Evaluation of the transmission and the scattering matrix applicability to the mufflers analysis

• Autorzy: Snakowska Anna , Gorazd Łukasz , Jurkiewicz Jerzy
• Języki publikacji: EN

Abstrakty

EN

The analysis of the acoustical systems can be carried out based on a number of different formalisms, of which applied frequently are the transfer matrix formalism, in which the chosen state variables are the sound pressure p and the sound velocity v, and the scattering matrix formalism adopting the sound pressures p⁺ and p⁻ and the sound velocities v⁺ and v⁻ of waves propagating through an element in both directions. Even though, they are mathematically equivalent, i.e. there exists the unequivocal transformation from one to another there are some advantages and disadvantages in applying one or the other to analyse mufflers or other acoustic system, especially when the propagation of a multimode wave is assumed and numerical calculations are indispensable. In the paper the transformation between the formalisms has been derived and applied to analyse the phenomena at a junction between the tail pipe and the chamber and also in mufflers composed of one or two chambers. The more flexible for numerical calculations seems the scattering matrix formalism, especially when the number of propagating modes differs on both sides of a junction. On the other hand the transmission matrix formalism is suitable for analysing systems constituting a cascade. The sources of the advantages and disadvantages of both formalisms are explained. The results obtained can be helpful in the effective design of silencers with specific properties.

Słowa kluczowe

EN

transmission matrix; scattering matrix; multimode wave; silencer; muffler

PL

macierz transmisji; macierz S; fala wielomodowa; tłumik

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2019
• Tom: Vol. 30, nr 1
• Strony: art. no. 2019102
• Opis fizyczny: Bibliogr. 14 poz., rys., wykr.

Twórcy

autor

Snakowska Anna

• AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics, Krakow, Poland

autor

Gorazd Łukasz

• AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics, Krakow, Poland

autor

Jurkiewicz Jerzy

• AGH University of Science and Technology, Krakow, Poland

Bibliografia

• 1. M. L. Munjal, Acoustics of ducts and mufflers, Willey 2 ed., New York 2014.
• 2. A. Snakowska., K. Kolber., Ł. Gorazd, J. Jurkiewicz, Derivation of an acoustic two-port scattering matrix for a multimode wave applying the single-mode generator, IEEE Digital Xplore Library, (2018) 294 - 298.
• 3. A. Sitel, J-M Ville, F. Felix, Multiload procedure to measure the acoustic scattering matrix of a duct discontinuity for higher order mode propagation conditions, J. Acoust. Soc. Am., 120 (2006) 2478.
• 4. M. L. Munjal, Plane wave analysis of side inlet/outlet chamber mufflers with mean flow, Applied Acoustics, 52 (1997) 165 - 175.
• 5. T. Kar, M. L. Munjal. Generalized analysis of a muffler with any number of interacting ducts, Journal of Sound and Vibration, 285 (2005) 585 - 596.
• 6. C. D. Gaonkar, M. L. Munjal, Theory of the double-tuned side-inlet side-outlet muffler, Noise Control Engineering Journal, 66 (2018) 489 - 495.
• 7. T. Elnady, M. Abom, S. Allam, Modeling perforates in mufflers using two-ports, Journal of Vibration and Acoustics, 132 (2010).
• 8. M. L. Munjal, K. Narayana Rao, A. D. Sahasrabudhe, Aeroacoustic analysis of perforated muffler components, Journal of Sound and Vibration, 114 (1987) 173 - 188.
• 9. R. Glav, P. Regaudb, M. Abom, Study of a folded resonator including the effects of higher order modes, J. Sound. Vib., 273 (2004) 777 - 792.
• 10. R. Kirby, P. T. Williams, J. Hill, A three dimensional investigation into the acoustic performance of dissipative splitter silencers, J. Acoust. Soc. Am., 135 (2014) 2727 - 2737.
• 11. F. D. Denia, A. Selamet, M. J. Martínez, F. J. Fuenmayor, Sound attenuation of a circular multi-chamber hybrid muffler, Noise Control Engineering Journal, 56(5) (2008) 356 - 364.
• 12. A. Snakowska, J. Jurkiewicz, Ł. Gorazd, A hybrid method for determination of the acoustic impedance of an unflanged cylindrical duct for multimode wave, J. Sound. Vib., 396 (2017) 325 - 339.
• 13. A. Snakowska, Ł. Gorazd, J. Jurkiewicz, K. Kolber, Generation of a single cylindrical duct mode using a mode synthesiser, Applied Acoustics, 114 (2016) 56 - 70.
• 14. M. L. Munjal, Recent advances in muffler acoustics, International Journal of Acoustics and Vibration, 18 (2013) 71 - 85.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).