Asymptotic analysis for a dynamic piezoelectric shallow shell |
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| Authors: | Yan Guan Bernadette Miara |
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| Affiliation: | 1. Mathematics and Science College, Shanghai Normal University, Shanghai, China;2. ESIEE, Laboratoire de Modélisation et Simulation Numérique Cité Descartes, Université Paris‐Est, Noisy‐le‐Grand Cedex, France |
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| Abstract: | 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. |
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| Keywords: | elastodynamic shell asymptotic analysis dynamic piezoelastic shallow shell |
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