A Unified Beam Finite Element Model for Extension and Shear Piezoelectric Actuation Mechanisms

Abstract

This paper presents a finite element model for adaptive sandwich beams to deal with either extension or shear actuation mechanism. The former corresponds to an elastic core sandwiched beam between two transversely polarized active surface layers; whereas, the latter consists of an axially polarized core, sandwiched between two elastic surface layers. For both configurations, an electric field is applied through thickness of the piezoelectric layers. The mechanical model is based on Bernoulli-Euler theory for the surface layers and Timoshenko beam theory for the core. It uses three variables, through-thickness constant deflection, and the mean and relative axial displacements of the core's upper and lower surfaces. Augmented by the bending rotation, these are the only nodal degrees of freedom of the proposed two-node adaptive sandwich beam finite element. The piezoelectric effect is handled through modification of the constitutive equation, when induced electric potential is taken into account, and additional electric forces and moments. The proposed finite element model is validated through static and dynamic analysis of extension and shear actuated, continuous and segmented, cantilever beam configurations. Finite element results show good comparison with those found in the literature, and indicate that the newly defined shear actuation mechanism presents several promising features over conventional extension actuation mechanism, particularly for brittle piezoceramics use and energy dissipation purposes.