Parameter optimization of a vibration-based energy harvester with an RL electric circuit

An alternative circuit to improve the performance of a vibration-based energy harvester is proposed. The harvesting device considered consists of a piezoceramic element operating in the {33} direction. In normal operating conditions, piezoceramics experience small deflection and hence the small signal linear constitutive law of piezoelectricity is adopted for the scope of this work. Typically, vibration-based energy harvesters are designed to operate at the resonance or antiresonance frequencies. This condition might be tolerable in many cases, but is often difficult to realize in real-life applications. In this work, the authors propose adding an inductor to the harvesting circuit. It is shown that the addition of this simple electric element modifies the performance remarkably in a qualitative and quantitative manner. The maximum power values obtained at the resonance and antiresonance frequencies can be achieved at any frequency ratio if optimal electric elements are used. This allows for harvesting a constant optimal power everywhere in the frequency domain. Further investigation reveals the existence of a singularity at low damping ratios (below a bifurcation damping ratio). In that case, the optimization scheme yields a negative value for the optimal inductance between the resonance and antiresonance frequencies. However, this singularity is not experienced at a high damping ratio (beyond a bifurcation damping ratio). Moreover, for high damping ratios, it is shown that the proposed circuit is superior to a circuit that does not deploy an inductor.