 | | 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
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| In English (Mech. Solids): | | 4760 |
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| L. D. Akulenko, L. I. Korovina, and S. V. Nestrerov, "Natural transverse vibrations of a rotating rod," Mech. Solids. 42 (1), 1-11 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
1 |
Pages |
1-11 |
| Title |
Natural transverse vibrations of a rotating rod |
| Author(s) |
L. D. Akulenko (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia)
L. I. Korovina (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia)
S. V. Nestrerov (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, kumak@ipmnet.ru) |
| Abstract |
We study the natural transverse vibration frequencies and modes of a rod rotating about an axis fixed at an end of the rod. The cases of low, moderately high, and asymptotically high angular velocities are considered. The case of a homogeneous rod with clamped left and free right end is considered in detail. A new constructive algorithm based on the notion of "sagittary function" is used to find the dependences of the natural frequencies and mode shapes on the angular velocity for lower vibration modes. We establish evolution to the model corresponding to vibrations of a rapidly rotating thread subjected to the centrifugal inertial forces. It is shown that the natural frequencies grow practically linearly with increasing angular rotation velocity. The results obtained can be of interest in technical applications, e.g., when studying vibrations of sensor elements in high-precision instruments or of rapidly rotating elongated mechanism elements (turbine or propeller blades, etc). |
| References |
| 1. | P. Appel,
Theoretical Mechanics. Vol. 2
(Fizmatgiz, Moscow, 1960)
[in Russian]. |
| 2. | L. G. Loytsyanskii and A. I. Lur'e,
Course in Theoretical Mechanics. Vol. 2
(Nauka, Moscow, 1983)
[in Russian]. |
| 3. | L. D. Akulenko and N. N. Bolotnik,
"On the Controlled Rotation of Elastic Rod,"
Prikl. Mat. Mekh.
46 (4), 587-595 (1982)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 4. | L. D. Akulenko and S. V. Nesterov,
High-Precision Methods in Eigenvalue Problems and Their Applications
(CRC Press Co., Boca Raton, 2005). |
| 5. | L. D. Akulenko, G. V. Kostin, and S. V. Nesterov,
"A Numerical-Analytical Method for the Analysis of Natural Vibrations of Nonhomogeneous Rods,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 180-191 (1995)
[Mech. Solids (Engl. Transl.)]. |
| 6. | L. D. Akulenko and S. V. Nesterov,
"Natural Transverse Vibrations of Nonhomogeneous Beams,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 179-192 (2003)
[Mech. Solids (Engl. Transl.)]. |
| 7. | L. D. Akulenko and G. V. Kostin,
"Perturbation Method in Problems of Dynamics of Nonhomogeneous Elastic Rods,"
Prikl. Mat. Mekh.
56 (3), 452-464 (1992)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 8. | S. H. Gould,
Variational Methods for Eigenvalue Problems
(Oxford Univ. Press, London, 1970). |
|
| Received |
11 May 2006 |
| Link to Fulltext |
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