A Note on Ring Source over Semi-Infinite Rigid Pipe

Öz

In this paper, rigid-lined infinite tube is considered. An analytical solution is presented for the diffraction problem of acoustic waves spreading from a ring source by an infinite tube. Applying the boundary and continuity conditions in conjunction with the Fourier transform technique, the boundary value problem is solved analytically. The influence of the problem parameters on the diffraction phenomenon is displayed graphically.

Anahtar Kelimeler

• Ring Source,Diffraction,Saddle Point,Pipe

A Note on Ring Source over Semi-Infinite Rigid Pipe

Öz

In this paper, rigid-lined infinite tube is considered. An analytical solution is presented for the diffraction problem of acoustic waves spreading from a ring source by an infinite tube. Applying the boundary and continuity conditions in conjunction with the Fourier transform technique, the boundary value problem is solved analytically. The influence of the problem parameters on the diffraction phenomenon is displayed graphically.

Anahtar Kelimeler

• Ring Source,Diffraction,Saddle Point,Pipe

Kaynakça

1. Büyükaksoy, A., and Demir, A. (2006). Radiation of sound from a semi‐infinite rigid duct inserted axially into a larger infinite tube with wall impedance discontinuity. ZAMM - Journal of Applied Mathematics and Mechanics, 86, 563-571.
2. Demir, A. (2017). Scattering matrices in non-uniformly lined ducts. Zeitschrift für angewandte Mathematik und Physik, 68, 1-15.
3. Nilsson, B., and Brander, O. (1980). 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, 269–298.
4. Rienstra, S. W. (1999). Sound transmission in slowly varying circular and annular ducts with flow, Journal of Fluid Mechanics, 380, 279-296.
5. Hassan, M., and Rawlins A. D. (1999). Sound radiation in a planar trifurcated lined duct. Wave Motion, 29, 157–174.
6. Tiryakioglu, B., and Demir, A. (2018). Radiation analysis of sound waves from semi-infinite coated pipe. International Journal of Aeroacoustics, https://doi.org/10.1177/1475472X18812802.
7. Büyükaksoy, A. and Polat, B. (1998). Diffraction of acoustic waves by a semi-infinite cylindrical impedance pipe of certain wall thickness. Journal of Engineering Mathematics, 33,333-352.
8. Tiryakioglu, B., and Demir, A. (2015). Wiener-Hopf Analysis of Sound Waves by a Rigid Cylindrical Pipe with External Impedance Surface. International Journal of Mathematical Models and Methods in Applied Sciences, 9, 558-565, 2015.