 | | 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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| A.K. Abramyan, D.A. Indeitsev, and V.A. Postnov, "Running and Standing Waves of Timoshenko Beam," Mech. Solids. 53 (2), 203-210 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
2 |
Pages |
203-210 |
| DOI |
10.3103/S0025654418020115 |
| Title |
Running and Standing Waves of Timoshenko Beam |
| Author(s) |
A.K. Abramyan (Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia)
D.A. Indeitsev (Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia, dmitry.indeitsev@gmail.com)
V.A. Postnov (St. Petersburg State Marine Technical University, ul. Lotsmanskaya 3, St. Petersburg, 190121 Russia) |
| Abstract |
Standing waves of a Timoshenko beam of finite length and their connection with running waves for an infinite beam are considered. It is shown that the principle of a "closed cycle" of a running wave is completely identical to the usual procedure of direct satisfaction from the side of the general solution for an infinite Timoshenko beam, to the boundary conditions of a beam of finite length. The question of the existence of a second frequency spectrum under arbitrary boundary conditions of a beam is discussed. A "relaxed approach" to the concept of the second frequency spectrum is proposed. The results of the theoretical analysis are confirmed by numerical calculations for the Timoshenko beam with elastic supports and elastic sealing of its end sections. |
| Keywords |
running and standing waves, Timoshenko beam, second frequency spectrum, "closed loop" principle, finite element method |
| References |
| 1. | D. A. Indeitsev, N. G. Kuznetsov, O. V. Motygin, and Yu. A. Mochalova,
Localization of Linear Waves
(Izdat. SPbGU, St. Petersburg, 2007)
[in Russian]. |
| 2. | D. J. Mead,
"Waves and Modes in Finite Beams: Application of the Phase-Closure Principle,"
J. Sound Vibr.
171 (5), 695-702 (1994). |
| 3. | K. T. Chan, X. Q. Wang, R. M. C. So, and S. R. Reid,
"Superposed Standing Waves in a Timoshenko Beam,"
Proc. Roy. Soc. London. Ser. A.
458, 83-108 (2002). |
| 4. | X. Q. Wang and R. M. C. So,
"Various Standing Waves in a Timoshenko Beam,"
J. Sound Vibr.
280 (1-2), 311-328 (2005). |
| 5. | R. W. Trail-Nash and A. R. Collar,
"The Effects of Shear Flexibility and Rotary Inertia on the
Bending Vibration of Beam,"
Quart. J. Mech. Appl. Math.
6, 186-222 (1953). |
| 6. | C. L. Dolph,
"On the Timoshenko Theory of Transverse Beam Vibrations,"
Quart. Appl. Math.
12 (2), 175-187 (1954). |
| 7. | M. Levinson and D. W. Cooke,
"On the Two Frequency Spectra of Timoshenko Beam,"
J. Sound Vibr.
84 (3), 319-326 (1982). |
| 8. | V. V. Nesterenko,
"A Theory for Transverse Vibration of a Timoshenko Beam,"
J. Appl. Math. Mech.
57 (4), 669-677 (1993). |
| 9. | N. G. Stephen,
"The Second Spectrum of Timoshenko Beam Theory - Further Assessment,"
J. Sound Vibr.
292 (1-2), 372-389 (2006). |
| 10. | D. A. Indeitsev and V. A. Postnov,
"About Existence of Second Spectrum in Timoshenko Beam Theory,"
in Conf. Proc. 36 The Int. Summer School "Advanced Problems in Mechanics," 6-10 July,
Russia, St. Petersburg
(St. Petersburg, 2008),
pp. 1-11. |
|
| Received |
05 October 2008 |
| Link to Fulltext |
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