MAGNETIC ELASTICITY CHAOTIC MOTION OF A THIN RECTANGULAR PLATE FIXED AT EACH EDGE WITH LARGE DEFLECTION

The chaotic motion for large deflection of a thin plate fixed at each edge under coupled action of mechanical load and electromagnetic field is investigated. Based on the theory of plates and shells and magnetic elastic mechanics,the nonlinear magnetic elastic coupled vibration equations of the plate under the coupled action of transverse steady magnetic field and mechanical load is derived. Using the Melnikov function method,the chaotic motion condition of the dynamic system under the meaning of Smale horseshoe transformation is obtained. The numerical simulation for the vibration equation of this system is 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 parameter variation of mechanical load and electromagnetic field to the chaotic motion are discussed. According to the simulation,the vibration characters of this system can be controlled by changing the parameters of mechanical load and electromagnetic field.