Problem of oscillations arising in an elastic base caused by rotor vibrations of an asynchronous driver near the critical angular velocity. The equations of slow motions. Oscillations in the absence of energy dissipation. Damped stationary oscillations.
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Synchronization and Sommerfeld as Typical Resonant Patterns Part I. Single Driver Example Kovriguine D.A. Abstract We analyze a classical problem of oscillations arising in an elastic base caused by rotor vibrations of an asynchronous driver near the critical angular velocity. The nonlinear coupling between oscillations of the elastic base and rotor takes place naturally due to unbalanced masses. This provides typical frequency-amplitude patterns, even let the elastic properties of the beam be linear one. As the measure of energy dissipation increases the effect of bifurcated oscillations can disappear. The latter circumstance indicates the efficiency of using vibration absorbers to eliminate or stabilize the dynamics of the electromechanical system. Key Words Sommerfeld effect, asynchronous device; Lyapunov criterion, Routh-Hurwitz criterion, stability. stationary oscillation resonance synchronization Introduction The phenomenon of bifurcated oscillations of an elastic base, while scanning the angular veloci
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