Locally Distributed Feedback Stabilization of Nonuniform Euler-Bernoulli Beam

In this article,we study the locally distributed feedback stabilization problem of a nonuniform Euler-Bernoulli beam.Firstly,using the semi-group theory,we establish the well- posedness of the associated closed loop system.Then by proving the uniqueness of the solution to a related ordinary differential equation,we derive the asymptotic stability of the closed loop sys- tem.Finally,by means of the piecewise multiplier method,we prove that,by either one distributed force feedback or a distributed moment feedback control,the closed loop system can be exponentially stabilized.