In this paper, the magneto-elastic nonlinear random vibration of a clamped rectangular thin plate in magnetic field is studied. According to the magneto-elastic theory of plates and shells and the theory of structural random vibration, the magneto-elastic nonlinear random vibration equation of a clamped rectangular thin plate in a magnetic field is derived. Then the nonlinear random vibration equation is transferred into the Ito differential equation, and the Ito differential equation is solved using FPK equation method. Thus the numerical characteristics of displacement response and velocity response of the rectangular thin plate are obtained. Finally, through a numerical example, the influences of magnetic field parameters on the numerical characteristics are discussed, and some methods which can be used to effectively control the random vibration responses of the plate are given.

Based on the vibration equation of beam plate, under mechanical loading in a uniform transverse magnetic field, the vibration equation of the conductive beam plate is reduced to two cases ,which is no-pertubation system and pertubation system. For pertubation system ,n-order harmonic orbit is given by means of the Melnikov method. Finally, the critical condition of chaos phenomena is given in the transformation of Smale horseshoe.