The study of the Sommerfeld effect of the passage
of synchronous machine through resonance.
Gennady Leonov
This study was stimulated by the work [1], where in the
neighborhoodof resonance it was observed a "hanging" of oscillation frequency
of an electromotor on elastic platform. This "hanging" is realized
in the form of random oscillations [1] and is often called a
Sommerfeld effect [1--7].
1. Blekhman I.I. Self-synchronization of vibrators for some
vibration machines// Ingenernyj sbornik. – 1953. – V.16. pp.49 – 72
(in Russian).
2. Blekhman I.I. Synchronization of dynamical systems. – Moscow.:
Nauka, 1971. 896 с. (in Russian).
3. Blekhman I.I. Vibrational Mechanics. Singapore-New
Jersey-London-Hong Kong: World Scientific. 2000. 509 p.
(In Russian: Fizmatlit, 1994. 400 p).
4. Fidlin A.. Nonlinear Oscillations in Mechanical Engineering.
Berlin, Heidelberg. Springer-Verlag. 2006. 358 p.
5. Neishtadt A.I. Passage through resonance in a two-frequency
problem. // Doklady AN SSSR. – 1975. – V.221. pp.. 301 – 304.
6. Pechenev A.V. On motion of oscillatory systems with bounded
excitation near resonance.// Doklady AN SSSR. – 1986. – V.290. –
N1, pp. 12 – 15.
7. Neishtadt A. Scattering by resonances Selestial Mechanics and
Dynamical Astronomy. 1997. – V.65. pp.1 – 20.