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Dynamic vibrations of a damageable viscoelastic beam in contact with two stops
Author(s) -
Campo Marco,
Copetti Maria I.M.,
Fernández José R.
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21727
Subject(s) - discretization , viscoelasticity , vibration , beam (structure) , mathematics , reduction (mathematics) , euler's formula , kelvin–voigt material , mathematical analysis , finite element method , partial differential equation , numerical analysis , mechanics , structural engineering , physics , geometry , thermodynamics , engineering , quantum mechanics
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