 | | 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: | | 12895 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8084
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| In English (Mech. Solids): | | 4811 |
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| L. D. Akulenko, L. I. Korovina, and S. V. Nesterov, "Self-induced vibrations in an essentially nonlinear system," Mech. Solids. 37 (3), 36-41 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
3 |
Pages |
36-41 |
| Title |
Self-induced vibrations in an essentially nonlinear system |
| Author(s) |
L. D. Akulenko (Moscow)
L. I. Korovina (Moscow)
S. V. Nesterov (Moscow) |
| Abstract |
We investigate self-induced vibrations in an essentially nonlinear
system with the restoring force described by an odd (for example,
cubic) function of the displacement. The self-induced vibrations
are excited in accordance with the standard mechanism, as is the case
for the van der Pol oscillator. An effective numerical-analytical
method is developed for calculating the basic characteristics of
the vibrations (the period, the amplitude, the phase trajectory,
and the limit cycle) in the case of small and moderately large
feedback gains. The analysis of the self-induced vibrations is carried
out and new qualitative mechanical effects are established. |
| References |
| 1. | A. A. Kharkevich, Self-induced Vibrations [in Russian],
Gostekhizdat, Moscow, 1953. |
| 2. | A. A. Andronov, A. A. Vitt, and S. E. Khaikin,
Theory of Oscillations [in Russian],
Fizmatgiz, Moscow, 1959. |
| 3. | A. A. Andronov, E. A. Leontovich,
I. I. Gordon, and A. G. Maier,
Qualitative Theory of Second-order Dynamical Systems
[in Russian], Nauka, Moscow, 1966. |
| 4. | S. Lefschetz, Geometrical Theory
of Differential Equations [Russian translation],
Izd-vo Inostr. Lit-ry, Moscow, 1961. |
| 5. | N. N. Bogolyubov and Yu. A. Mitropol'skii,
Asymptotic Method in the Theory of Nonlinear Oscillations
[in Russian], Nauka, Moscow, 1974. |
| 6. | H. Kauderer, Nonlinear Mechanics [Russian translation],
Izd-vo Inostr. Lit-ry, Moscow, 1961. |
| 7. | A. Blaquiére, Nonlinear System Analysis [Russian
translation], Moscow, Mir, 1969. |
| 8. | E. F. Mishchenko and N. Kh. Rozov, Differential Equations
with Small Parameters and Relaxation Oscillations [in Russian],
Nauka, Moscow, 1975. |
| 9. | V. M. Volosov and B. I. Morgunov,
Method of Averaging in the Theory of Nonlinear Oscillatory Systems
[in Russian], Izd-vo MGU, Moscow, 1971. |
| 10. | L. D. Akulenko, Asymptotic Methods of Optimal Control
[in Russian], Nauka, Moscow, 1987. |
| 11. | I. G. Malkin, Some Problems of the Theory of Nonlinear
Oscillations [in Russian], Gostekhizdat, Moscow, 1956. |
| 12. | L. D. Akulenko, S. V. Nesterov, and A. M. Shmatkov,
"Generalized parametric vibrations of mechanical systems,"
PMM [Applied Mathematics and Mechanics],
Vol. 63, No. 5, pp. 746-756, 1999. |
|
| Received |
20 June 2000 |
| << Previous article | Volume 37, Issue 3 / 2002 | Next article >> |
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