| Abstract: | We consider two mathematical models that describe the vibrations of spring-mass-damper systems with contact and friction.
In the first model, both the contact and frictional boundary conditions are described with subdifferentials of nonconvex functions.
In the second model, the contact is modeled with a Lipschitz continuous function, and the restitution force is described by
a differential equation involving a Volterra integral term. The two models lead to second-order differential inclusions with
and without an integral term, in which the unknowns are the positions of the masses. For each model, we prove the existence
of a solution by using an abstract result for first-order differential inclusions in finite dimensional spaces. For the second
model, in addition, we prove the uniqueness of the solution by using a fixed point argument. Finally, we provide examples
of systems with contact and friction conditions for which our results are valid. |
