Sound attenuation optimization using metaporous materials tuned on exceptional points

Analytic mode-matching for accurate handling of exceptional points in a lined acoustic waveguide

Exceptional points (which occur when two or more modes coalesce) have long been associated with optimal attenuation in lined acoustic waveguides. In recent years, with a view to optimizing sound absorption, some effort has gone into designing liners that generate exceptional points (EPs) at specified frequencies. However, analytic modelling of acoustic scattering in the presence of an EP is not well developed, with most authors relying on standard methods applied close to (but not at) EP conditions. Indeed, exact treatment requires care since the mathematical system under-pinning the scattering process is degenerate. This article presents an analytic mode-matching approach to modelling the scattering of a plane wave travelling towards the junction of a rigid duct with a lined duct at EP conditions. Both EP2 and EP3 (coalescence of two and three modes respectively) are considered. The enhanced mode-matching scheme is shown to be valid and numerically robust, and it is anticipated that it will be straightforward to adapt to a wide range of applications involving complex symmetric operators.

Gaussian-Based Machine Learning Algorithm for the Design and Characterization of a Porous Meta-Material for Acoustic Applications

The scope of this work is to consolidate research dealing with the vibroacoustics of periodic media. This investigation aims at developing and validating tools for the design and characterization of global vibroacoustic treatments based on foam cores with embedded periodic patterns, which allow passive control of acoustic paths in layered concepts. Firstly, a numerical test campaign is carried out by considering some perfectly rigid inclusions in a 3D-modeled porous structure; this causes the excitation of additional acoustic modes due to the periodic nature of the meta-core itself. Then, through the use of the Delany–Bazley–Miki equivalent fluid model, some design guidelines are provided in order to predict several possible sets of characteristic parameters (that is unit cell dimension and foam airflow resistivity) that, constrained by the imposition of the total thickness of the acoustic package, may satisfy the target functions (namely, the frequency at which the first Transmission Loss (TL) peak appears, together with its amplitude). Furthermore, when the Johnson–Champoux–Allard model is considered, a characterization task is performed, since the meta-material description is used in order to determine its response in terms of resonance frequency and the TL increase at such a frequency. Results are obtained through the implementation of machine learning algorithms, which may constitute a good basis in order to perform preliminary design considerations that could be interesting for further generalizations.