Wave propagation in a bifurcated impedance-lined cylindrical waveguide

Abstract

The radiation of a cylindrical-surface-wave mode which propagates towards the mouth of a semi- infinite cylindrical waveguide which supports surface waves is considered. This semi-infinite cylindrical waveguide is symmetrically located inside an infinite cylindrical waveguide whose surfaces are lined with an absorbent material. The whole system constitutes a new bifurcated cylindrical-waveguide boundary-value problem that has application in acoustics and electromagnetism. The mathematical model results in a scalar Wiener–Hopf problem which can be rigorously solved to give a closed-form solutio

On acoustic propagation in three-dimensional rectangular ducts with flexible walls and porous linings

“…The purpose of such ducts varies: circular cylindrical geometries have application, for example, to car exhaust systems, wave propagation in co-axial cables and noise emission by aeroengines [1,2,3,4,5,6,7,8] whereas ducts of rectangular cross-section are more usual in heating ventilation and air-conditioning (HVAC) systems [9,10,11,12,13,14]. Whatever the application there is a need to * Portions of this work were presented in "Acoustic propagation in 3-D, rectangular ducts with flexible walls", Proceedings of the Joint 159th Meeting of the Acoustical Society of America and NOISE-CON 2010, Baltimore, U.S.A., April 2010 [12].…”

“…The method is most appropriate for the solution of 2-D (or 3-D) boundary value problems involving a governing equation together with a two-part boundary condition imposed along one infinite coordinate line [16,4] (for example, one condition for x < 0, y = 0 and a different condition for x > 0, y = 0). Several extensions to the method are available [15]; the two most noteworthy being the modified Wiener-Hopf technique which enables the approach to be applied to boundary value problems involving three-part boundary data, and matrix formulations [5,8,17] which often arise when the mixed conditions are imposed for x < 0 and x > 0 but at different values of y.…”

Orthogonality relations for fluid-structural waves in a three-dimensional, rectangular duct with flexible walls

“…In recent years, there has been increasing interest in the effect that wave-bearing boundaries have on the propagating noise and, in this context, much of the analytic work concerns two-dimensional ducts or those circular cylindrical geometries. A wide range of analytic techniques, including the Wiener-Hopf technique (Rawlins 2007), Fourier methods (Huang 2002) and mode-matching (Lawrie & Guled 2006), have been employed to study this class of problem. The Wiener-Hopf technique has long been a convenient tool to tackle a wide range of two-part problems, whereas analytic mode-matching has only recently been established as a viable tool for two-dimensional structures in which the boundary conditions contain higher-order derivatives.…”

On the Green’s function for the Helmholtz operator in an impedance circular cylindrical waveguide

“…In the case of the particular domain considered in this paper -the circular cylindrical waveguide -it is worth mentioning some engineering applications of this problem. For instance, according to Rawlins [3], it arises in electromagnetic communications throughout underground tunnels, in the propagation of waves in fibre-optics waveguides and in the design of mufflers, exhaust and ventilation systems [4].…”