Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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STUDY OF DYNAMICAL MODEL FOR PIEZOELECTRIC CYLINDER IN FRICTIONAL ANTIPLANE CONTACT PROBLEM

  • S. MEDJERAB (Department of Mathematics, Laboratory of Analysis, Optimization and Treatment of information (LAOTI), Faculty of Exact Sciences and Informatic, Mohammed Seddik Ben Yahia University) ;
  • A. AISSAOUI (Department of Mathematics, Laboratory of Operator Theory and PDE, Foundations and Applications, Faculty of Exact Sciences, University of El Oued) ;
  • M. DALAH (Department of Mathematics, Faculty of Exact Sciences, Freres Mentouri Constantine University)
  • Received : 2021.06.16
  • Accepted : 2023.05.04
  • Published : 2023.05.30
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Abstract

We propose a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation. The behavior of the material is described with a linearly electro-viscoelastic constitutive law with long term memory. The mechanical process is dynamic and the electrical conductivity coefficient depends on the total slip rate, the friction is modeled with Tresca's law which the friction bound depends on the total slip rate with taking into account the electrical conductivity of the foundation both. The main results of this paper concern the existence and uniqueness of the weak solution of the model; the proof is based on results for second order evolution variational inequalities with a time-dependent hemivariational inequality in Banach spaces.

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Acknowledgement

We would like to thank the anonymous reviewers at Research Ethics and two anonymous reviewers at Theoria for commenting on earlier versions of this paper. For discussions on the topic and comments on the paper, thanks to participants of the practical mathematics working group at the University of Jijel, Algeria deserves our thanks for proofreading the paper. As always, any remaining errors are our own.

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