The chaotic vibration of a metal plate with large deflection under a transverse magnetic field

Abstract

By using Karman’s plate theory of large deflection, the nonlinear equation of motion of a thin metal plate with the coaction of a transverse uniform magnetic field and a transverse load is established. These equations consider the magnetic Lorentz force induced by the eddy current. Based on the Bubnov-Galerkin method, the nonlinear partial differential equation is transformed into a third-order nonlinear ordinary differential equation. By using the sub-harmonic orbit Melnikov function method, the criterion of the Smale-horseshoe chaos is also acquired. Furthermore, the chaotic motion is numerically simulated with Matlab. The bifurcation diagram, the phase curve, the Poincaré map and the evolution curve are calculated. The digital characteristics of the chaotic motions are provided based on the analysis. The analysis results show that the magnetic induction intensity and the external load may affect the vibration of the system.