Parametric resonance in non-linear viscoelasticity: solids of differential type

DOI10.1093/IMAMAT/HXQ017zbMATH Open1425.74115arXiv1109.5953OpenAlexW2108046544MaRDI QIDQ3588957

Edvige Pucci, Giuseppe Saccomandi

Publication date: 10 September 2010

Published in: IMA Journal of Applied Mathematics (Search for Journal in Brave)

Abstract: We consider nonlinear viscoelastic materials of differential type and for some special models we derive exact solutions of initial boundary value problems. These exact solutions are used to investigate the reasons of non-existence of global solutions for such equations.

Full work available at URL: https://arxiv.org/abs/1109.5953

zbMATH Keywords

parametric resonance shearing motions Mathieu equation non-linear viscoelasticity limit cycles

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Nonlinear constitutive equations for materials with memory (74D10) Parametric resonances for nonlinear problems in mechanics (70K28)

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