On acoustic absorption mechanisms of multiple coupled quarter-wavelength resonators: Mutual impedance effects

Abstract

This paper discusses the neighbouring interaction among multiple quarter-wavelength resonators that influences sound absorption. A circular two-cavity resonator covered by a very thin layer of porous material is introduced, which consists of a centre circular hole and an annular cavity. These coupled quarter-wavelength resonators can induce a shift of resonance frequency due to high-order evanescent modes. An analytical expression of mutual impedance is derived which explains the resonance frequency shift theoretically. After validating the theoretical method with numerical and experimental results, cavity height corrections are calculated to implicitly quantify the effects of mutual impedance which contribute significantly to the overall impedance of the resonators. The influences of mutual-impedance related parameters in terms of cavity properties and surface resistance on the sound absorption performance of the quarter-wave resonators are discussed. It is concluded that, apart from strong local resonances of individual resonators, mutual impedance plays a significant role in the absorption mechanisms of multiple coupled quarter-wavelength resonators.