Exponential Stability of Laminated Beams with Interfacial Slip

We study the stability of a one-dimensional laminated beam which consists of two identical layers of uniform thickness. An adhesive of small thickness is bonding the two layers and creating a restoring force thereby producing a damping called adhesive or structural damping at the interface. It is well-known in the literature that this single frictional damping is not strong enough to stabilize the system exponentially. On the contrary, we prove in this paper that the unique dissipation due to the structural damping is strong enough to exponentially stabilize the system provided the wave speeds of the system are equal.