Pointwise Stabilization in the Laminated Beam Model

We consider two identical beams on top of each other with an adhesive in the middle. A slip occurs naturally in the structure. In this work, we take this slip into account and show that we can stabilize the system exponentially using pointwise controls applied on the axial force and the bending moment. The model consists of three coupled equations. The first two equations are related to the Timoshenko system and the third equation describes the dynamics of the slip. Our result improves previous results in the sense that it addresses the smaller dissipative effect, the point mechanism. To do this, we introduce a new method that allows us to show the exponential stability of systems of partial differential equations with point dissipation.