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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 behavior of rectangular thin plate on a nonlinear Winkler foundation under moving loads is analyzed. Considering the existence of the foundation reaction force, based on Hamilton energy variational principle, the governing differential equation of the nonlinear vibration of vehicle, slab and foundation coupling system is established. The equations are normalized by dimension and a set of equations The control function of the coupled system is solved by using the Galerkin method and the harmonic balance method. The influences of the plate parameters, the foundation parameters and the vehicle system parameters on the vibration amplitude-frequency curve of the coupled system board are discussed. The results show that the vibration frequency of the coupled system increases with the increase of the plate amplitude. When the amplitude of the plate vibration is constant, the vibration frequency of the system varies with the thickness of the plate, the reaction modulus of the foundation, the running speed of the vehicle, Increases and increases, but decreases with the increase of body mass. Therefore, appropriately increasing the reaction modulus of the foundation can optimize the vibration of the substrate, and from the viewpoint of ride comfort, it is beneficial to appropriately control the vehicle speed and the rigidity of the vehicle body.