 | | 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 |
|
| << Previous article | Volume 46, Issue 1 / 2011 | Next article >> |
| L.D. Akulenko, L.I. Korovina, and S.V. Nesterov, "Natural Vibrations of a Pipeline Segment," Mech. Solids. 46 (1), 139-150 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
1 |
Pages |
139-150 |
| DOI |
10.3103/S0025654411010201 |
| Title |
Natural Vibrations of a Pipeline Segment |
| Author(s) |
L.D. Akulenko (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, bolotnik@ipmnet.ru)
L.I. Korovina (Russian State University of Trade and Economics, Smol'naya 36, Moscow, 125993 Russia)
S.V. Nesterov (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, kumak@ipmnet.ru) |
| Abstract |
Transverse natural vibrations of an extended segment of a pipeline conveying a uniformly moving fluid are studied. The mechanical model under study takes into account the pipe and fluid inertia forces and the moment of the Coriolis and centrifugal forces due to the medium motion. It is assumed that both ends are rigidly fixed and the elastic characteristics are constant along the pipe. A mathematical model is developed on the basis of a generalized procedure of separation of variables, and a boundary value problem for the eigenvalues and eigenfunctions (natural frequencies and vibration shapes) is posed. Ferrari's formulas are used to solve the fourth-order complex characteristic equation for the wave parameter, and a closed procedure of numerical-analytical determination of roots of the secular equation for the frequencies is obtained. The frequency curves for the firsts two vibration modes against the dimensionless velocity and inertia parameters are constructed. The forms of the observed motions at different times are obtained. Several effects are revealed indicating that there is a dramatic quantitative and qualitative difference between these vibrations and the standard vibrations corresponding to the case of immovable medium. We discover the absence of a rectilinear configuration of the axis, the variable number and location of nodes, their inconsistency with the mode number, and some other effects. |
| Keywords |
pipeline, fluid, model, transverse vibrations, inertia and velocity parameters, frequencies |
| References |
| 1. | S. V. Nesterov, L. D. Akulenko, and L. I. Korovina,
"Transverse Oscillations of a Pipeline with Uniformly Moving Fluid,"
Dokl. Ross. Akad. Nauk
427 (6), 781-784 (2009)
[Dokl. Phys. (Engl. Trans.)
54 (8), 402-405 (2009)]. |
| 2. | V. A. Svetlitskii,
Mechanics of Rods, Vol. 2
(Vysshaya Shkola, Moscow, 1987)
[in Russian]. |
| 3. | V. A. Svetlitskii,
Mechanics of Absolutely Flexible Rods
(Izd-vo MAI, Moscow, 2001)
[in Russian]. |
| 4. | R. Barakart,
"Transverse Vibrations of a Moving Thin Rod,"
J. Acoust. Soc. Am.
43 (3), 533-539 (1968). |
| 5. | S. V. Nesterov and L. D. Akulenko,
"Spectrum of Transverse Vibrations of a Moving Rod,"
Dokl. Ross. Akad. Nauk
420 (1), 50-54
[Dokl. Phys. (Engl. Trans.)
53 (5), 265-269 (2010)]. |
| 6. | A. I. Vesnitskii,
Waves in Systems with Moving Boundaries and Loads
(Fizmatlit, Moscow, 2001)
[in Russian]. |
| 7. | G. G. Denisov and V. V. Novikov,
"On Stability of an Infinite Beam with Two Limiters Moving along It,"
in Dynamics of Systems. Optimization and Adaptation
(Gorkii, 1982)
[in Russian]. |
| 8. | L. D. Akulenko and S. V. Nesterov,
High-Precision Methods in Eigenvalue Problems and Their Applications
(CRC Press, Boca Raton, 2005). |
| 9. | M. A. Naimark,
Linear Differential Operators
(Nauka, Moscow, 1969)
[in Russian]. |
| 10. | A. N. Tikhonov and A. A. Samarskii,
Equations of Mathematical Physics
(Nauka, Moscow, 1977; Dover, New York, 1990). |
| 11. | I. A. Birger and Ya. G. Panovko (Editors),
Strength. Stability. Vibrations, Vol. 3
(Mashinostroenie, Moscow, 1968)
[in Russian]. |
| 12. | N. P. Erugin,
Implicit Functions
(Izd-vo LGU, Leningrad, 1956)
[in Russian]. |
|
| Received |
02 June 2010 |
| Link to Fulltext |
|
| << Previous article | Volume 46, Issue 1 / 2011 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English