Analysis of lumped models with contact and friction

作者：Migorski Stanislaw^*; Ochal Anna; Sofonea Mircea

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2011, 62(1): 99-113.

DOI：10.1007/s00033-010-0081-4

• Spring-mass-damper system
• Contact
• Friction
• Clarke subdifferential
• Differential inclusion
• Existence and uniqueness

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.

• 出版日期2011-2