Bifurcation and chaos of a 4-side fixed rectangular thin plate in electromagnetic and mechanical fields

Abstract

We studied the problem of bifurcation and chaos in a 4-side fixed rectangular thin plate in electromagnetic and mechanical fields. Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and the expressions of electromagnetic forces, the vibration equations are derived for the mechanical loading in a steady transverse magnetic field. Using the 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 a fourth-order Runge-Kutta method. Its bifurcation diagram, Lyapunov exponent diagram, displacement wave diagram, phase diagram and Poincare section diagram are obtained.