The First Passage Of Current Carrying Circular Plate In Magnetic Field

In this paper,the first passage of current carrying circular plate in magnetic field is studied to investigate the failure mechanism of nonlinear vibration system in practical engineering application,enrich the research of the first passage problem and provide theoretical support for practical application.Based on the magneto elasticity theory of thin plates,the nonlinear random vibration mechanical model of the current carrying circular plate in magnetic field is built.The vibration equation of the circular plate in magnetic field is derived.Hamiltonian dynamical differential equation of the circular plate in the electromagnetic field is obtained by using the random vibration theory of continuous system and Galerkin integral method.The quasi-non-integrable Hamiltonian system converges to a one dimensional diffusion process by using the stochastic averaging method.The averaged Ito stochastic differential equation which is dominating the diffusion process is established.The conditional reliability function is proposed to describe the probability of this diffusion process in the special domain.A backward Kolmogorov equation governing the conditional reliability function is established.The conditional probability density of first-passage time is obtained subsequently.The first order conditional moment of the first passage time contents the generalized Pontryagin equation.The mean first passage time of the system is obtained by solving the generalized Pontryagin equation.Finally,the computing results of the conditional reliability function,the conditional probability density of first-passage time and the mean first passage time are analyzed synthetically.Using numerical analysis method,studied the first passage problem of circular thin plate.The influence of different boundary conditions,the changing of magnetic field,the changing of current density and the changing of other parameters on first passage time are discussed.The rationality of the method to investigate first passage problem in this paper is explained by using practical engineering applications and fundamental theorem.