 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ΟΜΜ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| A.A. Zevin, "The theory of parametric oscillations," J. Appl. Math. Mech. 78 (1), 30-38 (2014) |
| Year |
2014 |
Volume |
78 |
Issue |
1 |
Pages |
30-38 |
| Title |
The theory of parametric oscillations |
| Author(s) |
A.A. Zevin (Dnepropetrovsk, Ukraine, zevin@westa-inter.com) |
| Abstract |
The correctness of the existing definitions of the parametric oscillations of linear and non-linear systems is discussed. The possibility of an erroneous choice of the mathematical parametric model instead of the autooscillatory model, connected with the existence in such systems of the same periodic solutions, is pointed out. Some non-local properties of parametric oscillations in Hamiltonian systems are established. It is shown, in particular, that stability regions are convex with respect to the frequency of the parametric excitation (i.e., all the points between the boundaries of neighbouring instability regions correspond to stable solutions). At the critical frequencies of parametric resonance the well-known Rayleigh and Zhuravlev theorems on the behaviour of the frequencies of natural oscillations when the stiffness and inertia changes are generalized. Some additional assertions on the limits of the first instability region for the Hill vector equations are established. |
| Received |
20 November 2012 |
| Link to Fulltext |
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