A model for passive damping of a membrane

We introduce a model in which a wire made of shape memory alloy is used to passively damp the vibrations of a membrane. The mechanical energy of the membrane is transformed into heat via the thermo-elastic properties of the shape memory alloy. We describe the model and prove existence and uniqueness of solutions. Finally we will show that for suitable initial and boundary conditions, the energy of the entire system is a decreasing function.