Exponential stability for laminated beams with intermediate damping

Abstract

In this manuscript, we consider a system composed of two identical Timoshenko beams joined by an adhesive layer of negligible thickness, producing an interfacial slip. We introduce a dissipative mechanism not previously considered given by a(- ¿) ¿ut, 0 = ¿= 1 , a> 0 , which includes the frictional damping case (¿= 0) and the Kelvin–Voigt damping case (¿= 1). Using the semigroup theory of linear operators, we show the well-posedness of the system and demonstrate that its solutions decay exponentially.