RANDOM EXCITATIONS

This effort investigates and evaluates the prospect of using parametric instabilities for vibratory energy harvesting. To that end, we consider a parametrically-excited piezoelectric cantilever beam and study its performance as an energy harvester under i) fixed-frequency harmonic excitations, ii) time-varying frequency excitations, and iii) band-limited Gaussian noise. In the case of fixed-frequency excitations, we use the Method of Multiple Scales to obtain approximate analytical expressions for the steady-state response amplitude and instantaneous output power in the vicinity of the first principle parametric resonance. We show that the electromechanical coupling and load resistance play an important role in determining the output power and characterizing the bandwidth of the harvester. Specifically, we demonstrate that the region of parametric instability wherein energy can be harvested shrinks as the coupling coefficient increases, and that there exists a coupling coefficient beyond which the peak power decreases. We also show that there is a critical excitation level below which no energy can be harvested. The magnitude of this critical excitatio