应的收敛性。观察不同车速下的路面响应和车辆振动位移。当车身发生共振时,分析不同路面厚度下Galerkin截断数对系统收敛性的影响。讨论系统达到收敛时,车辆悬架刚度和阻尼,路面不平度波长和幅值对路面变形和车辆振动位移的影响。数值研究表明,提出的方案对车路耦合系统的收敛性判断具有较高的准确性,大大提高了计算效率,对研究人员解决车路耦合系统动力学问题有一定的促进作用。

The Galerkin truncation method is a commonly used method to study the dynamic response of vehicle-pavement systems. The pavement and the vehicle are modeled as a sandwich beam on the nonlinear viscoelastic foundation and a spring vibrator with uniform speed, respectively. The coupled vibration equation of vehicle-pavement system is established. Two effective schemes for determining the Galerkin truncation convergence term based on the linear natural frequency of the pavement are proposed. The convergence of the coupled vibration response is analyzed. The pavement response and the vehicle vibration displacement at different speeds are observed. The influence of the Galerkin truncation term on the convergence of the system under different pavement thickness is analyzed. The effects of the vehicle suspension stiffness and damping, road roughness wavelength and amplitude on the pavement deformation and the vehicle vibration displacement when the system reaches convergence are discussed. Numerical investigations prove that the proposed schemes have high accuracy for judging the convergence of the vehicle-pavement system, and can greatly improve the calculation efficiency. It has a certain role in promoting researchers to solve the dynamic problems of vehicle-pavement system.