非线性Winkler地基上矩形薄板在移动荷载作用下的非线性动力分析

Nonlinear dynamic analysis for thin rectangular plate under moving vehicle loads on nonlinear winkler foundation

分析了非线性Winkler地基上矩形薄板在车辆移动荷载作用下的非线性动力特性。考虑地基反力的存在,基于Hamilton能量变分原理,建立了车辆、板、地基耦合系统非线性振动的控制微分方程;并将方程进行了量纲归一化处理,构造了满足周边自由矩形薄板全部边界条件的试探函数;运用伽辽金法和谐波平衡法对耦合系统控制方程进行了求解,讨论了板参数、地基参数、车辆系统参数等变化对耦合系统板振动幅频曲线的影响。结果表明:该耦合系统振动的频率都随板振幅的增大而增大;当板振动的幅值一定时,系统振动频率随着板厚、地基反应模量、车辆运行速度、车体刚度的增大而增大,但随着车体质量的增大而减小。因此,适当增加地基的反应模量可优化地基板的振动,并且从行车舒适性角度考虑,适当控制车速和车体刚度是有益的。

The nonlinear dynamic analysis for thin rectangular plate under moving vehicle loads on nonlinear foundation is studied in this paper. Considering the nonlinear foundation, the coupled governing equations for the nonlinear vibration of the thin rectangular plate under moving vehicle loads on nonlinear foundation are established based on the Hamilton principle and the equations are made in dimensionless. The trial functions are constructed to satisfy all the boundary conditions and the governing equations are solved by the Galerkin method and harmonic balance method. The influence of the plate thickness, foundation modulus and moving vehicle loads on the dynamic properties for the coupled system is also discussed. Then the following conclusions are reached：（1） With the coupled system vibration amplitude increase, the frequency tend to increase too;（2） The plate＇s vibration frequency trends to increase with the increase of its thickness, foundation＇s reaction modulus, vehicle speed and suspension stiffness when its vibration amplitude is invariant but decrease with the increase of vehicle mass. So it can optimize the coupled system vibration by increasing foundation reaction modulus and it＇s better to control the vehicle speed and increase its suspension stiffness while considering travelling comfortableness.