The First Passage Problem Of Current Carrying Strip Plate In The Tmagnetic Field

In civil,mechanical,aerospace and other engineering fields,random vibration phenomena often occur.With the development of aircraft,medical equipment and other precision instruments and the speed by means of transport,the nonlinear vibration phenomenon happen in mechanical structure for the first time through the related topics of research increasingly important.The strip plate small deflection for the problem of first time through,the strip plate large deflection for the problem of the first time through and a current-carrying strip plate deflection deformation through problem in magnetic field is studied.By a random vibration model is established.According to the Hamilton theory and the Galerkin principle in random vibration theory,the Hamilton motion differential equation of strip plate excited by Gauss white noise is obtained.The Hamilton motion differential equation is transformed into Ito? partial differential equation to determine the diffusion coefficient and the drift coefficient,and then the diffusion coefficient and the drift coefficient are solved by using the stochastic average theory.And then we get the backward Kolmogorov equation and first moment of first crossing time which satisfy the generalized Pontryagin equation.The reliability of the system can be obtained by solving the backward kolmogorov equation.By solving the generalized Pontryagin equation,the average first crossing time of random vibration of the system can be obtained.Through the study of the first crossing of caring electricity strip plate,it is concluded that the Hamilton energy of the system,the intensity of Gauss white noise excitation,the intensity of the magnetic field and the current intensity are the factors affecting the diffusion coefficient and the drift coefficient.The diffusion coefficient and drift coefficient determine the solution of the backward Kolmogorov equation and the generalized Pontryagin equation.Therefore,the system's Hamilton energy,Gauss white noise excitation intensity,magnetic field intensity and current intensity determine the reliability and average first passage time.