Laminated beams with thermoelasticity acting on the shear force

Abstract

In this paper, we study the stabilization of a laminated beam system under the action of a new thermal coupling. Motivated by the work of Almeida Júnior et al. in the context of the Timoshenko system, we consider a thermoelastic coupling acting on the shear force. The present work constitutes a generalization of Almeida Júnior's paper because our study model considers an interfacial slip. More precisely, if we make the parameter 𝛾 of our system go to infinity, we obtain the Timoshenko beam system studied by the authors. We show that the weakly dissipative system of our manuscript is exponentially stable if, and only if, the wave propagation speeds are equal. Otherwise, we show that the system is polynomially stable and that the associated semigroup decays with rate t −1∕2 . Furthermore, we show that this decay rate is optimal.