Exploring the parametric amplification phenomenon for energy harvesting

Due to inherent system nonlinearities, many vibratory excitation sources possess a frequency spectrum which contains energy components at multiple integers of the fundamental frequency of the source. In this paper, we theoretically explore the prospect of enhancing the transduction of a vibratory energy harvester (VEH) by utilizing the parametric amplification phenomenon to channel energy from one of these superharmonics, namely the one at twice the fundamental frequency, to a purely resistive load. Towards that end, we consider a piezoelectric cantilevered-type bimorph harvester and show that by tilting the axis of the beam through a proper angle with respect to the direction of excitation, it is possible to utilize a parametric pump to enhance the output power at the fundamental frequency. Percentage improvement in the output power depends on the excitation's parameters and the mechanical damping ratio. It is observed that when the mechanical damping ratio is small, significant enhancement in the output power is attainable even when the magnitude of the superharmonic is small when compared to the fundamental frequency. Such findings reveal that, under certain conditions, parametric amplification can be utilized to enhance the output power of a VEH especially for microscale applications where the damping ratio can be easily controlled.