Optimized energy harvesting through piezoelectric functionally graded cantilever beams

The emergence of piezoelectric functionally graded materials (PFGMs) has sparked the present research interests toward their energy harvesting behaviors. This paper theoretically investigates the optimized energy harvesting characteristics of PFGM cantilever beams under harmonic excitation. The electromechanical coupling governing equations are formulated based on Euler–Bernoulli beam theory, and utilizing the Galerkin discretization yields the frequency-response relations of the voltage, current, and power parameters, and the analytical optimal resistance as well. The present theoretical model is validated by comparing with the experimental results in literature, and parametric studies are addressed to discuss the effects of the damping ratio, the inhomogeneous parameter of PFGMs and the electrical resistance on the structural responses. More importantly, the optimized energy harvesting characteristics of PFGM cantilever beams are captured during discussions on the optimal conditions of the frequency-ratio and the electrical resistance. Results reveal that the superiority of PFGM energy harvesters over the conventional piezoelectric laminate ones, basically, lies in the design toward constituent distribution of PFGMs enabling the control over the energy harvesting efficiency. Specifically, provides that both the optimal frequency-ratio and the optimal resistance hold simultaneously, there would be a critical value for the inhomogeneous parameter, which can be utilized to maximize the energy harvesting efficiency for PFGM beams. The present work may support the prospective material gradient design of piezoelectric energy harvesters. (paper)