Nonlinear Thermo-Electro-Magnetic Vibration And Chaos Of Rectangular Thin Plate

Thin plate is one kind of common project components, and they are usually installated in coupled fields, such as the mechanical field, electromagnetic field and temperature field and so on, the dynamic properties of the system have a significant impact on the structural safety. Therefore, study of many fields coupled dynamics of magneto-elastic thin plate is of great theoretical and practical significance. In this paper, the nonlinear elastic vibration and bifurcation and chaos or the rectangular thin plates in the electromagnetic fields, mechanical force and temperature field are studied. Based on the theory of sheet mechanics and magnetoelastic mechanics, the nonlinear system dynamics model of the rectangular Magnetoelastic thin plate is founded, the nonlinear free vibration, forced vibration and bifurcation and chaos of the thin plates are investigated and analyzed. Main results of the paper are as below:Nonlinear free vibration system dynamics model and dynamics differential equations of rectangular magnetoelastic thin plate are derived. Taken four-side simply supported rectangular plate as an example, the mode of free vibration for the thin plate is analysized. Approximative analytic solutions in time-domain of nonlinear free vibration are achieved by multiscale mechtod. Using the four-order Runge-Kutta method, the numerical solutions of the differential equations are got, and displacement curves and phase diagram of the system are drawn. The influences of the system response of electro-mechanical parameters are discussed.Nonlinear forced vibration system dynamics model and dynamics differential equations of rectangular magnetoelastic thin plate are reduced. Taken four-side simply supported rectangular plate as an example, one order approximative analytic solutions in time-domain of nonlinear forced vibration are achieved by multiscale mechtod. Stable time responses of the main resonance, superharmonic and subharmonic responses are computed and analyzed when excitation frequency is far from and near to natural frequencies of generating system. The influences of electromechanical parameters on the frequency responses of forced vibration system are discussed.The nonlinear vibration equations of thin rectangular plate coupled with electromagnetic fields and mechanical loads under different boundary conditions are obtained. The chaotic criterion of this system was got by Melnikov function method, and the vibration equation of the system was solved using the four-order Runge-Kutta method numerical method. And in the specific examples, the bifurcation diagram, the Lyapunov exponent diagram, the wave diagram of displacement, phase diagram and Poincare map are derived. The influences of magnetic parameter and mechanic loads on the vibration of the system are analyzed.Considering the influence of temperature field, the vibration equations of the rectangular thin plate under the action of mechanic field and steady transverse magnetic field are derived. By Melnikov function method, the chaos condition and judging criterion of the system under the condition of Smale horseshoe map are given. The vibration equations are solved numerically using the four-order Runge-Kutta method. By some examples, the bifurcation diagram, the Lyapunov exponents diagram, the displacement wave diagram, the phase diagram and the Poincare section diagram of the system are obtained. The influences of temperature field, electromagnetic field and mechanic loads on system vibration properties are analyzed.