Single and coupled Helmholtz resonators for low frequency sound manipulation

Abstract

In this work, we use the finite element method to study the acoustic properties of single and coupled Helmholtz resonators (HRs). Each HR consists of a sphere drilled with one or several small openings. For a single HR, we show that the total pressure computed at the opening's edge as a function of frequency reveals the presence of a local dip in addition to the well-known resonance peak. In the case of coupled resonators, we highlight two resonance peaks at low frequencies, arising from excitation of a monopolar breathing mode, for which the twin resonators are in phase ( S- peak), and a dipolar mode, where the two spheres resonate out of phase ( AS- peak). In the near field, we study the influence of the number of apertures, the distance between spheres and their orientation on the frequencies, and quality factors of the two resonances. In the far field, we show that the propagation of the scattered wave is quasi-isotropic for the S- peak, while it leads to a dipolar-type pressure distribution for the AS- peak, with a directionality depending on the relative orientation of the openings in adjacent HRs. By increasing the number of coupled HRs from two to four units, we investigate the effect of additional mode coupling. Accordingly, the present study aims to manipulate the sound at targeted frequencies, by varying the distance or orientation between twin resonators, and to discuss the effect of dissipation. The demonstration of the coupling between sub-wavelength units opens the way to multi-frequency functionalities of acoustic metasurfaces.