Characterization of Beam Stiffness Matrix with Embedded Piezoelectric Devices via Generalized Eigenvectors

The formulation described in this paper leads to the electro-elastic characterization of the sectional properties of elastic anisotropic prismatic beams with embedded piezoelectric devices. The related matrix is derived by analyzing a set of two-dimensional electro-elastic problems defined on the beam section. These problems allow to compute both the so-called beam de Saint-Venant’s solutions and the beam deformation field induced by an electric potential difference imposed between the piezoelectric conductive laminae. The results are compared to those obtained with three dimensional finite element models.