This week on 6th Oct 2021 our lunchtime Acoustics Research Seminars resume and we are happy that two recent MSc Audio Acoustics graduates – Johnny Lee and Kim Steele – will present their project work for us.
- Kim will tell us about her work on developing a time domain version of the transfer matrix method
- Johnny will tell us about his work on extending the bandwidth of a passive Bessel diffuser
Abstract for both are below. The seminar will be 12;30 – 13:30 on Teams. Click here to join the meeting
A Time Domain version of the Transfer Matrix Method
Kim Steele (supervised by Dr Jonathan Hargreaves)
The Transfer Matrix Method (TMM) is an established way of computing reflections from porous absorbers in the frequency domain. Recently there has been increasing interest in time domain simulation e.g. so that auralisation can be performed. Often this models materials by fitting a digital filter to the surface impedance. Here a different approach is proposed, using a filter network that is a time domain manifestation of the TMM equations. Together they compute the pressure wave reflected in response to a given incident wave. The porous material layers are modelled using the Miki model, with coefficients as modified by Dragna and Blanc-Benon to ensure passivity and causality. This includes fractional-order differentials, to which Infinite Impulse Response (IIR) filters are fitted using the Oustaloup method. Reflectance and transmission filters at the interfaces between layers can be found directly from these, but the dispersive nature of the porous material means propagation within each layer requires a 1D Finite Difference Time Domain (FDTD) scheme. This is wrapped within a filter-style interface for ease of use in the network. The new model is validated against the frequency-domain TMM through Fourier transform of the reflected wave signal it computes. Configurations using one or two layers of material on a rigid backing are presented. These show good agreement for a wide bandwidth, though differences appear at the lowest and highest frequencies due to approximations in the filter fitting. Future work could include adding mass layers and/or validation against measured reflectance impulse responses.
Extending the Bandwidth of a Passive Bessel Diffuser
Johnny Shu Shan Lee (supervised by Prof Trevor Cox)
The polar responses of the well-known Schroeder diffusers that were designed using number sequences exhibited grating lobes and are not perfect sound diffusers. To resolve this problem, Prof T.J. Cox designed the first diffuser inspired by Bessel arrays, which aims for “single-transducer”-like scattering at the design frequency (f0) when reflection coefficients are proportional to a Bessel function of the first kind. Through research, the number of working frequencies was increased to f0 = 500 Hz and 2f0 within 2D FEM and BEM. FEM impedance tube experiments were conducted to design each well to produce target reflection coefficients for f0 and 2f0, equivalent to the normalised Bessel coefficients. This was achieved by manipulating phase by combining Helmholtz resonator and acoustic metamaterial technology with damped and undamped quarter-wavelength resonators. It is discovered using BEM that the Bessel diffuser does not scatter as intended due to well interaction and edge diffraction from the diffuser back and sides. A characteristic destructive interference angle was also observed. Further investigation in BEM using a rectangular block with boundary impedance conditions matching that of an ideal Bessel diffuser at f0 and 2f0 showed us that well widths can be designed to control the degree of intercell cancellation, low frequency absorption while compromising either low or high frequency diffusion. The optimal well width where diffusion at f0 and 2f0 matched was at λ0/3.2. Diffraction from the diffuser back and sides were found to be the main culprit in lower frequency scattering not being “single-transducer”-like.