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Sound Wave Diffraction by a Cavity with Partial Lining

Year 2020, Volume: 8 Issue: 1, 123 - 133, 20.03.2020

Burhan Tiryakioğlu

https://doi.org/10.36753/mathenot.622522

Abstract

Diffraction of sound wave through a cavity with partial lining is analyzed rigorously. By using the Fourier transform technique in conjunction with the Mode Matching method, the related boundary value problem is formulated as a Wiener-Hopf equation. In the solution, three infinite sets of unknown coefficients are involved that satisfy three infinite systems of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem. The influence of the different parameters such as the lining length, cavity depth, etc. on the diffraction are illustrated graphically. A perfect agreement is observed when the results of diffracted field are compared numerically with a similar work existing in the literature.

Keywords

Cavity Diffraction Wiener-Hopf technique Fourier transform Mode Matching

References

  • Kobayashi K., Sawai A. Plane Wave Diffraction by an Open-Ended Parallel Plate Waveguide Cavity, Journal of Electromagnetic Waves and Applications, 6 (1992), 475-512.
  • Victoria A„ Kimberly S.R., Jonathan J., Rajind M., Daniel M.M. Terahertz multichannel microfluidic sensor based on parallel-plate waveguide resonant cavities, Appl. Phys. Lett. 100 (2012), 231108.
  • Tong Y., Pan J. Modal analysis of the scattering coefficients of an open cavity in a waveguide, Wave Motion, 68 (2017), 242-252.
  • Porter R., Evans D.V. Analysis of the effect of a rectangular cavity resonator on acoustic wave transmission in a waveguide, Journal of Sound and Vibration, 708 (2017), 138-153.
  • Rawlins A.D. Radiation of sound from an unflanged rigid cylindrical duct with an acoustically absorbing internal surface, Z. Proc. Roy. Soc. Lond. 361 (1978), 65-91.
  • Rienstra S.W. Acoustic scattering at a hard-soft lining transition in al flow duct, Journal of Engineering Mathematics. 59 (2007), 451-475.
  • Snakowska A., Jurkiewicz J., Gorazd L. A hybrid method for determination of the acoustic impedance of an unflanged cylindrical duct for multimode wave, Journal of Sound and Vibration. 396 (2017), 325-339.
  • Tiryakioglu B., Demir A. Radiation analysis of sound waves from semi-infinite coated pipe, International Journal of Aeroacoustics. 18 (2019), 92-111.
  • Tiryakioglu B., Demir A. Sound Wave Radiation from Partially Lined Duct, Archives of Acoustics. 44 (2019), 239-249.
  • Demir A., Buyukaksoy A., Polat B., Diffraction of plane sound wave by a rigid circular cylindrical cavity with an acoustically absorbing internal surface, Z. Angew. Math. Mech. 82 (2002), 619-629.
  • Matsui E. Free-field correction for laboratory standard microphones mounted on a semiinfinite rod, J. Acoust. Soc. Am. 49 (1970), 1475-1483.
  • Kuryliak D.B., Koshikawa S., Kobayashi K., Nazarchuk Z.T. Wiener-Hopf analysis of the vector diffraction problems for a circular waveguide cavity, Tech. Rep., IECE Japan, (2000), 73-80.
  • Kuryliak D.B, Koshikawa S., Kobayashi K., Nazarchuk Z.T. Wiener-Hopf analysis of the axial symmetric wave diffraction problem for a circular waveguide cavity, Int. Workshop on Direct and Inverse Wave Scattering. Gebze, Turkey, (2000), 25-29.
  • Noble B., Methods based on theWiener-Hopf Technique, 2nd edn. Chelsea Publishing Company, New York, 1988.
  • Watson G.N., A treatise on the theory of Bessel functions, 2nd edn. Cambridge University Press, London, 1944.
  • Mittra R., Lee S.W., Analytical Techniques in the Theory of Guided Waves, McMillan, New York, 1971.

Year 2020, Volume: 8 Issue: 1, 123 - 133, 20.03.2020

Burhan Tiryakioğlu

https://doi.org/10.36753/mathenot.622522

Abstract

References

  • Kobayashi K., Sawai A. Plane Wave Diffraction by an Open-Ended Parallel Plate Waveguide Cavity, Journal of Electromagnetic Waves and Applications, 6 (1992), 475-512.
  • Victoria A„ Kimberly S.R., Jonathan J., Rajind M., Daniel M.M. Terahertz multichannel microfluidic sensor based on parallel-plate waveguide resonant cavities, Appl. Phys. Lett. 100 (2012), 231108.
  • Tong Y., Pan J. Modal analysis of the scattering coefficients of an open cavity in a waveguide, Wave Motion, 68 (2017), 242-252.
  • Porter R., Evans D.V. Analysis of the effect of a rectangular cavity resonator on acoustic wave transmission in a waveguide, Journal of Sound and Vibration, 708 (2017), 138-153.
  • Rawlins A.D. Radiation of sound from an unflanged rigid cylindrical duct with an acoustically absorbing internal surface, Z. Proc. Roy. Soc. Lond. 361 (1978), 65-91.
  • Rienstra S.W. Acoustic scattering at a hard-soft lining transition in al flow duct, Journal of Engineering Mathematics. 59 (2007), 451-475.
  • Snakowska A., Jurkiewicz J., Gorazd L. A hybrid method for determination of the acoustic impedance of an unflanged cylindrical duct for multimode wave, Journal of Sound and Vibration. 396 (2017), 325-339.
  • Tiryakioglu B., Demir A. Radiation analysis of sound waves from semi-infinite coated pipe, International Journal of Aeroacoustics. 18 (2019), 92-111.
  • Tiryakioglu B., Demir A. Sound Wave Radiation from Partially Lined Duct, Archives of Acoustics. 44 (2019), 239-249.
  • Demir A., Buyukaksoy A., Polat B., Diffraction of plane sound wave by a rigid circular cylindrical cavity with an acoustically absorbing internal surface, Z. Angew. Math. Mech. 82 (2002), 619-629.
  • Matsui E. Free-field correction for laboratory standard microphones mounted on a semiinfinite rod, J. Acoust. Soc. Am. 49 (1970), 1475-1483.
  • Kuryliak D.B., Koshikawa S., Kobayashi K., Nazarchuk Z.T. Wiener-Hopf analysis of the vector diffraction problems for a circular waveguide cavity, Tech. Rep., IECE Japan, (2000), 73-80.
  • Kuryliak D.B, Koshikawa S., Kobayashi K., Nazarchuk Z.T. Wiener-Hopf analysis of the axial symmetric wave diffraction problem for a circular waveguide cavity, Int. Workshop on Direct and Inverse Wave Scattering. Gebze, Turkey, (2000), 25-29.
  • Noble B., Methods based on theWiener-Hopf Technique, 2nd edn. Chelsea Publishing Company, New York, 1988.
  • Watson G.N., A treatise on the theory of Bessel functions, 2nd edn. Cambridge University Press, London, 1944.
  • Mittra R., Lee S.W., Analytical Techniques in the Theory of Guided Waves, McMillan, New York, 1971.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Burhan Tiryakioğlu 0000-0003-1448-6147

Publication Date March 20, 2020
Submission Date September 20, 2019
Acceptance Date March 13, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Tiryakioğlu, B. (2020). Sound Wave Diffraction by a Cavity with Partial Lining. Mathematical Sciences and Applications E-Notes, 8(1), 123-133. https://doi.org/10.36753/mathenot.622522
AMA Tiryakioğlu B. Sound Wave Diffraction by a Cavity with Partial Lining. Math. Sci. Appl. E-Notes. March 2020;8(1):123-133. doi:10.36753/mathenot.622522
Chicago Tiryakioğlu, Burhan. “Sound Wave Diffraction by a Cavity With Partial Lining”. Mathematical Sciences and Applications E-Notes 8, no. 1 (March 2020): 123-33. https://doi.org/10.36753/mathenot.622522.
EndNote Tiryakioğlu B (March 1, 2020) Sound Wave Diffraction by a Cavity with Partial Lining. Mathematical Sciences and Applications E-Notes 8 1 123–133.
IEEE B. Tiryakioğlu, “Sound Wave Diffraction by a Cavity with Partial Lining”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 123–133, 2020, doi: 10.36753/mathenot.622522.
ISNAD Tiryakioğlu, Burhan. “Sound Wave Diffraction by a Cavity With Partial Lining”. Mathematical Sciences and Applications E-Notes 8/1 (March 2020), 123-133. https://doi.org/10.36753/mathenot.622522.
JAMA Tiryakioğlu B. Sound Wave Diffraction by a Cavity with Partial Lining. Math. Sci. Appl. E-Notes. 2020;8:123–133.
MLA Tiryakioğlu, Burhan. “Sound Wave Diffraction by a Cavity With Partial Lining”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, 2020, pp. 123-3, doi:10.36753/mathenot.622522.
Vancouver Tiryakioğlu B. Sound Wave Diffraction by a Cavity with Partial Lining. Math. Sci. Appl. E-Notes. 2020;8(1):123-3.
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