Brillouin-zone characterization of piezoelectric material intrinsic energy-harvesting availability

Vibration energy harvesting is an emerging technology that enables electric power generation using piezoelectric devices. The prevailing approach for characterization of the energy-harvesting capacity in these devices is to consider a finite structure operating under forced vibration conditions. Here, we present an alternative framework whereby the intrinsic energy-harvesting characteristics are formally quantified independent of the forcing and the structure size. In doing so, we consider the notion of a piezoelectric material rather than a finite piezoelectric structure. As an example, we consider a suspended piezoelectric phononic crystal to which we apply Bloch's theorem and formally quantify the energy-harvesting characteristics within the span of the unit cell's Brillouin zone (BZ). In the absence of shunted piezoelectric circuits, the wavenumber-dependent dissipation of the phononic crystal is calculated and shown to increase, as expected, with the level of prescribed damping. With the inclusion of the piezoelectric elements, the wavenumber-dependent dissipation rises by an amount proportional to the energy available for harvest which upon integration over the BZ and summing over all branches yields a quantity representative of the net available energy for harvesting. We investigate both monoatomic and diatomic phononic crystals and piezoelectric elements with and without an inductor. The paper concludes with a parametric design study yielding optimal piezoelectric element properties in terms of the proposed intrinsic energy-harvesting availability measure.