Performance investigations of nonlinear piezoelectric energy harvesters with a resonant circuit under white Gaussian noises

Vibration-based piezoelectric energy harvesting for powering low-energy consuming electronic equipment has received a great deal of attention in the last decade. Most researches applying deterministic approaches or theory of random vibrations have been concentrated on examining the performance of the piezoelectric energy harvesters with a purely resistive circuit under harmonic or random excitations. Here, the ambient excitations are assumed to be white Gaussian noises, we investigate a nonlinear piezoelectric energy harvester which utilizes a harvesting circuit with both a resistive load and an inductor, based on the fact that previous research has demonstrated that the intentional introduction of an inductor substantially improves the performance of energy harvesting device. Two scenarios, namely the purely inductive circuit and the resistive–inductive circuit, are examined. Exact stationary solution of the output voltage and closed-form expression of the mean square voltage are acquired for the purely inductive circuit. By combining the equivalent linearization method and the moment method of random process theory, analytical solutions of mean square voltage and averaged power output involving dimensionless parameters of the electromechanical system are derived for the resistive–inductive circuit. The energy conversion efficiency is analyzed by means of energy balance equation. Monte Carlo numerical simulations are implemented to validate the theoretical predictions. Results reveal unique characteristics of the nonlinear vibration systems with a resonant circuit, showing its superiority over the energy harvesters with a purely resistive circuit. The present study provides a paradigm in a simple but effective way to resolve strong electromechanical coupling systems under random excitations.