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
1．College of Sciences ,Yanshan University, Qinhuangdao 066004； 2．The State Key Laboratoryof Nonliner Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080;3. College of Civil Engineering and Mechanics，Yanshan University，Qinhuangdao 066004
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.
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]. , 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 . , 2013, 32(7): 129-134.
2013, Vol. 32 
