Two Waveguide Bifurcation Problems

Abstract

E. ; HURD, R. A. Two Waveguide Bifurcation Problems Wir betrachten die Beugung der Grundwelle i n einem Parallelplattenwellenleiter mit schallweichen und harten Randbedingungen an einer zentrierten Halbebene, auf deren beiden Seiten schallweiche und h r t e Randbedingungen herrschen. Eine geschlossene Losung des sich ergebenden gekoppelten Wiener-Hopf-Systems wird hergeleitet. Die Modenaqdituden in allen drei Cebieten werden berechnet, und die Relativleistung der Moden niederer Ordnung wird graphisch in Abhangigkeit vom Plattenabstand dargestellt. We consider the diffrraction of the dominant wawe mode in a parallel p2ate waveguide with hard and soft bozlndaries incident on a centred half plane on whose two faces hard and soft boundary conditions obtain. A closed form solution of the resulting coupled Wiener-Hopf system is derived. The modal amplitudes in all three regions are calculated and the relative powers of the low order modes versus the plate spacing are displayed graphically. TnepabiMM rpaHasHbiMII YCJIOBHIIMEI y 1tempMpoBamoCi noaynnocKocTn, c o6em CTOPOH ~B Y K O M R~K I I~ PI OrMaTpMBaeM nII4paHUMH, OCHOBHOg BOJIIIM B IIJIaCTLIII4aTaR B0JIHOBOil;IIaH JIMH3a C 3BYKOMHrKMMH II TUepAbIe IIOrpaHMsHbIe YCJIOBMR CY4eCTBYM)T. BhIBeJIH 3aMKHYTOe PeIUeHMe BbITeKaIoQea CMCTeMbI BmHepa M XOII@a. B6IqHCJIflIoT aMIIJlMTyA TMIIOB BOJIH XJIR BCeX TPeX 06naCTefi. nOKa3bIBaIoT C IIOMOLt[bIo rpa@MHM OTHOCMTeJIbHbIfi MOIIIHOCTb BMAOB BOjrII IIH3KOrO IIOpHHKa B BaBHCUMOCTM OT PBCCTOFIHMFI IIJIMT.

The Sommerfeld half‐plane problem revisited, V: The bifurcated guide with mixed boundary conditions on the septum

“…In the formulation used by Luneburg and Hurd [9], there is a strip -Im ,/kz -(~~/ 1 6 a~) < Im w < Im ,/k2 -(n2/16a2) (which they do not mention). That is, their Green's function C(x, y; x', y') now has a bilateral Fourier transform analytic in the above strip, whereas the unilateral [9] should be replaced by a path P which is a line parallel to the real axis of the w plane, drawn in the strip which we have described here.…”

“…Here we shall formulate two boundary value problems for the bifurcated duct which have been studied by Luneburg and Hurd [9]. These boundary value problems will lead to coupled pairs of Wiener-Hopf integral equations and the solutions will be provided for k real.…”

“…We continue our studies of parallel plate media with a discussion of a bifurcated duct problem recently considered by Luneburg and Hurd [9]. They have studied problems for which the Neumann boundary condition was applied on the lower wall of a duct and the Dirichlet one on the upper wall.…”

“…We regret that we did not make this point clear in [4] and [S]. A similar method should have been applied by Luneburg and Hurd in [7]- [9].…”

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We discuss the solution of the boundary value problem in a duct with a centered septum [9]. On the lower wall of the duct a Neumann condition is applied while on the upper wall a Dirichlet condition is applied.

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