A graph-theory approach to optimisation of an acoustic absorber targeting a specific noise spectrum that approaches the causal optimum minimum depth

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.