Bimodal Approach of a Frequency-Up-Conversion Piezoelectric Energy Harvester

This paper developed an analytical model for a piezoelectric energy harvester (PEH) composed of a piezoelectric bimorph and a stopper as shown in Fig. 1, which was subjected to a harmonic excitation. Frequency-up-conversion, which has proved to improve the energy harvesting efficiency, was achieved due to the mechanical impact between the piezoelectric bimorph and the stopper. The piezoelectric bimorph was modeled as Euler–Bernoulli beam. A bi-modal approach was adopted to animate the beam stopper reaction. When the tip of the bimorph is free for motion, a cantilever beam function is adopted, while the tip encounters a stop, a clamped-pinned beam function is used to model the bimorph. The periodic solutions and their corresponding output voltage and power were obtained. With the same initial conditions and base excitations, the output energies of transient vibrations are compared for two cases: (1) without impact between the piezoelectric beam and the stopper; (2) with impact by reducing the gap distance between the piezoelectric beam and the stopper. With the purpose of maximizing the output power, from the steady-state analytical solutions, we studied the optimum gap between the piezoelectric beam and the stopper when the base excitations are fixed and initial conditions are set to zero.