The Nonlinear Magneto-Elastic Vibration and Stability of Current-Conducting Thin Plate in Longitudinal Magnetic Field

Abstract

Based on the Maxwell equation and Kirchhoff assumption of thin plate, nonlinear magneto-elastic vibration equation, electrodynamics equation and electromagnetic force expressions of current-conducting thin plate were deduced. Furthermore, nonlinear super-harmonic resonance of thin beam-plate under lateral mechanical motive load in longitudinal magnetic field was studied. Considering the thin plate simply supported on two opposite sides, the magneto-elastic coupled vibration differential equations about function of displacement of vibration and electric field intensity were obtained by the method of Galerkin. Then, the amplitude-frequency response equation under super-harmonic resonance was derived by using method of Multiple scales. Correspondingly the stability of stable solution was analyzed. Through the numerical calculation, characteristic curves of amplitude changing with detuning parameter, the excitation amplitude and the magnetic intensity. At last, the influence of electric-magnetic and mechanic parameter on resonance phenomenon and stability of solution was analyzed.