Efficient acoustic energy harvesting by deploying magnetic restoring force

Abstract

Acoustic piezoelectric energy harvesters in quarter-wavelength resonator tubes undergo linear resonant vibration due to the external force. However, the variation of environmental conditions, such as temperature, directly alters the speed of sound in air, which in turn changes the tube resonance frequencies. This discrepancy between the tube acoustic and harvester resonance frequencies leads to reduced power generation. This paper proposes the addition of a nonlinear restoring force onto an acoustic cantilever beam piezoelectric energy harvester to tune and broaden the resonance bandwidth. The restoring force is applied by the attachment of permanent magnets at the beam tip and two external magnets. First, the nonlinear distributed parameter model of the bimorph is provided. Then, the associated dimensionless lumped-parameter model, including the magnetically coupled equations, is developed. To study the system response, an approximate-analytical solution based on the harmonic balance method is constructed. Initially, the variations of the speed of sound, and subsequently the tube resonance frequency, versus temperature, based on real statistical data, are studied. Furthermore, the effects of two scenarios of hardening and softening magnetic restoring forces are investigated. The results show that, at relatively low sound pressure levels (SPLs), the restoring forces can improve the efficiency by tuning the resonance frequency of the energy harvester. As the SPL increases, the force of the additional magnets tunes the natural frequency and broadens the resonance region. Finally, it is observed that the added magnets can change the optimum time constant ratio.