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Sound Wave Diffraction by a Cavity with Partial Lining

Burhan TİRYAKİOĞLU [1]

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.
Cavity, Diffraction, Wiener-Hopf technique, Fourier transform, Mode Matching
• 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.
Primary Language en Engineering Articles Orcid: 0000-0003-1448-6147Author: Burhan TİRYAKİOĞLU (Primary Author)Institution: Marmara UniversityCountry: Turkey Publication Date : March 20, 2020
 Bibtex @research article { mathenot622522, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2020}, volume = {8}, pages = {123 - 133}, doi = {10.36753/mathenot.622522}, title = {Sound Wave Diffraction by a Cavity with Partial Lining}, key = {cite}, author = {Ti̇ryaki̇oğlu, Burhan} } APA Ti̇ryaki̇oğlu, B . (2020). Sound Wave Diffraction by a Cavity with Partial Lining . Mathematical Sciences and Applications E-Notes , 8 (1) , 123-133 . DOI: 10.36753/mathenot.622522 MLA Ti̇ryaki̇oğlu, B . "Sound Wave Diffraction by a Cavity with Partial Lining" . Mathematical Sciences and Applications E-Notes 8 (2020 ): 123-133 Chicago Ti̇ryaki̇oğlu, B . "Sound Wave Diffraction by a Cavity with Partial Lining". Mathematical Sciences and Applications E-Notes 8 (2020 ): 123-133 RIS TY - JOUR T1 - Sound Wave Diffraction by a Cavity with Partial Lining AU - Burhan Ti̇ryaki̇oğlu Y1 - 2020 PY - 2020 N1 - doi: 10.36753/mathenot.622522 DO - 10.36753/mathenot.622522 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 123 EP - 133 VL - 8 IS - 1 SN - -2147-6268 M3 - doi: 10.36753/mathenot.622522 UR - https://doi.org/10.36753/mathenot.622522 Y2 - 2020 ER - EndNote %0 Mathematical Sciences and Applications E-Notes Sound Wave Diffraction by a Cavity with Partial Lining %A Burhan Ti̇ryaki̇oğlu %T Sound Wave Diffraction by a Cavity with Partial Lining %D 2020 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 8 %N 1 %R doi: 10.36753/mathenot.622522 %U 10.36753/mathenot.622522 ISNAD Ti̇ryaki̇oğlu, 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 AMA Ti̇ryaki̇oğlu B . Sound Wave Diffraction by a Cavity with Partial Lining. Math. Sci. Appl. E-Notes. 2020; 8(1): 123-133. Vancouver Ti̇ryaki̇oğlu B . Sound Wave Diffraction by a Cavity with Partial Lining. Mathematical Sciences and Applications E-Notes. 2020; 8(1): 123-133. IEEE B. Ti̇ryaki̇oğlu , "Sound Wave Diffraction by a Cavity with Partial Lining", Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, pp. 123-133, Mar. 2020, doi:10.36753/mathenot.622522

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