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Wave propagation in immersed waveguide with radial inhomogeneity
A Vatulyan1, V Yurov1, R Nedin1
1Department of Elasticity Theory, Institute of Mathematics, Mechanics and Computer Sciences named after I. I. Vorovich, Southern Federal University, Milchakova 8a, 344090 Rostov-on-Don, Russia.
Abstract:
In this paper, we investigate wave propagation in an inhomogeneous cylindrical waveguide immersed in a medium. To model external medium influence, we use the impedance boundary conditions on the waveguide outer wall. Some structural properties of the dispersion set are studied. To treat the problem of the waveguide forced oscillations, we solve boundary value problems for the first order vector differential equation sequentially in the Fourier transform space and then build the actual space on the basis of the residue theory. The residues for the numerically given function with the first order poles were found by considering auxiliary boundary value problems. The wave fields on the waveguide internal wall are obtained for different inhomogeneity laws and boundary conditions.
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