Exponential stability for laminated beams with intermediate damping

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 alpha(-Delta)(theta)u(t), 0 <= theta <= 1, alpha > 0, which includes the frictional damping case (theta = 0) and the Kelvin-Voigt damping case (theta = 1). Using the semigroup theory of linear operators, we show the well-posedness of the system and demonstrate that its solutions decay exponentially.