Diffraction of sound from semi-infinite perforated and semi-infinite coated duct with ring source

Year 2024, Volume: 73 Issue: 3, 588 - 603, 27.09.2024

Burhan Tiryakioğlu

https://doi.org/10.31801/cfsuasmas.1413499

Abstract

This study delves into the analysis of acoustic waves emanating from a ring source in an infinite cylindrical duct. The duct is equipped with an acoustically absorbing lining on its outer surface when $z$ is less than $l$, and is perforated when $z$ is greater than $l$. The inclusion of acoustically absorbing lining results in a substantial increase in the complexity of the equations compared to the scenario without such lining. Through rigorous efforts, these intricate equation systems are numerically solved, and graphs are generated across various parameter values. Furthermore, by adjusting the parameter values, a physical resemblance is established with an existing study in the literature, showcasing impeccable alignment in the results.

Keywords

Absorbing lining, perforated duct, Wiener-Hopf, ring source

References

• Noble, B., Methods Based on the Wiener-Hopf Techniques, Pergamon Press, London, 1958.
• Rawlins, A.D., Wave propagation in a bifurcated impedance-lined cylindrical waveguide, Journal of Engineering Mathematics, 59 (2007), 419–435. https://doi.org/10.1007/s10665-007-9172-4
• Rienstra, S.W., Acoustic scattering at a hard-soft lining transition in a flow duct, Journal of Engineering Mathematics, 59 (2007), 451–475. https://doi.org/10.1007/s10665-007-9193-z
• Peake, N., Abrahams, I.D., Sound radiation from a semi-infinite lined duct, Wave Motion, 92 (2020), 102407. https://doi.org/10.1016/j.wavemoti.2019.102407
• Hussain, S., Ayub, M., & Nawaz, R., Analysis of high frequency EM-waves diffracted by a finite strip with impedance in anisotropic medium, Waves in Random and Complex Media, (2021), 1–19. https://doi.org/10.1080/17455030.2021.2000670
• Tiryakioglu, A., Tiryakioglu, B., Acoustic wave radiation from a coaxial pipe with partial lining and inner perforated screen, International Journal of Aeroacoustics, 22 (2023), 278–292. https://doi.org/10.1177/1475472X231183152
• Alkinidri, M., Hussain, S., and Nawaz, R., Analysis of Noise Attenuation through Soft Vibrating Barriers: An Analytical Investigation, AIMS Mathematics, 8 (2023), 18066–18087. https://doi.org/10.3934/math.2023918
• Hussain, S., Javaid, A., Alahmadi, H., Nawaz, R., and Alkinidri, M., A mathematical study of electromagnetic waves diffraction by a slit in non-thermal plasma, Optical and Quantum Electronics, 56 (2024), 213. https://doi.org/10.1007/s11082-023-05730-8
• Levine, H., Schwinger, J., On the radiation of sound from an unflanged circular pipe, Physical Review, 73 (1948), 383–406. https://doi.org/10.1103/PhysRev.73.383
• Rawlins, A.D., Radiation of sound from an unflanged rigid cylindrical duct with an acoustically absorbing internal surface, Proc. Roy. Soc. Lond. A., 361 (1978), 65–91. https://doi.org/10.1098/rspa.1978.0092
• Demir, A., Rienstra, S., Sound Radiation from a Lined Exhaust Duct with Lined Afterbody, 16th AIAA/CEAS Aeroacoustics Conference, (2010) pp. 1–18, Stockholm, Sweden.
• Demir, A., Buyukaksoy, A., Radiation of plane sound waves by a rigid circular cylindrical pipe with a partial internal impedance loading, Acta Acustica United with Acustica, 89 (2003), 578–585.
• Safdar, M., Ahmed, N., Afzal, M., & Wahab, A., Acoustic scattering in lined panel cavities with membrane interfaces, The Journal of the Acoustical Society of America, 154 (2023), 1138-1151. https://doi.org/10.1121/10.0020724
• Tiryakioglu, B., Analysis of sound transmission loss in an infinite duct with three different finite linings, International Journal of Modern Physics B, (2023), 2450384. https://doi.org/10.1142/S0217979224503843
• Demir, A., Büyükaksoy, A., Transmission of sound waves in a cylindrical duct with an acoustically lined muffler, International Journal of Engineering Science, 41 (2003), 2411–2427. https://doi.org/10.1016/S0020-7225(03)00240-4
• Demir, A., Büyükaksoy, A., Wiener–Hopf approach for predicting the transmission loss of a circular silencer with a locally reacting lining, International Journal of Engineering Science, 43 (2005), 398–416. https://doi.org/10.1016/j.ijengsci.2004.12.003
• Nilsson, B., Brander, O., The propagation of sound in cylindrical ducts with mean flow and bulk-reacting lining I. modes in an infinite duct, IMA Journal of Applied Mathematics, 26 (1980), 269–298. https://doi.org/10.1093/imamat/26.3.269
• Tiryakioglu, B., Radiation of acoustic waves by a partially lined pipe with an interior perforated screen. Journal of Engineering Mathematics, 122 (2020), 17–29. https://doi.org/10.1007/s10665-020-10042-x
• Tiryakioglu, B., The effect of semi perforated duct on ring sourced acoustic diffraction, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70 (2021), 1073–1084. https://doi.org/10.31801/cfsuasmas.699831
• Jones, D. S., Acoustic and Electromagnetic Waves, Clarendon Press , Oxford, 1986.
• Sullivan, J.W., Crocker, M.J., Analysis of concentric-tube resonators having unpartitioned cavities, Journal of the Acoustical Society of America, 64 (1978), 207–215. https://doi.org/10.1121/1.381963
• Abramowitz, M., Stegun, I., Handbook of Mathematical functions, Dover, New York, 1964.
• Ayub, M., Tiwana, M.H., & Mann, A.B., Reflection coefficient of a dominant mode in a trifurcated duct of soft walls in the presence of mean flow, Meccanica, 48 (2013), 341–349. https://doi.org/10.1007/s11012-012-9605-7
• Tiwana, M.H., Nawaz, R., & Mann, A.B., Radiation of sound in a semi-infinite hard duct inserted axially into a larger infinite lined duct, Analysis and Mathematical Physics, 7 (2017), 525–548. https://doi.org/10.1007/s13324-016-0154-4
• Mittra, R., Lee, S.W., Analytical techniques in the theory of guided waves, The Macmillan Company, 1971.