Novel composite finite element model for piezoelectric energy harvesters based on 3D beam kinematics

In this study, piezoelectric smart structures are formulated using finite element method based on equivalent single layer theory for electromechanical domains, especially in energy harvesting. A model is derived where all displacement, strain, electric potential, and electric fields are decomposed into longitudinal and cross-sectional components and a finite element discretization is performed. All parameters are calculated for 3D active beam elements. Mechanical degrees of freedom are decoupled for both mechanical and electromechanical coupling matrices. Two local coordinate systems and a global one are introduced for this purpose. A method is presented and proved to transform element matrices between those systems. Natural frequencies of a cantilever harvester obtained from the theory are compared to those of ABAQUS model. Output voltage, current, RMS power, open and short circuit natural frequencies, and optimum resistive load are also calculated. Finally, the results of the present theory are compared to those presented in the literature.