On models of layered piezoelectric beams for passive vibration control

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.