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 OJA  Vol.3 No.3 , September 2013
The Corrected Expressions for the Four-Pole Transmission Matrix for a Duct with a Linear Temperature Gradient and an Exponential Temperature Profile
Carl Q. Howard*
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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.
Keywords: Duct; Transmission Matrix; Four-Pole; Temperature Gradient; Finite Element Analysis
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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