Current Carrying Circular Plate Stochastic Bifurcation In The Magneticfield

Circular thin plate in the aviation, shipbuilding, construction and other widely used in practical engineering. But it has large deflection deformation. Thus the stability of the domestic and foreign scholars on the vibration is analyzed, but is a deterministic system. Joined the random incentive factors in the study, by applying some nonlinear random vibration of plate and shell theory of stochastic stability is studied.This article first to the theory of stochastic averaging method and lyapunov index for simple instructions, and then through the magnetic elastic plate and shell theory of random vibration of circular plate under the magnetic field of establishing dynamics model, according to the Hamilton’s principle to analyze the local and global stability, deduces its bifurcation condition.For the first time through the problem did briefly the basic concept and meaning, and the reliability and its related functions, the concept of condition probability density and backward Kolmogorov equation and the formula derivation is presented, and then through the finite difference method and define the initial conditions and boundary conditions on the system of the backward Kolmogorov equation numerical solution, finally, the vibration model of the influence of various parameters on the reliability for the specific analysis.Finally, the concept and significance of the optimal control to do a simple introduction, and control of its related constraints, performance index, system controlled vibration equation, formula derivation of the concept of value function, control law, and so on made in this paper, and then through the stochastic averaging method and dynamic programming theory is deduced in the circular plate in the study of stochastic dynamic programming equation of random vibration system, and then through the finite difference method and the initial conditions and boundary conditions on the system of the definition of the stochastic dynamic programming equation numerical solution, finally, including control factor, the influence of parameters on the system reliability are detailed analyzed.