Analytical and numerical approaches to piezoelectric bimorph

Abstract

We propose an efficient and accurate approach to piezoelectric bimorph based on a refined expansion of the elastic displacement and electric potential. The field approximation of the through-the-thickness variation accounts for a shear correction and a layerwise modelling for the electric potential. A particular attention is devoted to the boundary conditions on the bottom and top faces of the plate as well as to the interface continuity conditions for the electromechanical variables. The continuity condition on the electric potential imposes some restrictions on the approximation of the electric potential. Moreover, the continuity condition on the normal component of the electric induction at the bimorph interface is ensured by a Lagrange multiplier. The equations of the piezoelectric bimorph are obtained by using variational formulation involving the appropriate boundary and continuity conditions. A selection of numerical illustrations is presented for the series and parallel piezoelectric bimorphs simply supported under cylindrical bending conditions. Two types of electromechanical load are considered (i) a surface density of force applied on the top face and (ii) an electric potential applied on the bottom and top faces of the bimorph. The results thus obtained are compared to those provided by finite element computations performed for the full 3D model and by a simplified model without shear effect. At last, the problem of piezoelectric bimorph vibration is also examined for both closed and open circuit conditions. Excellent predictions with low error estimates of the local (profile) and global responses as well as resonant frequencies are observed. The comparisons assess of the effectiveness of the present approach to piezoelectric bimorph.