Modeling, validation, and performance of low-frequency piezoelectric energy harvesters

Analytical and finite element electromechanical models that take into account the fact that the piezoelectric sheet does not cover the whole substrate beam are developed. A linear analysis of the analytical model is performed to determine the optimal load resistance. The analytical and finite element models are validated with experimental measurements. The results show that the analytical model that takes into account the fact that the piezoelectric patch does not cover the whole beam predicts accurately the experimental measurements. The finite element results yield a slight discrepancy in the global frequency and a slight overestimation in the value of the harvested power at resonance. On the contrary, using an approximate analytical model based on mode shapes of the full covered beam leads to erroneous results and overestimation of the global frequency as well as the level of harvested power. In order to design enhanced piezoelectric energy harvesters that can generate energy at low-frequency excitations, further analysis is performed to investigate the effects of varying the length of the piezoelectric material on the natural frequency and the performance of the harvester. The results show that there is a compromise between the length of the piezoelectric material, the electrical load resistance, and the available excitation frequency. By quantifying this compromise, we optimize the performance of beam–mass systems to efficiently harvest energy from a specified low frequency of the ambient vibrations.