Magneto-Aeroelastic Internal Resonances of a Rotating Circular Plate Based on Gyroscopic Systems Decoupling

Abstract

In this paper, a principal and 3:1 internal resonance of an edge-clamped conductive circular plate rotating in air-magnetic environment is investigated, where the electromagnetic force expressions and a simple empirical aerodynamic model are used in modelling. Based on the transverse displacement assumption with a combination of two degenerate linearized modes, the 2 degree of freedom (2-DOF) magneto-aeroelastic asymmetric nonlinear gyroscopic systems are derived by utilizing the Galerkin approach. The method of multiple scales and the solvable condition for the coefficient matrix of the gyroscopic systems is employed to decouple the 2-DOF nonlinear gyroscopic systems and achieve the nonlinear modulation equations of the steady state responses. The numerical results for the relationship between two eigenfrequencies verify the existence of 3:1 internal resonances of the circular plate rotating in air-magnetic field. In addition, the resonance amplitude varying with detuning parameters and excitation amplitudes are plotted under principal and 3:1 internal resonances, respectively. It is found that the system may lose stability generated by a Hopf bifurcation, which may finally evolve into chaotic state through period-doubling bifurcation of intermittent periodic responses.