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The Corrected Expressions for the Four-Pole Transmission Matrix for a Duct with a Linear Temperature Gradient and an Exponential Temperature Profile

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DOI: 10.4236/oja.2013.33010    4,871 Downloads   6,669 Views   Citations
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ABSTRACT

The purpose of this letter is to present the corrected expressions for the four-pole transmission matrix for a duct with a linear temperature gradient and an exponential temperature profile, described in Sujith [1]. The corrected equations are used in the analyses of a duct that is driven by a piston at one end and a rigid termination at the other end and the gas has a linear and exponential temperature gradients. The acoustic pressure and particle velocity along the duct are calculated and the theoretical results are compared with predictions using finite element analysis.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

C. Howard, "The Corrected Expressions for the Four-Pole Transmission Matrix for a Duct with a Linear Temperature Gradient and an Exponential Temperature Profile," Open Journal of Acoustics, Vol. 3 No. 3, 2013, pp. 62-66. doi: 10.4236/oja.2013.33010.

References

[1] R. I. Sujith, “Transfer Matrix of a Uniform Duct with an Axial Mean Temperature Gradient,” The Journal of the Acoustical Society of America, Vol. 100, No. 4, 1996, pp. 2540-2542. doi:10.1121/1.417362.
[2] M. L. Munjal, “Acoustics of Ducts and Mufflers with Application to Exhaust and Ventilation System Design,” Section 2.18, Wiley-Interscience, New York, 1987.
[3] A. G. Galaitsis and I. L. Ver, “Chapter 10: Passive Silencers and Lined Ducts,” In: L. L. Beranek and I. L. Ver, Eds., Noise and Vibration Control Engineering: Principles and Application, Wiley Interscience, New York, 1992, pp. 367-427.
[4] D. A. Bies and C. H. Hansen, “Engineering Noise Control: Theory and Practice,” 4th Edition, Spon Press, London, 2009. pp. 17-18, Equations (1.8).
[5] A. G. Galaitsis and I. L. Ver, “Chapter 10: Passive Silencers and Lined Ducts,” In: L. L. Beranek and I. L. Ver, Eds., Noise and Vibration Control Engineering: Principles and Application, Wiley Interscience, New York, 1992, p. 377, Equations (10.15).
[6] F. W. J. Olver, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” Dover Publications, New York, 1972, p. 360, Equation (9.1.16).

  
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