Acoustic metamaterials comprised of dead-end pores and black hole effect for low frequency sound absorption in linear and nonlinear regimes

Brooke, DC

Abstract

The aim of this work is to design and test acoustic metamaterial absorbers particularly for mitigation of
low frequency sound of high intensity. The absorbers designed are formed of a series of plates with a
central perforation, separated by air cavities. Two types of structures are investigated: the first has a
central perforation with a constant radius (pancake structure), while in the second the pore radius
gradually decreases along the thickness of the absorber (profile structures). In the structures of the first
type, the wave speed reduction is abrupt, while in the second a gradual impedance matching with air is
achieved. The structures developed are tested in a range of various experimental set-ups. This includes
performing measurements in a conventional impedance tube (linear regime), in a specially modified
impedance tube that allows pressures (RMS) up to 250 Pa using sine wave excitation (weakly nonlinear
regime for continuous sound) and in a shock tube (nonlinear regime for pulsed sound of amplitude of
up to 100 kPa). The models developed allow the predictions of the metamaterial structure performance
at low and high sound pressure levels. In order to test the models, the absorbers of various dimensions
are built, tested and the results of the measurements are compared with the model predictions. The
analytical model for the pancake absorber is used to derive simple formulae for the frequency and the
peak value of the absorption coefficient at the lowest frequency resonance in the linear regime,
depending on the geometrical parameters. This model is complemented by a Transfer Matrix Model
(TMM) and Finite Element Model (FEM) for both pancake and profile structures. The latter accounts for
the influence of the structural resonances and tortuosity effect of the plates on the absorber
performance.
To investigate the nonlinear regime, flow resistivity measurements are performed on the samples to
directly measure Forchheimer’s nonlinearity parameter. Flow resistivity measurements at low flow rates
show that the periodic set of cavities does not modify resistivity significantly when compared to a simple
perforated cylinder with same thickness. As flow rate increases, the flow resistivity grows linearly
according to Forchheimer’s law and has a significant dependence on the absorber thickness. A
nonlinear numerical model is developed accounting for the growth of flow resistivity with particle velocity
amplitude in the central perforation and compared with the measurements at high amplitudes of the
continuous incident sound. It is confirmed by measurements, that the peak absorption coefficient values
for both types of absorbers decrease as the sound amplitude grows (irrespective of dimensions of pore
radius and value of open surface area ratio). Where the peak values of absorption coefficient for the
pancake absorbers are shown to be significantly reduced compared to the profile structures as
amplitude strength grows to nonlinear regime. The resonance frequencies, however, remain close to
their measured values independent of amplitude strength and is advantageous for both structures.
Measurements in a shock tube are performed in both rigid backing and transmission set-ups, in time
domain. Fast Fourier Transform (FFT) is later performed to investigate the signals. It is demonstrated
that the profile absorber design is advantageous for the absorption of high amplitude pulsed sound.

Citation

Brooke, D. Acoustic metamaterials comprised of dead-end pores and black hole effect for low frequency sound absorption in linear and nonlinear regimes. (Thesis). University of Salford

• Thesis Type: Thesis
• Deposit Date: Oct 5, 2021
• Publicly Available Date: Oct 5, 2021
• Award Date: Aug 1, 2021