Hilbert Fractal Acoustic Metamaterials

Abstract

This PhD thesis delves into the novel exploration of Hilbert fractal acoustic metamaterials
(HFAM) and their potential application in sound insulation. Through rigorous analysis and
experimentation, several groundbreaking findings have emerged that contribute significantly to the field of acoustic engineering. The research primarily reveals a critical relationship
between the fractal order of Hilbert patterns and the absorption coefficient in acoustic metamaterials, identifying key factors such as slit gap width and length that influence the particle velocity field. Moreover, an analytical formulation linking acoustic cavity resonances to frequencies corresponding to peak transmission losses has been established. This predictive equation integrates variables like fractal order, frequency, slit gap width, and porosity, offering new design possibilities.
Furthermore, the thesis introduces design graphs formulated from the derived equations, enabling engineers to exemplify the design process with HFAM by selecting desired frequencies and fractal types and determining suitable dimensions of the hosted cubic geometry.
Coupled with practical design guidelines supported by both experimental and numerical results, these tools offer novel resources for engineering applications. One significant contribution of this research is the unveiling of potential for noise reduction solutions. Understanding how to intentionally employ Hilbert fractal patterns opens new roads for optimising acoustic properties across various engineering fields, like mechanical, civil and aerospace, where weight and space occupied by liners can be a problematic issue.
The dissertation starts with a thorough look at the problems and new ideas in low-middle-frequency sound insulation, with a focus on how relevant Hilbert fractal patterns are in the acoustic domain. The literature review undertakes a detailed examination of existing strategies and their potential synergies, establishing the scientific background for the subsequent investigations.
A detailed exposition of methodologies follows, elaborating on specialised techniques such as 3D printing, finite element modelling, and impedance tube testing.
To briefly summarise the main points and main results of the three technical chapters, the first one offers a new point of view on how coiled and fractal geometries absorb sound. It identifies a predictive equation that enables the accurate determination of absorption peak positions.
The following chapter investigates the effects of various factors, including porosity, gap width and fractal order, on transmission loss (TL). Employing analytical calculations, it offers a formula to predict the coordinates of peak transmission loss values.
In the last technical chapter, two equations are formulated to help with the design of Hilbert
fractal metamaterials, with the aim of achieving a certain transmission loss and magnitude
within a certain acoustic spectrum.
The conclusions derived from these technical chapters indicate that fractal-based acoustic metamaterials display extraordinary sound modulation characteristics across the investigated frequency range. Particularly, two predominant geometrical configurations—Hilbert and coiled formations—demonstrate similar efficacy in sound absorption. The Hilbert geometry, however, distinguishes itself through its superior spatial efficiency.
The acoustic absorption of Hilbert-patterned metamaterials can be described using the theoretical framework of a double-open resonator that has a section with uniform dimensions. Also, the size of the gap width in the Hilbert configuration has a big effect on the transmission loss of the acoustic metamaterials that are being studied.
Among a variety of parameters, gap width emerges as particularly important, having a major impact on acoustic properties. This phenomenon can be analytically explained through an
open-closed resonator model, which also features a section of uniform dimensions. In scenarios where plane wave propagation is relevant, Hilbert fractal metamaterials offer novel avenues for the development of advanced passive sound insulation technologies. This step forward is made possible by two equations and models that allow the exploitation of the Hilbert geometry inside a cubic sample.
In conclusion, the research culminates in an advancement in the understanding and practical
application of Hilbert fractal acoustic metamaterials. This lays a robust foundation for the genesis of novel noise abatement solutions. The insights gleaned into the intricate interplay among absorption coefficients, transmission loss, fractal order, frequency range, and geometric properties of the samples set the stage for the exploration of new frontiers in this rapidly growing area of passive sound insulation technology.

Date of Award	18 Jun 2024
Original language	English
Awarding Institution	University of Bristol
Supervisor	Fabrizio Scarpa (Supervisor), Valeska Ting (Supervisor) & Mahdi Azarpeyvand (Supervisor)