 | | 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 and S. V. Nesterov, "Parametric oscillations and stability of systems with large modulation coefficient," Mech. Solids. 43 (3), 366-371 (2008) |
| Year |
2008 |
Volume |
43 |
Number |
3 |
Pages |
366-371 |
| DOI |
10.3103/S0025654408030084 |
| Title |
Parametric oscillations and stability of systems with large modulation coefficient |
| Author(s) |
L. D. Akulenko (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, bolotnik@ipmnet.ru)
S. V. Nesterov (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, kumak@ipmnet.ru) |
| Abstract |
We study parametric oscillations of linear systems with one degree of freedom for large values of the modulation coefficient. We use the classical analytic Lyapunov-Poincaré perturbation methods and an original numerically-analytic method of accelerated convergence to construct periodic solutions and the corresponding eigenvalues. We find the boundaries of stability and instability domains. We use specific models to illustrate the main properties of parametric oscillations of systems with singular character of the perturbation dependence on the modulation coefficient. We consider periodic boundary value problems for the modified Mathieu equation and the Kochin equation modeling crankshaft torsional vibrations and show that there are significant differences between weakly and essentially perturbed periodicmotions both for the lowest and arbitrary oscillation modes. We also describe the unusual properties of the boundaries in the domain of the system determining parameters. |
| Received |
15 January 2008 |
| Link to Fulltext |
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