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 simulation results obtained using a six shell concentric Matryoshka system demonstrates the active frequency range spans 400-1600 Hz, providing decent levels of attenuation across this range. Moreover, the experimental results provided for the single Cshaped locally resonant sonic crystal, 6 offer $ 25 dB of attenuation for applications as a noise attenuation solution. …”

“…The preliminary results of this work are presented in Ref. 6. Previously Hu et al 7 constructed a sonic crystal lens composed of an array of two-dimensional Helmholtz resonators, which in the long-wave 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.…”

“…6 To operate below this Bragg gap, we now investigate a design of a locally resonant sonic crystal (LRSC), which is an array of slotted cylinders. An advantage of using COMSOL MULTIPHYSICS to compute the acoustic band structure is the capability of modeling more complex scatterer geometries.…”

“…One method to achieve this is to include multiple resonator sizes and "overlap" the individual resonance peaks. We have investigated mixed arrays that display this ability; 6 however, to save space and reduce the overall barrier thickness, we now propose a design of sonic crystal with resonators placed concentrically inside one another, extending the multistructure describe by Movchan et al 10 We coin this the Matryoshka (Russian doll) configuration. Specifically we investigate a Matryoshka sonic crystal the unit cell of which is defined with six concentric C-shaped resonators, all tuned to frequencies that lie within 200 Hz of each other in the low frequency regime.…”

Experiments on the low frequency barrier characteristics of cellular metamaterial panels in a diffuse sound field

“…This method is typically used to characterize sound absorbing materials [16,17,18]. There are also a few investigations involving sound source excitation with alternate experimental approaches [19,20,21,22], but these are also limited to normal incidence, one-dimensional wave propagation. While the work in references [4,7,12,13,14,15] focused on determining the sound transmission loss behavior of the proposed materials, particularly in the low audible frequency range, the work reported in references [19,20,21,22] primarily considered the verification of theoretical con-cepts of effective negative density, modulus and the co-existence of locally resonant band gaps and Bragg band gaps.…”