大挠度简支矩形薄板受热力磁耦合作用分岔与混沌  

Bifurcation and chaos of a thin rectangular plate simply supported with large deflection in a coupled environment of heating,force and magnetic field

作　　者：王平[1,2] 陈蜀梅[3] 王知人[2,3] 

机构地区：[1]燕山大学建筑工程与力学学院,河北秦皇岛066004 [2]中国科学院力学研究所非线性力学国家重点实验室,北京100080 [3]燕山大学理学院,河北秦皇岛066004

出　　处：《振动与冲击》2013年第7期129-134,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(11172024);非线性力学国家重点实验室开放基金资助项目;河北省自然科学基金(A2012203140)

摘　　要：研究大挠度四边不可移简支薄板在机械载荷、电磁场与温度场耦合作用下的混沌运动。在板壳与磁弹性力学理论基础上,考虑温度场影响,推导出在横向稳恒磁场与机械载荷共同作用下薄板的非线性磁弹性耦合振动方程。利用Melnikov函数法,求出该动力系统Smale马蹄变换意义下出现混沌运动条件,并对该系统振动方程进行数值模拟。通过算例得到系统分岔图、位移波形图、相平面轨迹及庞加莱截面图。讨论机械载荷、磁场及温度场参数对系统混沌运动影响。仿真结果表明,通过变化机械载荷、磁场及温度场参数,可控制系统的振动特性。Here, the chaotic motion of a thin rectangular plate simply supported with large deflection and four unmovable sides in a coupled environment of mechanical load, magnetic field and temperature field was investigated. Based on the theories of plates, shells and magnetic elasticity and considering the effect of temperature field, the nonlinear magnetic-elastic coupled vibration equations of the rectangular plate in the coupled environment of a transverse steady magnetic field and mechanical load were derived. Using Melnikov function method, the chaotic motion condition of the dynamic system under the meaning of Smale horseshoe transformation was obtained. The numerical simulations were performed with the vibration equations of the system. Through a specific example, the bifurcation diagram, the displacement wave diagram, the phase diagram and Poincare section diagram of this system were shown here. The influences of parameter variations including mechanical load, magnetic field and temperature field on the chaotic motion of this system were discussed. The simulation results shgowed that the vibration characters of this system can be controlled by changing parameters of mechanical load, magnetic field and temperature field.

关 键 词：大挠度 热磁弹性 耦合场 Melnikov函数法 分岔 混沌 

分 类 号：O343.1[理学—固体力学]