The Magnetoelastic Nonlinear Random Vibration Of Thin Plates

The theory and the application of random vibration involve many fields such asmathematics, mechanics and engineering. The theory of random vibration can servemultiple purposes, and its main purpose is to provide a solid foundation to improve thereliability for mechanical and structure which is under random load.A large share of magnetoelastic problems in engineering practice, are related to therandom vibration.The thin plates are widely used in the practical engineering application as structuralelements, and are often worked in coupled fields, such as electromagnetic field andmechanical field. The thin plate has great flexibility, so it’s easy to vibrate under theaction of the external excitation; properly speaking, all vibration is nonlinear, and manydynamic systems are nonlinear systems in essence. So the studying of magnetoelasticnonlinear random vibration problem has important theoretical significance and practicalapplication value.In this paper, we’ll study the problem of the magnetoelastic nonlinear randomvibration of a thin plate in the electromagnetic field.First, the partial differential equation of magnetoelastic nonlinear vibration of a thinplate in the electromagnetic field is derived; then, using the Galerkin method, thenonlinear random vibration equations of a rectangular or bar-type thin plate whose edgesare simply supported or clamped and a circular thin plate whose edge is simply supportedare derived, so the ITO equation of state is gotten; then, using FPK equation method, theprobability density function and variance of displacement response and speed response ofthe nonlinear random vibration are gotten. At last, using numerical simulation, theprobability density function and variance of displacement response and speed response ofthe nonlinear random vibration are gotten, and through analyzing the probability densityfunction and variance, so we get some features of the nonlinear random vibration andprovide some methods to control the responses of the nonlinear random vibration.