Bifurcation and Chaos of a 4-Side Simply Supported Rectangular Thin Electro-Magneto-Elastic Plate in Many Fields

Abstract

The problem of bifurcation and chaos in a 4-side simply supported rectangular thin electro-magneto-elastic plate in electro-magnetic, mechanical and temperature fields is studied. Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and expressions of electromagnetic forces, vibration equations are derived for the mechanical loading in a nonlinear temperature field and a steady transverse magnetic field. By using Melnikov function method, the criteria are obtained for chaos motion to exist as demonstrated by the Smale horseshoe mapping. The vibration equations are solved numerically by using a fourth-order Runge-Kutta method. Its bifurcation diagram, Lyapunov exponents diagram, displacement wave diagram, phase diagram and Poincare section diagram are obtained for some examples. The characteristics of the vibration system are analyzed, and the roles of parameters on the systems are discussed separately as well, such as electromagnetic field intensity, temperature and mechanical force.