Study on primary resonance and bifurcation of a conductive circular plate rotating in air-magnetic fields

摘要

Based on the Kirchoff plate theory and Hamiltonian principle, the magneto-aeroelastic nonlinear governing equation for the forced vibration of the rotating conductive circular plate is derived. According to principles of electromagnetic field combined with a simplified aerodynamic model, the expressions of electromagnetic force and aerodynamic load of rotating circular plate are presented. The transverse nonlinear forced vibration differential equation of simply edge rotating circular plate is achieved by Galerkin method, where Bessel functions are utilized to a mode shape. Amplitude-frequency response equation of the system is obtained by using averaging. By numerical calculation, the amplitude-frequency curves of circular plate are plotted, and the influences of different parameters on amplitude-frequency characteristics of systems are analyzed, respectively. The dynamic behaviors of the system are investigated by means of bifurcation diagrams, maximum Lyapunov exponents and system responses under different controlling parameters.