Trampoline metamaterial coupled with Helmholtz resonator for enhanced acoustic piezoelectric energy harvesting

Abstract

To enhance acoustic piezoelectric energy harvesting at lower frequencies, this study proposes a coupled structure comprising a trampoline metamaterial and a Helmholtz resonator. The trampoline metamaterial incorporates periodically arranged composite resonant pillars embedded in a perforated thin plate. By designing a point defect in the metamaterial, vibro-acoustic energy can be intentionally confined to the defect location at the defect band frequency. Considering the amplified acoustic pressure in the Helmholtz resonator, the incorporation of the trampoline metamaterial into a Helmholtz resonant cavity enables enhanced energy localization. Initially, a mathematical model for calculating the first resonant band gap is established. The band gap and corresponding defect band frequency are then validated by comparing numerical simulation with experimental results. Subsequently, numerical simulations are conducted to investigate the influences of hole radius and coupled structure on piezoelectric energy harvesting performance. These simulations revealed that an increase in the hole radius significantly enhances vibro-acoustic localization and piezoelectric conversion efficiency of the trampoline metamaterial. Furthermore, the synergistic interaction of the coupled structure between the defect state in the trampoline metamaterial and the acoustic pressure amplification in the Helmholtz resonator further enhances the energy harvesting performance. At an acoustic incident amplitude of 2 Pa and a defect band frequency of 1068.5 Hz, the coupled structure attains a maximum output voltage of 5.94 V and power of 39.10 μW. These values demonstrate enhancements of 2.65 times and 2.80 times, respectively, compared to the uncoupled trampoline metamaterial with a hole radius of r₀=1.5 mm. Such findings offer guidance for designing piezoelectric energy harvester in applications such as self-powered sensors and small electrical devices.