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

School of Mechanical Engineering, The University of Adelaide, Adelaide, Australia.

DOI: 10.4236/oja.2013.33010                

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

Conflicts of Interest

The authors declare no conflicts of interest.

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.
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[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).
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