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Asymptotic analysis for a dynamic piezoelectric shallow shell
Author(s) -
Guan Yan,
Miara Bernadette
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4380
Subject(s) - piezoelectricity , displacement (psychology) , cartesian coordinate system , shell (structure) , mathematics , mathematical analysis , limit (mathematics) , convergence (economics) , asymptotic analysis , plane (geometry) , coupling (piping) , transverse plane , classical mechanics , physics , geometry , acoustics , engineering , structural engineering , mechanical engineering , psychology , civil engineering , economics , psychotherapist , economic growth
The paper deals with the asymptotic formulation and justification of a mechanical model for a dynamic piezoelastic shallow shell in Cartesian coordinates. Starting from the three‐dimensional dynamic piezoelastic problem and by an asymptotic approach, the authors study the convergence of the displacement field and of the electric potential as the thickness of the shell goes to zero. In order to obtain a nontrivial limit problem by asymptotic analysis, we need different scalings on the mass density. The authors show that the transverse mechanical displacement field coupled with the in‐plane components solves an problem with new piezoelectric characteristics and also investigate the very popular case of cubic crystals and show that, for two‐dimensional shallow shells, the coupling piezoelectric effect disappears. Copyright © 2017 John Wiley & Sons, Ltd.