 | | 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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| K. I. Romanov, "A multifrequency model of rod buckling under creep conditions," Mech. Solids. 41 (5), 147-151 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
5 |
Pages |
147-151 |
| Title |
A multifrequency model of rod buckling under creep conditions |
| Author(s) |
K. I. Romanov (Moscow) |
| Abstract |
A scleronomous rod with a nonlinear characteristic was studied in [1] with
the use of a perfect I-beam scheme on the basis of a representation of the
desired deflection by a series with bounded number of terms. The method
developed in [1] was used in [2] to determine the critical time typical of
a rheonomic rod. In the present paper, to solve the buckling problem, we
propose a new mathematical model based on the pure buckling scheme [3].
We establish an analogy concerning the results of solution of three
deformation problems for a hinged rod: creep buckling, stability, and
transverse vibrations within the elastic range. In the study of a
two-frequency model with two functions of time, we also find an integrating
factor, which allows us to relate the amplitudes of the first and second
harmonics and analytically show that the first harmonic dominates. |
| References |
| 1. | N. Hoff,
Buckling and Stability [Russian translation],
Izd-vo Inostr. Lit-ry, Moscow, 1955. |
| 2. | S. Patel and J. Kempner,
"Effect of higherharmonic deflection components on
the creep buckling of columns,"
Aeronaut. Quart., Vol. 8, No. 3, pp. 215-225, 1957. |
| 3. | K. I. Romanov,
"Buckling of nonlinearly viscous rods,"
Raschety na Prochnost', No. 33, pp. 139-151, Mashinostroenie, Moscow,
1993. |
| 4. | V. I. Feodos'ev,
Strength of Materials [in Russian],
Izd-vo MGTU im. N. E. Baumana, Moscow, 1990. |
| 5. | V. L. Biderman,
Theory of Mechanical Oscillations [in Russian],
Vysshaya Shkola, Moscow, 1980. |
| 6. | E. Kamke,
Handbook of Ordinary Differential Equations [Russian translation],
Izd-vo Inostr. Lit-ry, Moscow, 1951. |
| 7. | Yu. S. Sikorskii, Ordinary Differential Equations with Applications
to Some Technical Problems [in Russian], Gostekhizdat, Moscow, 1940. |
|
| Received |
16 June 2004 |
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