大挠度梁混沌运动的双模态分析

Study on the Chaotic Motion of a Large Deflection Beamby the Double Mode Analysis

本文计及几何非线性效应，研究了两端简支梁在横向周期性微扰作用下的混沌运动，建立了相应的非线性动力方程，采用Ｇａｌｅｒｋｉｎ原理将其化为二自由度的Ｈａｍｉｌｔｏｎ系统，利用Ｍｅｌｎｉｋｏｖ函数判定系统是否发生混沌运动，并与单模态法进行了对比分析，从中得到了一些有益的结论。

In this paper,the chaotic motion of a simply supported beam is studied.The nonlinear dynamic equation is established by Galerkin principle. It can be changed into a Hamilton system with 2-D.Using the method of Melnikov function whether the chaotic vibration occurs is determined.In the end,the double mode model is compared with the single mode model,some important conclusions are obtained.