Abstract
dc:description.abstractThis thesis considers the sound scattering by thin perforated plates, to further understand and develop analytic models for porous noise reduction metamaterials. The semi-analytic Fokas method is extended to periodic geometries, and the resulting integral equation, recognised as a generalised Dirichlet-to-Neumann map, is solved numerically; the scattering solution is recovered through a Green's integral representation. The approximation method is based on a pseudospectral collocation approach, forming a rectangular system solved via a least-squares approach. The conditioning and stability of the system is managed by oversampling collocation points. A wide variety of boundary conditions are considered, including sound-hard, sound-soft, impedance and elastic. The rigid perforated plate solution is compared against techniques for infinite gratings, such as the Wiener--Hopf technique. It is found that the novel method shows much greater flexibility around the lengths of the apertures; furthermore, the evaluation of the scattered field is easier and faster. This work further extends to problems that have not yet been robustly considered; periodic structures constructed from multiple layers of perforated plates, each with possibly differing boundary conditions and periods. Engineering applications include the use of layered perforated structures such as anti-reflection or anti-transmission coatings. The investigation of the acoustic behaviour of these periodic structures is used to construct a homogenisation model for an effective surface with an effective impedance parameter. The homogenised model produces an estimate for the compliance of a homogeneous plate that exhibits the same acoustic properties as the infinite grating in the far field. This thesis constructs such a compliance for gratings with arbitrary parameter values and validates against the existing grating compliance, which is only valid for normally incident waves. We further demonstrate that the homogenised parameter found by our method provides greater accuracy in the low-frequency, low-porosity limit than alternatives.
Degree
thesis:*- Name dc:type.qualificationname
- Doctor of Philosophy (PhD)
- Level dc:type.qualificationlevel
- Doctoral
- Grantor dc:publisher.institution
- University of Cambridge
- Year dc:date.issued
- 2025
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Naqvi, Shiza
- Advisor dc:contributor.advisor
-
- Ayton, Lorna
Subjects
dc:subject × 2Rights
dc:rightsIdentifiers
dc:identifier.*- DOI dc:identifier.doi
- https://doi.org/10.17863/CAM.121696
- OAI identifier oai:identifier
- oai:www.repository.cam.ac.uk:1810/389976