弹性基支自由边矩形板的非线性振动问题  

Nonlinear Problem of Vibration for Free Edge Rectangular Plate on Elastic Foundation

作　　者：曲庆璋[1] 梁兴 

机构地区：[1]青岛建筑工程学院基础部

出　　处：《振动工程学报》1996年第4期411-414,共4页Journal of Vibration Engineering

基　　金：冶金部基础研究"有偿与资助"项目

摘　　要：弹性地基上四边自由矩形板的非线性振动分析是板理论中一个相当困难的问题，到目前为止这个问题还没有得到解决。本文首先给出一个包含三角函数和多项式组成的挠度函数和应力函数，这些函数满足在四个自由边上的全部边界条件。然后利用伽辽金法得到Ｄｕｆｉｎｇ方程。The nonlinear vibration analysis of rectangular plates with free edges on elastic foundation is a rather complicated problem in the theory of plates.Up to now,the problem has not been solved.In this paper,the deflection and stress function which consists of trigonometrical function and polynomial expression are first proposed.The two functions yield the whole boundary conditions on four free edges.Then the Duffing equation is derived got by using Galerkin method.

关 键 词：非线性振动 地基 弹性地基 矩形板 伽辽金方法 

分 类 号：O322[理学—一般力学与力学基础] TU435[理学—力学]