参数激励和外激励联合作用下薄板的非线性动力学  

NONLINEAR DYNAMICS OF A PARAMETRICALLY AND EXTERNALLY EXCITED THIN PLATE

作　　者：郝五零[1] 张伟[2] 

机构地区：[1]云南师范大学数学学院,昆明650500 [2]北京工业大学机械工程与应用电子技术学院,北京100124

出　　处：《动力学与控制学报》2014年第2期139-146,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金重点资助项目(10732020);国家自然科学基金资助项目(11072008和10972011);国家自然科学青年基金资助项目(11002005)~~

摘　　要：研究了在参数激励和外激励联合作用下四边简支矩形薄板的非线性动力学.基于von Karman理论,推导出了在参数激励和外激励联合作用下四边简支矩形薄板的动力学方程.利用Galerkin法对偏微分方程进行三阶离散,得到一个三自由度的常微分方程.考虑1:2:4内共振-主参数共振-1/2亚谐共振的情况,利用多尺度法得到了薄板系统的六维的平均方程.最后,采用数值方法研究了薄板的周期和混沌运动.结果发现外激励对薄板的混沌运动是敏感的.The nonlinear dynamics of a four-edge simply supported rectangular thin plate under the combination of the parametrical and external excitations were investigated.Based on the von Karman theory,the formulas of motion for the four-edge simply supported rectangular thin plate under the combination of the parametrical and external excitations were derived.The partial differential equations were discretized to the ordinary differential equations with three-degree-of-freedom using the Galerkin approach.Considering the resonant cases of 1：2：4 internal resonance and principal parametric resonance-1/2 subharmonic resonance,the method of multiple scales was utilized to obtain the six-dimensional averaged equations.Furthermore,numerical method was carried out to investigate the periodic and chaotic motions of the thin plate.The results show that the chaotic responses of the thin plate are sensitive to the external excitation.

关 键 词：非线性系统 矩形薄板 多尺度法 平均方程 混沌 

分 类 号：O322[理学—一般力学与力学基础]