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IssuesArchive of Issues2003-1pp.41-44

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M. E. Gerts and M. M. Gerts, "Autoresonant oscillations in a restricted-excitation system," Mech. Solids. 38 (1), 41-44 (2003)
Year 2003 Volume 38 Number 1 Pages 41-44
Title Autoresonant oscillations in a restricted-excitation system
Author(s) M. E. Gerts (Moscow)
M. M. Gerts (Moscow)
Abstract To provide desirable oscillation modes in mechanical systems, a coordinate feedback is frequently utilized. An influence of the auto-oscillation-type excitation of a system on the Sommerfeld effect is considered. The Sommerfeld effect is modeled by restricted-excitation oscillating systems [1-4]. The conditions for the existence, stability, and self-excitation of self-sustained oscillations of a linear oscillator are analyzed in the first approximation of the averaging method. The excitation is caused by the inertial forces of an unbalanced rotor of the electric motor. The derivative of the driving torque of the motor is defined as a function of the angle of rotation of the rotor and the displacement of the oscillator.

The parameters providing an autoresonance in the system are determined. Autoresonance is understood as "a resonance under the action of a force generated by the motion of the system" [5]. The autoresonance mode in the case under consideration is shown to be preserved when the parameters of the oscillator and the motor change. In addition, the oscillation modes which are unstable when the traditional excitation schemes are utilized can become stable.
References
1.  I. I. Blekhman, Self-synchronization in Dynamical Systems [in Russian], Nauka, Moscow, 1971.
2.  V. O. Kononenko, Oscillating Systems with Restricted Excitation [in Russian], Nauka, Moscow, 1964.
3.  A. A. Alifov and K. V. Frolov, Interaction of Nonlinear Oscillating Systems with Energy Sources [in Russian], Nauka, Moscow, 1985.
4.  V. Ph. Zhuravlev and A. I. Menyailov, "Investigation of a vibroimpact system with restricted excitation," Izv. AN SSSR. MTT [Mechanics of Solids], No. 2, pp. 45-50, 1978.
5.  A. A. Andronov, A. A. Vitt, and S. E. Khaikin, Theory of Oscillations [in Russian], Fizmatgiz, Moscow, 1959.
6.  M. E. Gerts, "Autoresonant oscillations in an inertially excited system," Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 3-9, 1994.
7.  Yu. A. Mitropol'skii, Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev, 1971.
8.  V. I. Babitskii and B. A. Borovkov, "Stabilization of the autoresonance mode in vibration machines," Mashinovedenie, No. 1, pp. 15-20, 1979.
Received 15 October 2000
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