Dynamic vibrations of a damageable viscoelastic beam in contact with two stops

Abstract

A model for the material damage, due to dynamic vibrations of a Kelvin‐Voigt viscoelastic beam whose tip is constrained to move between two stops, is presented and numerically analyzed. The contact of the free tip with the stops is described by the normal compliance condition. The evolution of damage of the beam's material, which measures the reduction of its load carrying capacity, is modeled with a parabolic inclusion. The existence of the unique local solution is stated. A numerical algorithm is presented, in which spatially it is approximated by finite elements, and the time derivatives are discretized with the Euler scheme. Error estimates are derived for sufficiently regular solutions, and four numerical simulations are shown. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

Analysis of a contact problem for a viscoelastic Bresse system

“…A first approach of research in such a context is the mathematical formulation of the contact models leading to PDE systems that are worth analyzing also regarding the existence, uniqueness, and regularity of the solutions (see, e.g., [3,30,31]), or their numerical analysis (see, e.g., [5,6,10,15,[17][18][19]).…”