Time and frequency domain analysis of piezoelectric energy harvesters by monolithic finite element modeling

The successful design of piezoelectric energy harvesting devices relies upon the identification of optimal geometrical and material configurations to maximize the power output for a specific band of excitation frequencies. Extendable predictive models and associated approximate solution methods are essential for analysis of a wide variety of future advanced energy harvesting devices involving more complex geometries and material distributions. Based on a holistic continuum mechanics modeling approach to the multi-physics energy harvesting problem, this article proposes a monolithic numerical solution scheme using a mixed-hybrid 3-dimensional finite element formulation of the coupled governing equations for analysis in time and frequency domain. The weak form of the electromechanical/circuit system uses velocities and potential rate within the piezoelectric structure, free boundary charge on the electrodes, and potential at the level of the generic electric circuit as global degrees of freedom. The approximation of stress and dielectric displacement follows the work by Pian, Sze, and Pan. Results obtained with the proposed model are compared with analytical results for the reduced-order model of a cantilevered bimorph harvester with tip mass reported in the literature. The flexibility of the method is demonstrated by studying the influence of partial electrode coverage on the generated power output.