Exact Solution for Thick, Laminated Piezoelectric Beams

The paper presents exact solutions for thick composite beams composed of multiple lamina made of arbitrary orthotropic elastic and/or piezoelectric materials. A state-space formulation is presented through the formulation of a transfer matrix relation from layer to layer and therefore a global relation governing the top layer through the bottom layer can be derived. No shear correction factor needs to be considered because the thick beam is assumed as a plane-stress problem in the cross section. Some exemplary examples with exact modeling and numerical solutions are presented to illustrate the application of the method. The effects of combination of mechanical and electrical loadings are also presented. Especially, the higher-mode deflection appearance instead of simple fundamental mode of the beam under uniform loads is discussed.