Sensitivity Analysis of Frequency Response Functions for Load Resistance of Piezoelectric Energy Harvesters

Piezoelectric energy harvesting from ambient energy sources, particularly vibrations, has attracted considerable interest throughout the last decade. Sensitivity analysis is a promising method used for many engineering problems to assess input-output systems based on vibration. In this paper, the formulation of first order sensitivity (FOS) of complex Frequency Response Functions (FRFs) is developed to evaluate the output responses of piezoelectric energy harvesters. The adapted approach for the FOS is the finite difference method, which consists in computing an approximation of the first derivation. Furthermore, the main goal is to study the influence of the variation of the load resistance from the short circuit (load resistance tends to zero) to open circuit (load resistance tends to the infinity) conditions on the tip displacement and the voltage FRFs of a Bimorph Piezoelectric Energy Harvester (BPEH). The determination of FRFs of the harvester are derived using Finite Element Modelling for a bimorph piezoelectric cantilever beam based on Euler-Bernoulli theory, which is composed of an aluminum substrate covered by two PZT-5A layers. The results show a high sensitivity of the FRFs of the BPEH to the load resistance at the natural frequencies. For each excitation frequency, the sensitivity near the resonance frequencies decreases from the short circuit conditions to the open circuit conditions.