 | | 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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| << Previous article | Volume 38, Issue 3 / 2003 | Next article >> |
| L. D. Akulenko and S. V. Nesterov, "Natural transverse vibrations of nonhomogeneous beams," Mech. Solids. 38 (3), 144-154 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
3 |
Pages |
144-154 |
| Title |
Natural transverse vibrations of nonhomogeneous beams |
| Author(s) |
L. D. Akulenko (Moscow)
S. V. Nesterov (Moscow) |
| Abstract |
Natural vibrations of a strongly nonhomogeneous straight beam
with arbitrary boundary conditions corresponding to elastic
attachment of its ends are studied. An effective computational
procedure is developed for determining transverse vibration
frequencies and shapes on the basis of the solution of the
eigenvalue/eigenfunction problem for the respective differential
operator. On the basis of this procedure, a shooting-type method
is developed. Propositions similar to
Sturm's comparison theorems and corollaries from these theorems
are formulated. The algorithm is tested on standard problems.
A parametric synthesis is performed for a family of tapered beams
with various boundary conditions that are frequently encountered
in applications. The obtained results are compared with
the classical results by Kirchhoff, Timoshenko, and Gould. |
| References |
| 1. | S. Timoshenko, Vibration Problems in Engineering,
D. van Nostrand Co., Inc., Toronto, N.-Y., London, 1955. |
| 2. | S. H. Gould, Variational Methods for Eigenvalue
Problems, Oxford Univ. Press, London, 1966. |
| 3. | L. Collatz, Eigenwertaufgabem mit technischen
Anwendungen, Akad. Verlag, Leipzig, 1963. |
| 4. | L. D. Akulenko, G. V. Kostin, and S. V. Nesterov,
"A numerical-analytical method for the analysis of natural
vibrations of nonhomogeneous rods,"
Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 180-191, 1985. |
| 5. | L. D. Akulenko and G. V. Kostin, "Perturbation method
in problems of dynamics of nonhomogeneous elastic rods,"
PMM [Applied Mathematics and Mechanics], Vol. 56,
No. 3, pp. 452-464, 1992. |
| 6. | Yu. A. Mitropol'skii and B. I. Moseenkov,
Asymptotic Solutions of Partial Differential Equations
[in Russian], Vishcha Shkola, Kiev, 1976. |
| 7. | Ph. Hartman, Ordinary Differential Equations,
J. Wiley and Sons, N.-Y., London, Sydney, 1964. |
| 8. | E. Kamke, Differentionalgleichungen Lösungsmethoden
und Lösungen, Akad. Verlag, Leipzig, 1959. |
|
| Received |
13 January 2003 |
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