Geodesic
Acoustic eigen oscillations near thin-walled obstacles in an annular cylindrical channel
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 116-125.

Voir la notice de l'article provenant de la source Math-Net.Ru

The articlepresents the analytical and numerical investigations of acoustic eigen oscillations near thin-walled obstacles in a uniform annular cylindrical channel. Acoustical eigen oscillations are described with the help of the Neumann problem for the Laplace operator. Using representation of symmetry groups in the solution space, it is shown that for the large class of thin-walled obstacles in annular channels there always exists a pure point spectrum that is embedded into a continuous spectrum of a self-adjoint extension of the Laplace operator appropriate to the homogeneous Neumann problem. Also we present the results on dependence of eigenfrequencies on the geometrical parameters of thin-walled obstacles in a uniform annular cylindrical channel as well as on the form of eigenfunctions. The influence is also addressed of the geometric characteristics of oscillations on the frequencies, quantity and and form of eigen oscillations.
Keywords: acoustic eigen oscillations in unbounded domains, resonance phenomena, spectral properties of Laplace operator. 
@article{SJIM_2013_16_1_a11,
     author = {N. A. Khasanov and S. V. Sukhinin},
     title = {Acoustic eigen oscillations near thin-walled obstacles in an annular cylindrical channel},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {116--125},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a11/}
}
TY  - JOUR
AU  - N. A. Khasanov
AU  - S. V. Sukhinin
TI  - Acoustic eigen oscillations near thin-walled obstacles in an annular cylindrical channel
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2013
SP  - 116
EP  - 125
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a11/
LA  - ru
ID  - SJIM_2013_16_1_a11
ER  - 
%0 Journal Article
%A N. A. Khasanov
%A S. V. Sukhinin
%T Acoustic eigen oscillations near thin-walled obstacles in an annular cylindrical channel
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2013
%P 116-125
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a11/
%G ru
%F SJIM_2013_16_1_a11
N. A. Khasanov; S. V. Sukhinin. Acoustic eigen oscillations near thin-walled obstacles in an annular cylindrical channel. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 116-125. http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a11/

[1] Parker R., “Resonance effects in wake shedding from parallel plates: some experimental observation”, J. Sound and Vibrat., 4:1 (1966), 62–72 | DOI

[2] Sukhinin S. V., “Sobstvennye kolebaniya okolo plastiny v kanale”, Prikl. mekhanika i tekhn. fizika, 39:2 (1998), 78–90 | MR | Zbl

[3] Sukhinin S. V., “Eolovy tona reshetki plastin”, Izv. RAN. Mekhanika zhidkosti i gaza, 2000, no. 2, 171–186 | MR | Zbl

[4] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, v. 4, Mir, M., 1982

[5] Sukhinin S. V., “Akusticheskie kolebaniya okolo tonkostennykh tsilindricheskikh prepyatstvii v kanale”, Prikl. mekhanika i tekhn. fizika, 40:4 (1999), 133–142 | MR | Zbl

[6] Sukhinin S. V., Volnovodnye, tsiklicheskie i anomalnye svoistva kolebanii okolo reshetki plastin, Preprint, IGiL SO RAN, Novosibirsk, 1998, 23 pp.

[7] Mexiner J., The behavior of electromagnetic fields at edges, Tech. Rpt. Em-72, N.Y. Univ. Press, N.Y., 1954