Magneto-Aero-Elastic Superharmonic and Subharmonic Resonances, Bifurcations and Chaos of Conductive Spinning Circular Plates

Abstract

This paper focuses on the magneto-aero-elastic nonlinear resonances, bifurcations and chaos for superharmonic and subharmonic responses of conductive circular plates spinning in air and magnetic fields. The electromagnetic forces acting on in-plane are presented by using electromagnetic field theory, and a rotational dissipative damping aerodynamic model is employed to characterize the aerodynamic forces acting on the plates. Considering the effects of the geometric nonlinearity and centrifugal tensioning, the magneto-aero-elastic governing equations of spinning conductive circular plates are derived by the Hamiltonian principle. Based on the mode shapes with Bessel functions, the transverse nonlinear vibration differential equations of spinning plates with clamped-edge are derived by the Galerkin method. Amplitude-frequency equations for subharmonic and superharmonic responses are obtained by using the approach of multiple scales, respectively. Numerical calculations indicate the influences of important parameters (e.g. magnetic field intensity, excitation amplitude and rotational speed) on amplitude frequency characteristics. Moreover, it is demonstrated by the numerical results that system responses are sensitive to the variation of these important parameters, where the complex intermittency, period-doubling and chaotic dynamical behaviors exist.