亚音速气流作用下薄板结构混沌运动的时滞反馈控制  

TIME-DELAYED FEEDBACK CONTROL OF THE CHAOTIC MOTION OF THE THIN PLATE IN SUBSONIC AIR FLOW

作　　者：姚国[1] 李凤明[1,2] 

机构地区：[1]哈尔滨工业大学航天学院,137信箱哈尔滨150001 [2]北京工业大学机电学院,北京100124

出　　处：《固体力学学报》2013年第5期521-526,共6页Chinese Journal of Solid Mechanics

基　　金：国家重点基础研究发展计划(973)项目(2011CB711100);国家自然科学基金项目(11172084和10672017)资助

摘　　要：研究了亚音速气流下非线性二维薄板结构在横向周期载荷作用下的混沌运动及控制问题.基于von Karman板理论和分离变量法,建立了亚音速下薄板结构的运动控制方程.对于未控系统,采用Melnikov方法判断其混沌运动阈值,并用Runge-Kutta法进行数值验证.对处于混沌运动状态的系统,采用时滞反馈控制方法对混沌运动进行控制.结果表明,Melnikov方法可以有效地预测系统的混沌运动行为,时滞反馈控制方法可以有效地将系统的混沌运动转化为周期运动.The chaotic motion and its control of a two-dimensional simply supported thin plate with geometric nonlinearity subjected to subsonic air flow and transverse periodical load are studied.Based on von Karman＇s plate theory and the variable separation method,the equation of motion of the thin plate under subsonic air flow is established.For the uncontrolled system,the Melnikov＇s method is used to predict the threshold values for the chaotic motion,and the results are verified numerically through the RungeKutta method.For the system under chaotic motion,the time-delayed feedback control is used to control the chaotic motion of the plate.From the analytical and numerical results,it is shown that the Melnikov＇ s method is effective in estimating the threshold values for the chaotic motion,and the time-delayed feedback control method can effectively transform the chaotic motion of the plate into periodical one.

关 键 词：亚音速 薄板 几何非线性 混沌运动 MELNIKOV方法 时滞反馈控制 

分 类 号：O415.5[理学—理论物理]