大挠度简支矩形薄板在热、力、磁耦合作用下的分岔与混沌

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振动与冲击 ›› 2013, Vol. 32 ›› Issue (7) : 129-134.

论文

大挠度简支矩形薄板在热、力、磁耦合作用下的分岔与混沌

王　平１，２，陈蜀梅３，王知人２，３

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BIFURCATION AND CHAOS OF A THIN RECTANGULAR SIMPLY SUPPORTED PLATE WITH LARGE DEFLECTION IN A COUPLED ENVIRONMENT OF HEATING, FORCE AND MAGNETIC FIELD

Chen-shumei Wang-ping Wang-zhiren Bai-xiangzhong

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摘要

本文针对大挠度四边不可移简支薄板，研究其在机械载荷、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的基础上，考虑温度场的影响，推导出在横向稳恒磁场和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的条件，并对该系统振动方程进行数值模拟。通过具体算例，得到了系统的分岔图、位移波形图、相平面轨迹及庞加莱截面图，讨论了机械载荷、磁场以及温度场的参数对系统混沌运动的影响。由仿真结果可知，通过变化机械载荷、磁场和温度场参数，可以控制系统的振动特性。

Abstract

In this paper, the chaotic motion for large deflection of a thin plate simply supported on the four sides and unmovable in a coupled environment of mechanical load, magnetic field and temperature field is investigated. Based on the theory of plates and 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 is derived. Using Melnikov function method, the chaotic motion condition of the dynamic system under the meaning of Smale horseshoe transformation is obtained.The numerical simulations about the vibration equation of the system are also presented. Through specific example, the bifurcation diagram, the displacement wave diagram, the phase diagram and the Poincare section diagram of this system are shown here. The influences of the parameters variation of mechanical load, magnetic field and temperature field to the chaotic motion of this system are discussed. From the simulation, the vibration characters of this system can be controlled by changing the parameters of mechanical load, magnetic field and temperature field.

导出引用

王　平;陈蜀梅;王知人;. 大挠度简支矩形薄板在热、力、磁耦合作用下的分岔与混沌 [J]. 振动与冲击, 2013, 32(7): 129-134

Chen-shumei Wang-ping Wang-zhiren Bai-xiangzhong. BIFURCATION AND CHAOS OF A THIN RECTANGULAR SIMPLY SUPPORTED PLATE WITH LARGE DEFLECTION IN A COUPLED ENVIRONMENT OF HEATING, FORCE AND MAGNETIC FIELD [J]. Journal of Vibration and Shock, 2013, 32(7): 129-134