BIFURCATION AND CHAOS OF A SIMPLY SUPPORTED THIN CIRCULAR PLATE UNDER COUPLING ACTION OF AN ELECTROMAGNETIC FIELD AND A MECHANICAL FIELD

The problem of bifurcation and chaos of a simply supported thin circular plate under coupling action of a electromagnetic field and a mechanical field is studied.Based on nonlinear electro-magneto-elastic equations of the thin circular plate and the expression of electromagnetic forces,the vibration equations of the thin circular plate under an uniform transverse magnetic field,a round current and a mechanical loading are obtained and then solved numerically using the fourth order Runge-Kutta method.By varying the frequency of the mechanical loading,the state of the system is changed from periodic to chaos.This can be determined by the bifurcation diagram and the Lyaponov exponent diagram.Diagrams of displacement,phase trajectory and Poincare map are given for some examples.The infliences of the magnetic field and the electrical current on the vibration behavior of the system are discussed.