横向均布载荷下亚音速大挠度薄板的混沌运动  

Chaotic motion of the subsonic plate with large deflection subjected to the transverse uniform load

作　　者：姚国[1] 李凤明[1] 

机构地区：[1]哈尔滨工业大学航天学院,黑龙江哈尔滨150001

出　　处：《振动工程学报》2012年第6期674-679,共6页Journal of Vibration Engineering

基　　金：国家重点基础研究发展计划(973)资助项目(2011CB711100)

摘　　要：研究了亚音速气动力与横向均布周期载荷共同作用下,四边简支大挠度板的混沌运动。采用von Karman板大变形理论与Hamilton变分原理,建立亚音速下大挠度板的运动方程,采用Lyapunov指数方法分析板从周期运动到混沌运动的来流速度阈值,应用四阶Runge-Kutta法对运动方程进行数值求解,计算系统的分岔图、位移时间历程曲线、相图和Poincaré映射,并与Lyapunov指数方法所得结果进行比较。研究结果表明,Lyapunov指数方法可以有效地判断出系统从周期运动到混沌运动的来流速度阈值,当来流速度达到速度阈值时,板由周期运动转化为混沌运动。The chaotic motion of a fully simply supported plate periodical uniform load is studied. The equation of motion of with large deflection subjected to subsonic flow and transverse the subsonic plate with large deflection was established using yon Karman＇ s large deflection theory and Hamiltonf s principle. The Lyapunov exponent method was used to determine the threshold value of the flow velocity when the periodic motion of the plate was transformed into chaotic one. Four-order Runge-Kutta method was used to solve the equation of motion. The bifurcation diagram, displacement-time history, phase di- agram and Poincar6 map were computed and compared with the results obtained by the Lyapunov exponent method. From the results, it is shown that the Lyapunov exponent method is an effective method in estimating the threshold value of the flow velocity for the chaotic motion of the system. When the flow velocity exceeds the threshold value, the periodic motion of the plate is transformed into chaotic one.

关 键 词：非线性 混沌运动 大挠度板 HAMILTON原理 LYAPUNOV指数 

分 类 号：O322[理学—一般力学与力学基础]