J. Phys. IV France 115 (2004) 307
On models of layered piezoelectric beams for passive vibration controlC. Maurini1, 2, F. dell'Isola3 and J. Pouget1
1 LEMA (CNRS-FRE 2481), Université de Versailles/Saint-Quentin-en-Yvelines, 45 Av. des États-Unis, 78035 Versailles, France
2 Dipartimento di Meccanica e Aeronautica, Univertità di Roma "La Sapienza", via Eudossiana 18, 00184 Roma, Italy
3 Dipartimento di Ingegneria Strutturale & Geotecnica, Univertità di Roma "La Sapienza", via Eudossiana 18, 00184 Roma, Italy
In this paper models of layered piezoelectric beams are discussed. The attention is focused on the analysis of the assumptions on transversal stress and strain distribution and their influence on the deduction of the beam constitutive equations from a three dimensional description. A model accounting for non trivial transversal interactions between different layers is deduced from a mixed variational formulation where non-local conditions on transversal stress are enforced by Lagrange multipliers method. The fully coupled electromechanical nature of the system is described. For a sandwich piezoelectric beam, analytical expressions of the beam constitutive coefficients are provided and comparisons to standard modelling approaches are presented. Finally, the fundamental features of the proposed model are highlighted by presenting the through-the-thickness distribution of the 3D state fields.
© EDP Sciences 2004