Dynamics of thin tubes under the influence of fluid flow
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 2, pp. 183-194.

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Proposed simple model movements thin tubes under the influence of fluid flow. Was obtained a nonlinear equation for the string with the flow. Demonstrated the possibility of tube vibrations under the influence of fluid flow and criterion was found linear instability at a constant flow rate. In the condition where the linear instability conditions are violated the possibility of oscillations detected during the presence of small periodic oscillation of flow.
Keywords: string, fluid flow, the equation of motion, instability, parametric resonance.
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Victor P. Berezovoj; Anatoly V. Tur; Vladimir V. Yanovsky. Dynamics of thin tubes under the influence of fluid flow. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 2, pp. 183-194. http://geodesic.mathdoc.fr/item/ND_2014_10_2_a4/

[1] Timoshenko S. P., Kolebaniya v inzhenernom dele, Nauka, M., 1957, 575 pp.

[2] Timoshenko S. P., Voinovskii-Kriger S., Plastiny i obolochki, Fizmatlit, M., 1963, 635 pp.

[3] Grinchenko V. T., Meleshko V. V., Garmonicheskie kolebaniya i volny v uprugikh telakh, Naukova dumka, Kiev, 1981, 104 pp. | MR | Zbl

[4] Kolskii G., Volny napryazheniya v tverdykh telakh, IL, M., 1955, 192 pp.

[5] Mindlin R. D., McNiven H. D., “Axially symmetric waves in elastic rods”, J. Appl. Mech., 27 (1960), 145–151 | DOI | MR | Zbl

[6] Pao Y.-H., “Elastic waves in solids”, J. Appl. Mech., 50:4b (1983), 1152–1164 | DOI | Zbl

[7] Volobuev A. N., “Techenie zhidkosti v trubkakh s elastichnymi stenkami”, UFN, 165:2 (1995), 177–186 | DOI

[8] Litvinov W. G., “A problem of nonsteady flow of a nonlinear viscous fluid in a deformable pipe”, Methods Funct. Anal. Topology, 2:3–4 (1996), 85–113 | MR | Zbl

[9] Welander P., “On the oscillatory instability of a differentially heated fluid loop”, J. Fluid Mech., 29:1 (1967), 17–30 | DOI | Zbl

[10] Naife A., Metody vozmuschenii, Mir, M., 1997, 455 pp. | MR

[11] Olkhovskii I. I., Kurs teoreticheskoi mekhaniki dlya fizikov, Nauka, M., 1970, 441 pp.

[12] A. V. Borisov, I. S. Mamaev (red.), Negolonomnye dinamicheskie sistemy: Integriruemost, khaos, strannye attraktory, Sb. st., Institut kompyuternykh issledovanii, M.–Izhevsk, 2002, 328 pp. | MR | Zbl

[13] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, V 10 tt., v. 7, Teoriya uprugosti, Izd. 5-e, stereotipnoe, Fizmatlit, M., 2003, 264 pp.

[14] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, V 10 tt., v. 1, Mekhanika, Izd. 5-e, stereotipnoe, Fizmatlit, M., 2004, 224 pp.