An experimentally validated double-mass piezoelectric cantilever model for broadband vibration–based energy harvesting

Narrow bandwidth is the major challenge to today’s vibration-based energy harvesters. Compared with other broadband approaches that involve moving parts and control electronics, a double-mass piezoelectric cantilever beam provides a simple and reliable solution to widen the effective bandwidth as a vibration energy harvester. In this article, a continuum model of a double-mass lead zirconate titanate cantilever subject to sinusoidal base excitation is presented. First, the undamped equation of motion along with boundary and transition conditions is derived from Hamilton’s principle, followed by modal analysis that determines the eigenfunctions and natural frequencies. Next, the coupled electromechanical equations for sinusoidal base excitation are obtained. The output voltage and relative displacement are solved analytically. The frequency response function and mode shapes predicted by the model are validated against experiments.