受热双层圆薄板的混沌运动  

Chaotic Motion of a Heated Double-Layer Thin Circular Plate

作　　者：王永岗[1] 丁道红[1] 戴诗亮[2] 王新志[3] 

机构地区：[1]中国农业大学,北京100083 [2]清华大学,北京100084 [3]兰州理工大学,兰州730050

出　　处：《应用力学学报》2005年第4期653-656,共4页Chinese Journal of Applied Mechanics

摘　　要：考虑几何非线性和均匀静态温度的影响,研究了双层圆薄板在周期时变横向载荷作用下的混沌现象。首先采用Galerkin法得到了双层板关于时间的非线性动力学方程,而后利用Melnikov函数法,从理论上研究了双层板发生混沌的临界条件及参数范围。最后以某热致微型泵的驱动膜片为例,借助于计算机代数系统Maple进行定量搜索与模拟,并利用Poincaré映射和相平面轨迹以及Lyapunov指数等加以判断,结果表明受热双层板在非线性强迫振动时存在复杂的混沌运动。Considering the effect of geometric nonlinearity and uniformly distributed stationary temperature, the chaotic phenomena of a double-layer thin circular plate under transverse periodic excitation are investigated. The nonlinear dynamic equations for the double-layer plate are established by employing the Galerkins technique, then the critical condition for occurrence of chaotic motions is discussed theoretically with Melnikov function method. The chaotic motions are searched and simulated numerically for a driving membrane of thermal actuated micropump via Computer Algebra Systems Maple, and the Poincare map and phase curve along with Lyapunov exponent are used to evaluate if a chaotic motion appears. The results indicate some complex chaotic motions in the heated double-layer plate.

关 键 词：双层薄板 静态温度 MELNIKOV函数 混沌运动 POINCARÉ映射 LYAPUNOV指数 

分 类 号：O322[理学—一般力学与力学基础]