 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| L.D. Akulenko, A.A. Gavrikov, and S.V. Nesterov, "Natural Vibrations of a Liquid-Transporting Pipeline on an Elastic Base," Mech. Solids. 53 (1), 101-110 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
1 |
Pages |
101-110 |
| DOI |
10.3103/S0025654418010120 |
| Title |
Natural Vibrations of a Liquid-Transporting Pipeline on an Elastic Base |
| Author(s) |
L.D. Akulenko (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5 str. 1, Moscow, 105005 Russia)
A.A. Gavrikov (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, gavrikov@ipmnet.ru)
S.V. Nesterov (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia) |
| Abstract |
Flexural free vibrations of an ideal-liquid-transporting pipeline on an elastic base are studied. A numerical-analytical method for finding the pipeline natural frequencies and vibration modes is developed, which permits one to determine the natural frequencies and modes for the case in which the tension or compression (the longitudinal force acting along the pipeline axis), the pipe diameter, and hence the velocity of the incompressible fluid being transported are arbitrary functions of the longitudinal coordinate measured along the pipeline axis. The least natural frequencies are calculated for the case in which the variable elasticity of the base is given by some test functions. |
| Keywords |
pipeline vibration, natural frequency, Winkler base |
| References |
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"Basic Properties of Natural Vibrations of an Extended Segment of a Pipeline,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela.
No. 4, 119-134 (2013)
[Mech. Solids (Engl. Transl.)
48 (4), 458-472 (2013)]. |
| 2. | G. W. Housner,
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19 (2), 205-208 (1952). |
| 3. | C. D. Jr. Mote,
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43 (3), 533-539 (1968). |
| 5. | M. P. Paidoussis,
Fluid-Structure Interactions. Vol. 1: Slender Structures and Axial Flow
(Academic Press, Oxford 2014). |
| 6. | S. V. Nesterov and L. D. Akulenko,
"Spectrum of Transverse Vibrations of a Moving Rod,"
Dokl. Ross. Akad. Nauk
420 (1), 50-54 (2008)
[Dokl. Phys. (Engl. Trans.)
53 (5), 265-269 (2010)]. |
| 7. | L. D. Akulenko and S. V. Nesterov,
"Flexural Vibrations of a Moving Rod,"
Prikl. Mat. Mekh.
72 (5), 759-774 (2008)
[J. Appl. Math. Mech. (Engl. Transl.)
72 (5), 550-560 (2008)]. |
| 8. | L. D. Akulenko, A. A. Gavrikov, and S. V. Nesterov,
"Natural Oscillations of Multidimensional Systems Nonlinear in the Spectral Parameter,"
Dokl. Ross. Akad. Nauk
472 (6), 654-658 (2017)
[Dokl. Phys. (Engl. Trans.)
62 (2), 90-94 (2017)]. |
| 9. | L. D. Akulenko, A. A. Gavrikov, and S. V. Nesterov,
"Numerical Solution of Vector Sturm-Liouville Problems with Dirichlet Conditions and
Nonlinear Dependence on the Spectral Parameter,"
Zh. Vych. Mat. Mat. Fiz.
57 (9), 1503-1516 (2017)
[Comp. Math. Math. Phys. (Engl. Transl.)
57 (9), 1484-1497 (2017)]. |
| 10. | A. A. Gavrikov,
"Numerical Solution of Vector Sturm-Liouville Problems with a Nonlinear
Dependence on the Spectral Parameter,"
AIP Conf. Proc.
1863, 560032 (2017). |
| 11. | A. A. Gavrikov,
"An Iterative Solution Approach to Eigenvalue Problems for Linear Hamiltonian
Systems and its Application to a Hybrid System Control Problem,"
in 22st Int. Conf. Methods and Models in Automation and Robotics (MMAR). Miedzyzdroje, Poland, 2017
(IEEE, 2017),
pp. 588-593. |
| 12. | V. Ph. Zhuravlev and D. M. Klimov,
Applied Methods in Theory of Vibrations
(Nauka, Moscow, 1988)
[in Russian]. |
| 13. | F. Riesz and B. Sz.-Nagy,
Lectures in Functional Analysis
(Budapest, 1953; Mir, Moscow, 1979). |
|
| Received |
18 September 2017 |
| Link to Fulltext |
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