非线性弹性地基上矩形薄板产生分叉的参数条件

Parametric Conditions for Bifurcation of Rectangular Thin Plate on Nonlinear Elastic Foundation

根据非线性振动理论,以考虑地基板阻尼和非线性效应的小挠度非线性弹性地基上矩形薄板为研究对象;在得出的受横向均布简谐激励作用下,矩形薄板非线性运动学方程的基础上,对非线性弹性矩形薄板产生分叉的参数条件进行了研究;获得了非线性地基上矩形薄板产生静态和动态分叉的参数条件;得出了在横向激励幅值q或角频率ω很小时,非线性弹性地基上矩形薄板不容易产生静态和动态分叉;在一定的角频率ω以后,横向激励幅值q取任何值都会出现动态分叉;当横向激励幅值q和角频率ω同时取值比较大时,将产生静态分叉等结论。

This paper studies the thin rectangular plates on the nonlinear elastic foundation with small deflection and nonlinear effects based on the theory of nonlinear vibration. First, a nonlinear dynamical equation of the small deformation thin rectangular plate on nonlinear elastic foundation is established under the effect of transverse uniform distribution and harmonic excitation,. Then, the parametric conditions for bifurcation of nonlinear elastic rectangular plates are studied based on the equation from which the parameters of static and dynamic bifurcation of rectangular thin plate on nonlinear elastic foundation are obtained. It turns out that static and dynamic bifurcations will not be generated when the lateral excitation amplitude is q or the angular ω frequency is very small, dynamic bifurcations will occur within a certain angular frequency range,. and static bifurcation will occur when the lateral excitation amplitude q and the angular frequency ω are both large,.