Archives of Acoustics, 45, 4, pp. 655–662, 2020
10.24425/aoa.2020.135253

Radiation of Sound from a Coaxial Duct Formed by a Semi-Infinite Rigid Outer Cylinder and Infinite Inner Cylinder Having Different Linings

Hülya ÖZTÜRK
Gebze Technical University
Turkey

Burhan TIRYAKIOGLU
Marmara University
Turkey

In the present work, the radiation of sound waves from a coaxial duct is considered. This coaxial duct has an inner wall which is infinite and has piecewise acoustically absorbent material, while the outer wall is semi-infinite and rigid. The analytical solution of the problem is found by means of the Wiener-Hopf technique. Applying the Fourier transformation to the boundary value problem, the explicit expression for the scattered field is obtained. In the end, some numerical results are displayed for different parameters and compared to rigid case.
Keywords: Wiener-Hopf technique; absorbent lining; coaxial duct; acoustic radiation
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).

References

Buyukaksoy A., Polat B. (1998), Diffraction of acoustic waves by a semi-infinite cylindrical impedance pipe of certain wall thickness, Journal of Engineering Mathematics, 33(4): 333–352, doi: 10.1023/A:1004301829276.

Çınar Ö.Y. (2013), Scattering of plane acoustic waves by a circular semi-infinite pipe with a rigid end face placed axially in an infinite circular duct, Journal of Applied Mathematics and Mechanics, 93(12): 963–976, doi: 10.1002/zamm.201200062.

Çınar G., Öztürk H., Çınar Ö.Y. (2011), Reflection and transmission of plane acoustic waves in an infinite annular duct with a finite gap on the inner wall, Mathematical Methods in Applied Sciences, 34(2): 220–230, doi: 10.1002/mma.1351.

Cremer L. (1953), Theorie der Luftschall Ddmpfung im Rechteckkanal mitschluckender Wand und das sich daboi ergebendehochste Dampfungs, Acoustica, 3: 249–263.

Demir A., Buyukaksoy A. (2003), Radiation of plane sound waves by a rigid circular cylindrical pipe with a partial internal impedance loading, Acta Acustica United with Acustica, 89(4): 578–585.

Demir A., Rienstra S. (2010), Sound radiation from a lined exhaust duct with lined afterbody, 16th AIAA/CEAS Aeroacoustics Conference, 18 pages, Stockholm, Sweden, doi: 10.2514/6.2010-3947.

Lapin A.D. (1975), Sound attenuation in waveguides (review), Soviet Physics Acoustics, 21(3): 215–222.

Lawrie J.B., Abrahams I.D., Linton C.M. (1993), Acoustic radiation from two opposed semi-infinite coaxial cylindrical waveguides. I: Overlapping edges, Wave Motion, 18(2): 121–142, doi: 10.1016/0165-2125(93)90044-G.

Levine H., Schwinger J. (1948), On the radiation of sound from an unflanged circular pipe, Physical Review, 73(4): 383–406, doi: 10.1103/PhysRev.73.383.

Morse P.M. (1939), The transmission of sound inside pipes, Journal of the Acoustical Society of America, 11(2): 205–210, doi: 10.1121/1.1916024.

Ozturk H. (2020), Radiation of acoustic waves from a circumferential slot on a circular waveguide, TWMS Journal of Applied and Engineering Mathematics, 10(3): 690–701.

Peake N., Abrahams I.D. (2020), Sound radiation from a semi-infinite lined duct, Wave Motion, 92: 102407, doi: 10.1016/j.wavemoti.2019.102407.

Rawlins A.D., Jones D.S. (1978), Radiation of sound from an unflanged rigid cylindrical duct with an acoustically absorbing internal surface, Proceedings of the Royal Society London. Series A, Mathematical and Physical Sciences, 361(1704): 65–91, doi: 10.1098/rspa.1978.0092.

Rienstra S.W. (2007), Acoustic scattering at a hardsoft lining transition in a flow duct, Journal of Engineering Mathematics, 59(4): 451–475, doi: 10.1007/s10665-007-9193-z.

Rienstra S.W., Peake N. (2005) Modal scattering at an impedance transition in a lined flow duct, 11th AIAA/CEAS Aeroacoustics Conference, pp. 1–19, Monterey, CA, USA, doi: 10.2514/6.2005-2852.

Snakowska A., Idczak H. (2006), The saddle point method applied to selected problems of acoustics, Archives of Acoustics, 31(1): 57–76.

Snakowska A., Jurkiewicz J., Gorazd L. (2017), A hybrid method for determination of the acoustic impedanceof an unflanged cylindrical duct for multimode wave, Journal of Sound and Vibration, 396: 325–339, doi: 10.1016/j.jsv.2017.02.040.

Tiryakioglu B. (2019), Sound radiation from the perforated end of a lined duct, Acta Acustica united with Acustica, 105(4): 591–599, doi: 10.3813/ AAA.919340.

Tiryakioglu B. (2020), Radiation of sound waves by a semi infinite duct with outer lining and perforated end, Archives of Acoustics, 45(1): 77–84, doi: 10.24425/aoa.2020.132483.

Tiwana M.H., Nawaz R., Mann A.B. (2017), Radiation of sound in a semi-infinite hard duct inserted axially into a larger infinite lined duct, Analysis and Mathematical Physics, 7(4): 525–548, doi: 10.1007/s13324-016-0154-4.




DOI: 10.24425/aoa.2020.135253