Sound radiation from a semi-infinite lined duct

• Published in: Wave motion 2020-01, Vol.92, p.102407, Article 102407
• Main Authors: Peake, N., Abrahams, I.D.
• Format: Article
• Language: English
• Subjects: Acoustic lining; Ducts; Ductwork; Factorization; Far fields; Matrix; Mechanical properties; Radiation; Sound; Sound waves; Wiener–Hopf technique
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2019.102407

In this paper we consider the radiation properties of a pair of semi-infinite, parallel-plate ducts in which the inner duct is buried inside the outer duct. A Robin condition is applied to one of the inner walls (to represent an acoustic lining), while Neumann conditions are applied on all other surfaces. This leads to a matrix Wiener–Hopf problem, which requires the factorisation of a 3×3 matrix of a form which, to our knowledge, has not previously been considered in the literature and which is not directly amenable to standard pole-removal techniques. We derive the exact factorisation of this matrix here, and present results for the far-field scattered sound which show the effect of varying the properties of the wall lining. •Factorisation of a form of Wiener–Hopf matrix not previously treated, using a novel double application of the pole removal technique.•Quantitative prediction of sound radiation from a trifurcated waveguide containing acoustic lining.•Sound directivity can be strongly affected by lining, especially directly downstream and in side line directions.•Solution is amenable to extension to include effects of different flow streams and cylindrical geometry.