The rate at which energy decays in a viscously damped hinged Euler–Bernoulli beam

Abstract

We study the best decay rate of the solutions of a damped Euler–Bernoulli beam equation with a homogeneous Dirichlet boundary conditions. We show that the fastest decay rate is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup, if the damping coefficient is in L∞(0,1).