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MATHEMATICAL MODELLING OF NOVEL METAMATERIALS FOR NOISE REDUCTION APPLICATIONS

Rowley, William

[Thesis]. Manchester, UK: The University of Manchester; 2018.

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Abstract

In this thesis we investigate acoustic metamaterials and how they can influence incident sound waves. Specifically we are interested in the mathematical technique of transformation acoustics and how several simple examples of metamaterials, devised via transformation acoustics, can be realised physically. We present a simple methodology for optimising microstructure consisting of rods with elliptical cross sections arranged on a rectangular array in order to best fit the material properties required by a desired transformation. We present in detail three such examples: a one dimensional scaling, the beam shifter, and a right angle bend. We apply the one dimensional scaling to a quarter wavelength resonator, theoretically predicting that we are able to lower the active frequency of the resonator without increasing its physical length. This result is then confirmed experimentally. We provide further experimental evidence of the broad band nature of the microstructure and suggest how it could be applied as a one dimensional acoustic cloak. Finally we present numerical simulations of acoustic propagation through microstructure chosen to realise a beam shifter and right angle bend. These are devices associated with more complicated two dimensional transformations that may prove useful in the field of noise control and redirection.

Bibliographic metadata

Type of resource:
Content type:
Administered thesis
Form of thesis:
Alternative format
Type of submission:
Doctoral level ETD - final
Thesis title:
MATHEMATICAL MODELLING OF NOVEL METAMATERIALS FOR NOISE REDUCTION APPLICATIONS
Degree type:
Doctor of Philosophy
Degree programme:
PhD Mathematical Sciences
Publication date:
2018-11-15T09:25:45
Institution:
The University of Manchester
Location:
Manchester, UK
Total pages:
182
Abstract:
In this thesis we investigate acoustic metamaterials and how they can influence incident sound waves. Specifically we are interested in the mathematical technique of transformation acoustics and how several simple examples of metamaterials, devised via transformation acoustics, can be realised physically. We present a simple methodology for optimising microstructure consisting of rods with elliptical cross sections arranged on a rectangular array in order to best fit the material properties required by a desired transformation. We present in detail three such examples: a one dimensional scaling, the beam shifter, and a right angle bend. We apply the one dimensional scaling to a quarter wavelength resonator, theoretically predicting that we are able to lower the active frequency of the resonator without increasing its physical length. This result is then confirmed experimentally. We provide further experimental evidence of the broad band nature of the microstructure and suggest how it could be applied as a one dimensional acoustic cloak. Finally we present numerical simulations of acoustic propagation through microstructure chosen to realise a beam shifter and right angle bend. These are devices associated with more complicated two dimensional transformations that may prove useful in the field of noise control and redirection.
Keyword(s):
Thesis main supervisor(s):
Thesis co-supervisor(s):
Funder(s):
Degree grantor:
Language:
en

Institutional metadata

University researcher(s):
Academic department(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:317247
Created by:
Rowley, William
Created:
15th November, 2018, 09:25:45
Last modified by:
Rowley, William
Last modified:
3rd January, 2019, 13:48:45

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