Stability of an interconnected system of Euler–Bernoulli beam and wave equation through boundary coupling

Abstract

In this paper, we study the stabilization of a coupled system of Euler–Bernoulli beam through boundary coupling with a wave equation, where the dissipative damping is designed only at the wave equation. By using the Riesz basis approach, we prove the whole system is exponentially stable, which says that the damped wave equation can stabilize the Euler–Bernoulli beam only through boundary coupling. The theoretical results are validated via a numerical simulation.