Abstract
Equivalent circuit analysis is a powerful tool for analysing acoustic systems where a lumped element model is valid. These equivalent circuits allow an overall impedance of the structure to be estimated which facilitates predictions of the reflectivity, transmissibility and/or absorptivity of the system. Complex acoustic systems are represented by non-planar equivalent circuits which are challenging to simplify to a single overall impedance value using traditional Kirchoff’s Law simplifications. A two-point impedance method using graph theory allows the impedance of a circuit to be estimated without simplification. The graph theory method is applied to a type of acoustic absorber structure named SeMSA (Segmented Membrane Sound Absorber) which had previously been investigated for a two-segment cell design. This method allows the SeMSA analysis to be expanded to multi-sector designs with a wider parameter space. A local optimisation routine is applied to the graph theory impedance estimation to maximise acoustic absorption of SeMSA under consideration of absorber depth, causal optimality and the targeted noise spectra. Analytical predictions are validated using numerical simulations. The optimised multi-sector absorber demonstrates 70.5% white noise absorption in the 20–4500 Hz frequency range with an absorber depth of 16 mm and is just 0.5 mm from the theoretical minimum depth to achieve this absorption response.
Highlights
Acoustic materials for sound absorption have evolved significantly from traditional bulk porous/fibrous absorbers to modern materials such as membrane-based metamaterials [1], absorbers consisting of arrangements of axially-coupled channels [2], acoustic black holes that direct acoustic waves to an absorptive core [3] and coiled Helmholtz resonators [4]
The cost function in Eq (17) has been minimised in order maximise white noise absorption in the 20–4500 Hz frequency range (Gxx[k] = 1, for all k). This optimisation procedure was repeated for a range of absorber depths
The presented graph theory method for calculating the two-point impedance of a circuit may be applied to any acoustic system e.g. waveguide, absorber or barrier where a lumped-element model is valid
Summary
Acoustic materials for sound absorption have evolved significantly from traditional bulk porous/fibrous absorbers to modern materials such as membrane-based metamaterials [1], absorbers consisting of arrangements of axially-coupled channels [2], acoustic black holes that direct acoustic waves to an absorptive core [3] and coiled Helmholtz resonators [4]. These modern materials typically target sub-wavelength absorption i.e. absorption coefficients of close to unity are achieved with material depths of order λ/100, where λ is the acoustic wavelength. Traditional bulk absorbers such as melamine or polyurethane acoustic foams generally exhibit poor absorption performance below 1 kHz unless depths of order 100 mm are used [6]
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