Abstract
Mechanical models are governed either by partial differential
equations with boundary conditions and initial conditions (e.g.,
in the frame of continuum mechanics) or by ordinary differential
equations (e.g., after discretization via Galerkin procedure or
directly from the model description) with the initial conditions.
In order to study dynamical behavior of mechanical systems with a
finite number of degrees of freedom including nonsmooth terms
(e.g., friction), we consider here problems governed by
differential inclusions. To describe effects of particular
constitutive laws, we add a delay term. In contrast to previous
papers, we introduce delay via a Volterra kernel. We provide
existence and uniqueness results by using an Euler implicit
numerical scheme; then convergence with its order is established.
A few numerical examples are given.