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

Authors

  • Marco Campo,

    1. Centro Universitario de la Defensa, Escuela Naval Militar, Plaza de España s/n, 36920 Marín, Spain
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  • Maria I.M. Copetti,

    1. Laboratório de Análise Numérica e Astrofísica, Departamento de Matemática, Universidade Federal de Santa Maria, 97105-900 Santa Maria, RS, Brazil
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  • José R. Fernández

    Corresponding author
    1. Departamento de Matemática Aplicada I, Universidade de Vigom, ETSI de Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
    • Departamento de Matemática Aplicada I, Universidade de Vigo, ETSI de Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain
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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

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