An exact transfer matrix formulation of plane sound wave transmission in inhomogeneous ducts


Dokumaci E.

JOURNAL OF SOUND AND VIBRATION, vol.217, no.5, pp.869-882, 1998 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 217 Issue: 5
  • Publication Date: 1998
  • Doi Number: 10.1006/jsvi.1998.1786
  • Journal Name: JOURNAL OF SOUND AND VIBRATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.869-882
  • Dokuz Eylül University Affiliated: No

Abstract

The impedance, or the reflection coefficient, of plane sound waves in inhomogeneous ducts satisfies a Riccati equation. The present paper shows that the duct impedance matrix, or the scattering matrix, can be related explicitly to the solutions of the associated linear equation of the Riccati equation for duct impedance, or reflection coefficient, respectively. New exact analytical scattering matrix solutions, which follow as consequences of this connection, are given for two significant duct acoustics problems, namely, the sound transmission in non-uniform ducts carrying an incompressible subsonic low Mach number mean flow and the transmission of sound in uniform ducts with a full quadratic axial mean temperature gradient. (C) 1998 Academic Press.