四边固支热磁弹性矩形薄板的分岔与混沌  

Bifurcation and chaos of a four-sides fixed thermo-magneto-elastic rectangular thin plate

作　　者：朱为国[1,2] 白象忠[1] 

机构地区：[1]燕山大学建筑工程与力学学院,秦皇岛066004 [2]淮阴工学院交通工程系,江苏淮安223001

出　　处：《振动与冲击》2009年第5期59-62,共4页Journal of Vibration and Shock

基　　金：河北省自然科学基金资助项目(A2006000190)

摘　　要：研究在温度场、机械场与电磁弹性耦合作用下四边固定支撑矩形薄板的分岔与混沌运动问题。考虑温度场的影响,推导出在横向稳恒磁场和载荷共同作用下的四边固支矩形薄板的非线性磁弹性耦合振动方程。运用Melnikov函数方法,求出该问题在Smale马蹄映射下发生混沌运动的条件解。并对其进行了数值仿真,给出了该系统的分岔图、Lyapunov指数图、位移波形图、相平面轨迹图以及Poincare截面图,讨论了温度及电磁场强度对系统运动状态的影响。由仿真结果可知,通过变化温度场和电磁参数可以使系统进入混沌运动状态,或者避免混沌运动,以实现对系统振动特性的控制。Considering the effect of temperature,the vibration equations of the rectangular thin plate were derived under the coupled action of mechanic field,temperature and steady transverse magnetic field.By use of Melnikov function method,the chaos condition and judging criterion of the system under the condition of Smale horseshoe map were given.The numerical simulation was carried out.With some examples given,the bifurcation diagram,the Lyapunov exponents diagram,the displacement wave diagram,the phase diagram and the Poincare section diagram of the system were presented.The influences of electromagnetic field and temperature on system vibration properties were analyzed.From the simulation,it indicates that the characteristics of the vibration system can be modified and controlled and the system can be made to produce chaos motion or avoid chaos motion by changing the temperature and electromagnetic parameters.

关 键 词：弹性矩形薄板 热磁弹性耦合 四边固支 Melnikov函数方法 分岔与混沌 

分 类 号：O343.1[理学—固体力学] O482.6[理学—力学]