First Passage Failure And Optimal Control Of Double-layer Microplate

With the development of applied science,the research of slab,beam and other basic structures has entered the micro level.In previous studies,the work on static deformation,boundary condition analysis and vibration characteristics acquisition of micro-mechanical components has been relatively perfect,but the work on establishing a universal stochastic dynamic model and analyzing the reliability of micro-structures under random excitation is still weak.The main objective of this study is to determine the region where the local stability of the piezoelectric double-layer micro-plate system is low under electrostatic excitation.Firstly,based on strain gradient theory and Hamilton's principle,the dynamic governing equation of simply supported double-layer micro-plates driven by electrostatic force is established.Then,the first passage failure of double-layer micro-plates in piezoelectric model is analyzed by using stochastic averaging theory.The average first-passage time?₁?H ₀?,conditional reliability function R?t H₀?and conditional probability density of the first-passage time P??H₀?are obtained.Finally,the above-mentioned first-passage characteristic parameters are numerically simulated by using MATLAB,and the effects of different intensity electrostatic excitation on the first-passage phenomenon of double-layer micro-plates are compared.The optimal control of the mathematical model of piezoelectric system is realized by Hamilton-Jacobi-Bellman equation.The feedback response of the controlled system is compared with that of the uncontrolled system.The results of numerical examples show that with the increase of service time,the decline speed of system reliability has undergone a process of first slow,then fast and then slow.The conditional probability density of the first passage time P??H₀?is very sensitive to the change of the excitation,although the effect of the change of the excitation on the average first-passage time?₁?H ₀?is not obvious on the whole.When the system is in the stage of rapid reliability reduction,the impact of excitation amplitude on the first passage failure of the system is most obvious.This interval is the optimum interval to improve the system reliability and achieve optimal control by controlling the excitation intensity.