摘要
研究了大挠度矩形薄板受迫振动时的混沌运动，导出了矩形薄板的非线性控制方程；利用Ｇａｌｅｒｋｉｎ原理，将其化为二自由度的常微分方程组，从理论上证明了在讨论其混沌运动时可以归结为一个单模态问题；利用Ｍｅｌｎｉｋｏｖ函数法给出了发生混沌运动的临界条件，揭示出在此类新的非线性动力系统中。
The primary aim of this paper is to study the chaotic motion of a large deflection plate. Considered here is a buckled plate, which is simply supported and subjected to a lateral harmonic excitation. At first, the partial differential equation governing the transverse vibration of the plate is derived. Then, by means of the Galerkin approach, the partial differential equation is simplified into a set of two ordinary differential equations. It is proved that the double mode model is identical with the single mode model. The Melnikov method is used to give the approximate excitation thresholds for the occurrence of the chaotic vibration. Finally numerical computation is carried out.
出处
《应用数学和力学》
EI
CSCD
北大核心
1999年第4期346-350,共5页
Applied Mathematics and Mechanics
基金
国家自然科学基金
山西省自然科学基金
