Geodesic
Axiradial acoustic eigenoscillations near a~thin-walled obstacle in a~cylindrical channel with narrowing steps
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 4, pp. 131-141

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We study the dependence of the eigenfrequencies and eigenfunctions of acoustic axiradial oscillations near a thin-walled obstacle in a channel with narrowing steps of the geometric parameters of the oscillation domain. It is discovered that, near thin-walled cylindrical obstacles, in an inhomogeneous cylindrical channel with two-sided narrowing cylindrical step, the number of the acoustic eigenfrequencies of acoustic axisymmetric oscillations of the gas can increase. We obtain the dependencies of the eigenfrequencies on the geometric parameters of the obstacle and on the inhomogeneities of the channel. We study the dependence of the eigenfrequencies and eigenfunctions of acoustic axiradial oscillations near a thin-walled obstacle in a channel with narrowing steps of the geometric parameters of the oscillation domain. It is discovered that, near thin-walled cylindrical obstacles, in an inhomogeneous cylindrical channel with two-sided narrowing cylindrical step, the number of the acoustic eigenfrequencies of acoustic axisymmetric oscillations of the gas can increase. We obtain the dependencies of the eigenfrequencies on the geometric parameters of the obstacle and on the inhomogeneities of the channel.
Keywords: acoustic eigenoscillations in an unbounded domain, resonance phenomena, spectral properties of a Laplace operator, thin-walled obstacle in channels and tubes. 
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     author = {N. A. Khasanov and S. V. Sukhinin},
     title = {Axiradial acoustic eigenoscillations near a~thin-walled obstacle in a~cylindrical channel with narrowing steps},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {131--141},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2013_16_4_a11/}
}
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N. A. Khasanov; S. V. Sukhinin. Axiradial acoustic eigenoscillations near a~thin-walled obstacle in a~cylindrical channel with narrowing steps. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 4, pp. 131-141. http://geodesic.mathdoc.fr/item/SJIM_2013_16_4_a11/