 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| L.D. Akulenko, V.G. Baidulov, and S.V. Nesterov, "Dependence of the Natural Frequencies and Mode Shapes of Vibrations of an Ideal Gas on the Acoustic Resonance Parameters," Mech. Solids. 52 (1), 41-51 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
1 |
Pages |
41-51 |
| DOI |
10.3103/S002565441701006X |
| Title |
Dependence of the Natural Frequencies and Mode Shapes of Vibrations of an Ideal Gas on the Acoustic Resonance Parameters |
| Author(s) |
L.D. Akulenko (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia)
V.G. Baidulov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, baydulov@gmail.com)
S.V. Nesterov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia) |
| Abstract |
The problem of plane wave propagation through a circular hole is studied in the framework of long-wave approximation. The constructive notion of "apparent mass of holes" (Rayleigh; Fok) is used to construct a mathematical model of gas vibrations in an acoustic resonator and determine and analyze the natural frequencies and mode shapes for the velocity potential depending on the relative geometric parameters of the system. The high-precision calculations of the boundary value problem for the natural frequencies and mode shapes in the parametric approximation to the cross-section are based on a numerical-analytical accelerated convergence method. Two models are analyzed and compared, and the basic qualitative properties of gas vibrations are revealed depending on the basic parameters such as the mode number, relative size of the hole, and the dividing wall location. |
| Keywords |
resonator, natural vibrations of a gas, accelerated convergence method |
| References |
| 1. | J. W. Strutt (Lord Rayleigh),
The Theory of Sound, Vol. II
(Macmillan, London, 1926; GITTL, Moscow-Leningrad, 1944). |
| 2. | V. A. Fok, "Theoretical Study of Conductivity of a Circular Hole
in a Wall across a Tube," Dokl. Akad. Nauk SSSR 31 (9),
875-878 (1941). |
| 3. | V. S. Nesterov, "Experimental Study of Conductivity of a Circular
Hole in a Wall across a Tube," Dokl. Akad. Nauk SSSR 31 (9), 879-882 (1941). |
| 4. | S. N. Rzhevkin,
A Course of Lectures on the Theory of Sound
(Izdat. MGU, Moscow, 1960; Pergamon Press, London, 1963). |
| 5. | L. D. Akulenko and S. V. Nesterov,
High-Precision Methods in Eigenvalue Problems and Their Applications
(Chapman and Hall/CRC, Boca Raton, 2005). |
| 6. | S. V. Nesterov, L. D. Akulenko, and V. G. Baidulov,
"Eigenoscillations of an Acoustic Cavity with a Local Membrane,"
Dokl. Ross. Akad. Nauk 470 (3), 279-282 (2016) [Dokl.
Phys. (Engl. Transl.) 61 (9), 467-470 (2016)]. |
| 7. | L. D. Akulenko and S. V. Nesterov, "Determination of the Frequencies and Forms of Oscillations of Non-Uniform Distributed
Systems with Boundary Conditions of the Third Kind," Prikl. Mat. Mekh. 61 (4), 547-555 (1997) [J. Appl. Math. Mech. (Engl.
Transl.) 61 (4), 531-538 (1997)]. |
|
| Received |
15 August 2016 |
| Link to Fulltext |
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