Mode-Matching Analysis of Acoustic Wave Propagation along a Rigid Coaxial Pipe with an Internal Impedance Loading

Öz

Mathematical analysis of the acoustic wave propagation along the coaxial waveguide, whose right part of the outer wall is impedance-coated, is considered. By determining the boundary conditions corresponding to the relevant geometry, the boundary value problem is solved by applying the Mode-Matching technique. At the end of the analysis, numerical computations are carried out to illustrate the affect of some parameters. The results demonstrate the significance of the absorbing lining in reducing the unwanted noise.

Anahtar Kelimeler

• Mode-Matching
• Coaxial Waveguide
• Acoustics
• Absorbent Lining.

Dış Duvarının Yarısı Akustik Yutucu Malzeme ile Kaplı Rijit Koaksiyel Bir Boruda Akustik Dalgaların Yayılımının Mod-Uydurma ile Analizi

Öz

Dış duvarının yarısı akustik yutucu malzeme ile kaplı koaksiyel bir boruda akustik dalgaların yayılımının analizi yapılmıştır. İlgili geometriye karşılık gelen sınır koşulları belirlenmiş ve bu koşullardan faydalanılarak mod uydurma tekniği ile sınır değer problemi çözülmüştür. Analizin sonunda ise, bazı parametrelerin ses yayılımına etkisi nümerik sonuçlar ile sunulmuştur. Akustik yutucu malzeme sayesinde istenmeyen gürültünün azaltılabileceği görülmüştür.

Anahtar Kelimeler

• Mod-Uydurma
• Koaksiyel Dalga Kılavuzu
• Akustik
• Yutucu Malzeme.

Kaynakça

1. Rawlins, A. D. “Radiation of sound from an unflanged rigid cylindrical duct with an acoustically absorbing internal surface,” Proc. R. Soc. A., vol. 361, pp. 65-91, 1978.
2. Rienstra, S. W. “Acoustic scattering at a hard–soft lining transition in a flow duct,” J. Eng. Math., vol. 59, pp. 451-475, 2007.
3. Lawn, C. “Calculation of acoustic absorption in ducts with perforated liners,” Appl. Acoust., vol. 89, pp. 211-221, 2015.
4. Çınar, G., Öztürk H., and Çınar, Ö. Y. “Reflection and transmission of plane acoustic waves in an infinite annular duct with a finite gap on the inner wall,” Math. Methods Appl. Sci., vol. 34, pp. 220-230, 2011.
5. Levine H., and Schwinger, J. “On the radiation of sound from an unflanged circular pipe,” Phys. Rev., vol. 73, pp. 383-406, 1948.
6. Sobolev, A. F., and Yakovets, M. A. “Application of the Wiener-Hopf method for describing the propagation of sound in cylindrical and rectangular channels with an impedance jump in the presence of a flow,” Acoust. Phys., vol. 63, pp. 623-636, 2017.
7. Peake, N., and Abrahams, I. D. “Sound radiation from a semi-infinite lined duct, ” Wave Motion, vol. 92, 102407, 2020.
8. Öztürk, H. “Radiation of acoustic waves from a circumferential slot on a circular waveguide,” TWMS J. of Appl. and Eng. Math., vol. 10, pp. 690-701, 2020.

9. Hassan, M., Meylan, H. M., Bashir, A., and Sumbul, M. “Radiation matching analysis for wave scattering in triple and pentafurcated spaced ducts,” Math. Methods Appl. Sci., vol. 39, pp. 3043-3057, 2016.
10. Shafique, S., Afzal, M., and Nawaz, R. “On mode-matching analysis of fluid structure coupled wave scattering between two flexible waveguides,” Can. J. Phys., vol. 95, pp. 585-589, 2017.
11. Hassan, M., and Bashir, A. “Effect of soft outer lining in pentafurcated duct,” Can. J. Phys., vol. 96, pp. 165-173, 2018.
12. Kuryliak, D. B., and Sharabura, O. M. “Wave diffraction from the biconical section in the semi-infinite conical region,” Math. Methods Appl. Sci., vol. 43, pp. 1565-1581, 2019.
13. Khalid, A., Younas, S., Khan, I., Manzoor, R., Rab, N., and Sherif, E. M. “Mode-matching analysis for two-dimensional acoustic wave propagation in a trifurcated lined duct,” J. Interdiscip Math., vol. 22, pp. 1095-1112, 2020.