Asymptotic Modelling of Linearly Piezoelectric Plates

Abstract

Here, we rigorously derive a theory of linearly piezoelectric plates by studying the limit behaviour of a three-dimensional flat body as its thickness tends to zero. In the static case, two limit models appear depending essentially on the nature and the magnitude of the electromechanical loading. In the dynamic case, under the realistic quasi-electrostatic approximation, the limit behaviour depends further more on the relative magnitudes of the density and of the thickness of the plate. The transient problems can be formulated in term of evolution equation in Hilbert spaces of possible states with finite electromechanical energy, so that the studies of these transient problems are easily deduced from the static case trough the Trotter theory of convergence of semi-groups of operators acting on variable spaces.KeywordsLimit BehaviourPiezoelectric PlateDynamic CaseAsymptotic ModellingTransient ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.