Magneto-Elastic Combination Resonance of Rotating Circular Plate with Varying Speed Under Alternating Load

Abstract

Nonlinear magneto-elastic combined resonance of parametric and forced excitations is investigated for a rotating circular plate with a variable speed under alternating load. According to the magneto-elastic vibration equations of a conductive rotating thin circular plate, the axisymmetric vibration differential equations of the rotating circular plate under transverse magnetic field are obtained through the application of the Galerkin integral method. The method of multiple scales is applied to solve the differential equations of the circular plate under alternating magnetic field, and the resonance states of the system under combined parametric and forced excitations are obtained by analyzing secular terms. The respective amplitude–frequency response equations are also derived, as well as the necessary and sufficient conditions of the system to make it stable. A numerical method is adopted to acquire amplitude–frequency response curves, bifurcation diagrams of amplitude and the variation pattern of amplitude with magnetic induction intensity and radial force. The influence of parameter variation on stability of the system is also investigated. Based on the global bifurcation diagram of the system, the influence of the change of bifurcation parameters on the system dynamics is discussed.