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To cite this version: Nadal, Clément and Pigache, François Multimodal electromechanical model of piezoelectric transformers by Hamilton's principle. OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Abstract—This work deals with a general energetic approach to establish an accurate electromechanical model of a piezoelectric transformer (PT). Hamilton's principle is used to obtain the equations of motion for free vibrations. The modal characteristics (mass, stiffness, primary and secondary electro-mechanical conversion factors) are also deduced. Then, to illustrate this general electromechanical method, the variational principle is applied to both homogeneous and nonhomogeneous Rosen-type PT models. A comparison of modal parameters, mechanical displacements, and electrical potentials are presented for both models. Finally, the validity of the electro-dynamical model of nonhomogeneous Rosen-type PT is confirmed by a numerical comparison based on a finite elements method and an experimental identification.
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