The First Passage Of Current Carrying Micro-nano Plate In Magnetic Field

When the structure is under the micro-nano scale,the mechanical properties of materials will be significantly different from the macroscopic case,and the traditional continuum theory is no longer applicable to study the mechanical properties of micro-nano structures.However,by considering the interaction factors of the internal structure of the material,the micro-scale theory introduces additional constants related to the intrinsic length of the material into the constitutive relation,and accurately describes the scale effect.Considering that there are many uncertain factors in the external excitation of micro-nano structure in practical engineering application,so it is necessary to study the nonlinear dynamics of micro-nano structure under random excitation.In this paper,the first passage of current-carrying micro-nano thin rectangular plates in magnetic field is studied based on two micro-scale theories.The nonlinear stochastic dynamics model of the four-sided simply supported current-carrying micro-plate under the action of magnetic field is established by using the modified couple stress theory and Galerkin method.And the backward Kolmogorov equation and the generalized Pontryagin equation describing the first passage problem are obtained by using the oIt ? stochastic differential equation of the system derived by Hamilton stochastic average method.The numerical solutions of the two equations were obtained by Matlab,and the effects of the initial vibration energy,material intrinsic length,noise amplitude and magnetic induction intensity on the first passage of the system are discussed.The nonlinear stochastic dynamics model of four-sided simply supported current-carrying nano-plate under the action of magnetic field is established by combining the nonlocal elasticity theory and Galerkin method.The oIt ? stochastic differential equation of the system is derived by Hamilton stochastic averaging method,and the backward Kolmogorov equation related to the reliability function of the system and the generalized Pontryagin equation related to the average first passage time are obtained.Let the reliability function,the probability density function of the first passage time and the average first passage time are taken as the three measures of the first passage problem.And according to the simulation results of Matlab,to study the variation law of the system's first passage problem under four different system parameters: initial vibration energy,material intrinsic length,noise amplitude and magnetic induction intensity.