Research On The Stability Of Euler-Bernoulli Beams System

Researches concerning the stabilization is always one of important research prob-lems for modern control theory.In this thesis,we consider the stability of Euler-Bernoulli beam with interior time delays and the stability of Euler-Bernoulli beam equation with locally distributed disturbance,respectively.The main contents are as following:Firstly,we consider the stability of Euler-Bernoulli beam with interior time delays and boundary damping.The well-posedness of the closed-loop system is investigated by the C₀semigroup theory.Using the Lyapunov function method,we constructed a Lyapunov functional for the system,transformed the exponential stability issue of system into the solvability of the inequality equations.By analyzing the relationship between delays parameters?and damping parameters?,we obtain the??,??-region of the exponentially stability for the system,and analyze the best decay rate?^*.At the same time,numerical simulations are carried out to prove the validity of the research result.Secondly,we study the stability of Euler-Bernoulli beam equation with locally distributed disturbance.We design a feedback controller to reduce the effects of the disturbances.We prove the well-posedness of the nonlinear closed-loop system by the theory of maximal monotone operator.We study the asymptotic stability of the system by constructing appropriate Lyapunov functionals.