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Abstract

We propose an accurate and efficient approach to laminated piezoelectric plates based on a refinement of elastic displacement and electric potential through the plate thickness. More precisely, the model accounts for a shearing function and a layerwise approximation for the electric potential. The layerwise approach becomes a necessity in order to accommodate electric potential at the electrode interfaces. The equations of motion for the piezoelectric composite are deduced from a variational formulation incorporating the continuity conditions at the layer interfaces by using Lagrange multipliers. Different situations are investigated among them (i) bimorph and (ii) sandwich structures for two kinds of electro-mechanical loads applied (density of force and electric potential) and are compared to the finite element computations performed on the 3D model. The vibration problem is also presented and the frequencies for the axial and flexural modes are obtained. At last performance and effectiveness of the model are also discussed and applications to control of the structure shape and vibration are proposed.

Keywords

laminated plates piezoelectric composites vibrations piezoelectric actuators

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Analytical and Numerical Modelling of Laminated Composites with Piezoelectric Elements

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