Exponential Stabilization of Nonhomogeneous Timoshenko Beam with Locally Distributed Feedbacks

摘要

In this paper, we prove that the nonuni-form Timoshenko beam is exponentially stabi-lizable with locally distributed feedbacks. We will apply the multiplier technique and the frequency domain method to prove our result. Indeed, finding an appropriate multiplier is crucial in establishing the exponential stabilization of nonuniform elastic systems whenever one uses the energy method or the frequency domain method. Recently, K. Liu and Z. Liu [6] introduced two quite efficient multipliers to establish the boundary exponential stabilization of the nonuniform Euler-Bernoulli beam equation with only bending moment feedback. We will employ the multiplier introduced in [6].