Reflection coefficient of a dominant mode in a pentafurcated duct

Buyukaksoy, A, Tayyar, IH, Uzgoren, G: Influence of the junction of perfectly conducting and impedance parallel plate semi-infinite waveguides to the dominant mode propagation. J. Math. Anal. Appl. 143, 341-357 (2006)

Rawlins, AD: A bifurcated waveguide problem. J. Appl. Math. 54, 59-81 (1995)

Mahmood-ul-Hassan, Rawlins, AD: Two problems of waveguide carrying mean flow. J. Sound Vib. 216(4), 713-738 (1999)

Mahmood-ul-Hassan, Rawlins, AD: Sound radiation in a planar trifurcated lined duct. Wave Motion 29, 157-174 (1998)

Ayub, M, Tiwana, MH, Mann, AB, et al.: Acoustic wave propagation in a trifurcated lined waveguide. ISRN Appl. Math. 2011, Article ID 532682 (2011)

Ayub, M, Tiwana, MH, Mann, AB: Wiener-Hopf analysis of an acoustic plane wave in a trifurcated waveguide. Arch. Appl. Mech. 81, 701-713 (2011)

Ayub, M, Tiwana, MH, Mann, AB: Influence of the dominant mode propagation in a trifurcated lined duct with different impedance. Phys. Scr. 81(3), Article ID 035402 (2010)

Demir, A, Cinar, OY: Propagation of sound in an infinite two-part duct carrying mean flow inserted axially into a large infinite duct with wall impedance discontinuity. J. Appl. Math. Mech. 89(6), 454-465 (2009)

Andronov, IV, Belinskii, BP: On acoustic boundary-contact problems for a vertically stratified medium bounded from above by a plate with concentrated inhomogeneities. J. Appl. Math. Mech. 54, 366-371 (1990)

Lawrie, JB, Abrahams, ID: An orthogonality condition for a class of problems with high order boundary conditions, application in sound/structure interaction. Q. J. Mech. Appl. Math. 52, 161-181 (1999)

Lawrie, JB, Kirby, R: Mode-matching without root-finding: application to a dissipative silencer. J. Acoust. Soc. Am. 119, 2050-2061 (2006)

Lawrie, JB: On eigenfunction expansions associated with wave propagation along ducts with wave bearing boundaries. IMA J. Appl. Math. 72, 376-394 (2007)

Lawrie, JB: Analytic mode-matching for acoustic scattering in three dimensional waveguides with flexible walls, application to a triangular duct. Wave Motion 50(3), 542-557 (2013)

Mahmood-ul-Hassan, Meylan, MH, Peter, MA: Water-wave scattering by submerged elastic plates. Q. J. Mech. Appl. Math. 62(3), 321-344 (2009)

Nawaz, R, Lawrie, JB: Scattering of a fluid-structure coupled wave at a flanged junction between two flexible waveguides. J. Acoust. Soc. Am. 134(3), 1939-1949 (2013)

Decrossas, E, Sabbagh, MAE, Hanna, VF, El-Ghazaly, SM: Mode matching technique-based modeling of coaxial and circular waveguide discontinuities for material characterization purposes. Int. J. Microw. Wirel. Technolog. 3(6), 679-690 (2011)

Ranajit, D, Chakarbarty, S, Ranjeev, J, et al.: Synthesis and analysis of multi-mode profile horn using mode-matching technique and evolutionary algorithm. IET Microw. Antennas Propag. 10(3), 1-7 (2016)

Meylan, MH, Bennets, LG, Peter, MA: Water-wave scattering and energy dissipation by a floating porous elastic plate in three dimensions. Wave Motion 70, 240-250 (2017). doi: 10.1016/j.wavemoti.2016.06.014

Sanchis, P, Marti, J, Balasco, J, Martinez, A, et al.: Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits. Opt. Express 10, 1391-1397 (2003)

Mahmood-ul-Hassan: Wave scattering by soft-hard three spaced waveguide. Appl. Math. Model. 38, 4528-4537 (2014)

Mahmood-ul-Hassan, Meylan, MH, Amna, B, et al.: Mode matching analysis for wave scattering in triple and pentafurcated spaced ducts. Math. Methods Appl. Sci. 39(11), 2783-3158 (2016)

Mahmood-ul-Hassan, Mahvish, N, Nawaz, R: Reflected field analysis of soft-hard pentafurcated waveguide. Adv. Mech. Eng. 9(2), 1-11 (2017). doi: 10.1177/1687814017692697

Afzal, M, Nawaz, R, Ayub, M, Wahab, A: Acoustic scattering in flexible waveguide involving step discontinuity. PLoS ONE 9(8), e103807 (2014)

Mei, CC (ed.): The Applied Dynamics of Ocean Surface Waves. Wiley, New York (1983)

Linton, CM, Mclver, P (eds.): Handbook of Mathematical Techniques for Wave/Structure Interactions. Chapman and Hall/CRC, New York (2001)

Riley, KF, Hobson, MP, Bence, SJ: Mathematical Methods for Physics and Engineering, 3rd edn. Cambridge University Press, Cambridge (2006)