Modeling and analysis of a macro-fiber piezoelectric bimorph energy harvester operating in d33-Mode using Timoshenko theory

Abstract

Piezoelectric bimorph cantilevered beams are frequently employed in energy harvesting applications. The use of macro-fiber composites, which combine piezoelectric fibers with rectangular cross-sections and interdigitated electrodes, has significantly enhanced their performance by enabling operation in the 33-mode of piezoelectricity, thereby increasing conversion efficiency. In this article, the Timoshenko beam theory is applied to overcome the limitations of the Euler-Bernoulli theory in modeling transverse vibrations of harvesters with low slenderness ratios (length to thickness ratios). The mixture rule formulation is applied to determine the equivalent properties of the macro-fiber composite (MFC) structure. The electromechanical properties of a representative volume element (RVE) bounded by two successive interdigitated electrodes are coupled to the overall electro-elastic dynamic model of the structure using the Timoshenko theory. Frequency response functions for the power and tip vibration displacement of the MFC bimorph beam are determined from the model. Experimental data from the literature are used to validate the improved results predicted by the model developed in this article. A comparative analysis between the electromechanical responses predicted using a model based on Timoshenko and a model based on Euler-Bernoulli theory is conducted showing agreement, for harvesters with large slenderness ratios and discrepancies of up to 30% for low slenderness ratios. It has also been shown that the model based on Euler-Bernoulli theory overestimates both the mechanical and the electrical responses for low slenderness ratios as the shear and rotary inertia effects are not negligible in this case.