Acoustic Band Gap Formation in Two-Dimensional Locally Resonant Sonic Crystals Comprised of Helmholtz Resonators

Abstract

We present a new type of sonic crystal technology offering a novel method of achieving broad acoustic band gaps. The proposed design of a locally resonating sonic crystal (LRSC) is constructed from "C"-shaped Helmholtz resonators as opposed to traditional solid scattering units. This unique construction enables a two band gap system to be generated in which the first — a Bragg type band gap, arises due to the periodic nature of the crystal, whilst the second gap results from resonance of the air column within the resonators. The position of this secondary band gap is found to be dependent upon the dimensions of the resonating cavity. The band gap formation is investigated theoretically using finite element methods, and confirmed through experimental testing. It is noted that the resonance band gaps detected cover a much broader frequency range (in the order of kHz) than has been achieved to date. In addition the possibility of overlapping such a wide band gap with the characteristic Bragg gap generated by the structure itself could yield gaps of even greater range. A design of sonic crystal is proposed, that comprises of several resonators with differing cavity sizes. Such a structure generates multiple resonance gaps corresponding to the various resonator sizes, which may be overlapped to form yet larger band gaps. This multiple resonance gap system can occur in two configurations. Firstly a simple mixed array can be created by alternating resonator sizes in the array and secondly using a system coined the Matryoshka (Russian doll) array in which the resonators are distributed inside one another. The proposed designs of LRSC's offer a real potential for acoustic shielding using sonic crystals, as both the size and position of the band gaps generated can be controlled. This is an application which has been suggested and investigated for several years with little progress. Furthermore the frequency region attenuated by resonance is unrelated to the crystals lattice constant, providing yet more flexibility in the design of such devices.

Matryoshka locally resonant sonic crystal

“…The proposed systems have been studied numerically with the use of finite elements methods (FEM). So far the results are in complete agreement with laboratory experiments, see also Refs [4].…”

“…The proposed sonic crystal forms broad attenuation bands in the lower frequency regime and comprises concentric slotted cylinders. The preliminary results of this work is presented in Refs [4]. Previously Hu et al [5] constructed a sonic crystal lens composed of an array of two-dimensional Helmholtz resonators, which in the longwave regime was found to have a high relative acoustic refractive index n and at the same time, a small acoustic impedance Z mismatch with air for airborne sound.…”

Fast multipole boundary element method for the acoustic analysis of finite periodic structures

“…With respect to the BEM, Duhamel [23] extended the two-dimensional modeling approach by incoherent line sources and refers to it as 2.5-dimensional boundary element method. In contrast, Chalmers et al [24] and Elford et al [8] assumed that the height of the sonic crystals is infinite and that ground effects are negligible. This allows to modify the cross section of the sound barrier along its length.…”

Liquid sensor composed of one-dimensional sonic Helmholtz resonator array

“…Devices based on HRs have been studied theoretically and experimentally over the last decade [19][20][21]. The periodic properties of 2D phononic crystals and HRs have also been discussed extensively; it has been proposed that these types of structures contained acoustic band gaps and that these band gaps could prevent sound waves from specific frequency regions from propagating inside the structures [22][23][24][25][26]. It was also indicated that the type of band gap that occurs in HR arrays was decoupled from the Bragg gaps [24].…”

“…When we compared the structures used in the literature [24][25][26] with our proposed structure, we found that the HR structures in the literature were arranged in a square lattice. However, this type of arrangement should consider the influences of both HR (local resonance) and the square lattice structure (Bragg's law).…”