Stability Results for a Laminated Beam with Kelvin–Voigt Damping

Abstract

In this work, we consider a laminated beam subjected to Kelvin–Voigt damping. Under the semigroup theory approach, applying the Lumer–Phillips Theorem, we establish the well-posedness of the associated initial value problem. This paper aims to prove exponential and polynomial stability results when the system is fully and partially damped. First, using the method developed by Z. Liu and S. Zheng, we show that the semigroup associated with the fully damped system is analytic and, consequently, exponentially stable. On the other hand, we prove the lack of exponential stability when the system is partially damped, and then, using the Borichev and Tomilov Theorem, we prove its polynomial stability.