Research Of Stochastic Bifurcation And Reliability On Rectangular Thin Plate Vibration System

Rectengular thin plate is a kind of basic structure which is widely used in many engneering fields. Thin plate is easy to have big deformations and obvious vibration. Lots of researches have been done at home and abroad, but most of them focus on certainty system. It is necessary to discuss the character of rectengular thin plate vibration system in the frame of stochastic nonlinear dynamics theory for the external excitation is obviously stochastic excitation. This dissertation studies the complex nonlinear phenomenon in the semi-active suspension system and the control strategy using stochastic nonlinear dynamics theory. The main content is as follows:1. Applying the stochastic nonlinear dynamics theory to rectengular thin plate vibration system considering the impact of random factors. Simplifying in plate excitation as gauss white noise, establish v rectengular thin plate vibration system model based on stochastic nonlinear dynamics theory and Galerkin method, considering the law of force and acceleration. The max Lyapunov exponent is calculated by quasi non-integrable Hamiltonian theory and Oseledec multiplicative ergodic theory, the local stability conditions have been obtained; the global stability conditions have also been obtained by judging the modality of the singular boundary; the stochastic Hopf bifurcation is analyzed from the sharp change of stable and joint probability densities, and the parameter condition of stochastic Hopf bifurcation have been discussed through the numerical simulation.2. A two-dimension stochastic nonlinear dynamical model of rectengular thin plate vibration system has been presented considering the stochastic factor. The Hamilton function is described as one dimension diffusion process by using stochastic average method, the global stability conditions is also obtained by judging the modality of the singular boundary; the backward Kolmogorov equation for reliability function and the generalized Pontryagin equation for conditional moment of the first-passage time have been established, the numerical results are given according to the classification of boundary conditions and initial conditions of these two equations. At last, the charactor of first-passage on system had been analyzed.3. The optimal control strategy aimed to obtain the maximization of reliable function has been accessed by dynamic programming principles. The optimal control laws are"bang-bang"controls which are derived from the finit control force. Numerical simulations have been done with the backward Kolmogorov equation for reliability function and the generalized Pontryagin equation for conditional moment of the first-passage time which is under control by using finite difference method. The numerical results indicated that the security enhanced when the constrained control force increasd.