Metric-based optimisation of acoustic lenses and waveguides

MacDonald, L

Abstract

This dissertation develops an automated procedure for the design of acoustic waveguides that can support single parameter (1P) wave propagation over a large bandwidth. 1P waves include plane, cylindrical and spherical waves, and the waveguides aim to either perturb their path or convert between these types. This technology could, for example, be employed in the design of high-precision waveguides and horns for concert sound applications. The design process is driven by two performance metrics proposed by Oclee-Brown, which are calculated from the solution of Laplace’s equation in the waveguide. These highlight regions of error in the relative pathlength (“stretch”) and change in area (“flare”) through the domain. Finite Element Analysis (FEA) is used to calculate these metrics on several test cases. A technique for tracing streamlines of a vector function through the FEA mesh is developed, and these are used to further manipulate the waveguide performance metrics. The method of equalising the relative pathlength by distorting regions of a thin domain, which is covered in the GP Acoustics patent EP3806086A1 (Dodd & Oclee-Brown, 2021), is then investigated. Combined with FEA analysis, this becomes an optimisation tool aiding the design process, and the acoustic performance of the optimised designs is evaluated by FEA simulations of the Helmholtz equation. This is quantified by the uniformity of SPL across the exit of the device. The relationship between arc length and perturbation amplitude is found for triangular and sinusoidal corrugations and used to equalise the relative pathlength in waveguides modelled as shell meshes. The modulated meshes are then re-analysed and the metrics indicate that they are better able to support 1P wave propagation. Thickened 3D waveguides are then considered, and both pathlength and area are optimised using the metrics as design tools. These are shown to perform better acoustically than the unoptimized geometry. Some of the limitations of the pathlength equalisation technique are then explored and discussed.

Citation

MacDonald, L. (2022). Metric-based optimisation of acoustic lenses and waveguides. (Dissertation). University Of Salford

• Thesis Type: Dissertation
• Deposit Date: Feb 2, 2023
• Publicly Available Date: Jan 27, 2025
• Award Date: Aug 26, 2022