The work presented within this thesis pertains to the use of acoustic metamaterials for low frequency absorption and attenuation of sound. Acoustic metamaterials are structures composed of periodic and sub-wavelength locally resonant unit cells and are typically an order of magnitude or smaller than the associated wavelength of the frequency they are designed to manipulate. All naturally occurring materials have both positive mass density and bulk modulus; acoustic metamaterials have the ability to artificially manipulate these properties to have negative effective quantities dependant on the frequency of the incident acoustic wave.
Within this thesis, a general analytical method based upon the linear superposition of terms derived with the transfer matrix method are used to derive simple analytical expressions for complex acoustical systems. Good agreement is found when in comparison to results produced using the transfer matrix method and numerically. One limitation with the effective property models presented is the inability to capture the evanescent coupling between Helmholtz resonators.
The mechanism to achieve perfect absorption for one port systems has been explored with the development of single frequency and broadband frequency perfect absorbing acoustic metamaterial unit cells. Through the use of Helmholtz resonators with porous inclusions within their cavities, one port perfect absorbers have been developed that obtain perfect absorption at 290 Hz using a single Helmholtz resonator with a sample thickness of 1/28 the wavelength, and over a broadband frequency range between 275 and 625 Hz using a system of three Helmholtz resonators with a sample thickness of 1/10 the wavelength.
In a two port system, Helmholtz resonators with porous inclusions within the cavity have been utilised to achieve perfect absorption at a single frequency and over a broadband frequency range. The single frequency perfect absorber has a sample thickness of 1/16 the wavelength at a frequency of 300 Hz. The broadband perfect absorber presented within this chapter exhibited perfect absorption at 312, 426 and 576 Hz, with a sample thickness of 1/8 the wavelength at the lowest critically coupled frequency.
A method of simplification has been proposed for impedance terms derived by the transfer matrix method. This has been applied to the case of a serial array of $M$ coupled identical Helmholtz resonators. The simplification method is reliant upon the use of an impedance contrast to create a small order term which can be used in the Taylor expansion of the impedance expressions. By utilising the leading order term from the Taylor series expansions, simple expressions were found composed of polynomials of the same order as $M$. It was also found that the resonant frequencies of the modelled systems can be obtained through the solution of the polynomials present within the numerator of the impedance approximations.
Finally, an ideal analytical model has been developed to model the acoustic attenuation achieved by periodic arrays of non-rigidly backed perforations acting as sound-soft scatterers. It has been shown that periodic arrays of sound soft scatterers produce a low frequency band gap from 0 Hz to a frequency determined by the geometry of the perforations and the unit cell length. Acoustic waves within the frequency range of the bandgap become evanescent, achieving large amounts of attenuation for finite systems, and no wave propagation for infinite systems. To confirm the existence of the low frequency band gap, an experimental setup to investigate the sound propagation in an open ended perforated pipe was designed. The experimental transmission loss highlights that periodically arranged holes in the rigid pipe create a low frequency band gap. The band gap produced experimentally matches the predictions obtained for the simplified numerical model in which the perforations were idealised with an acoustical soft backed elliptical geometry in the 3D finite element model.
