However, with the growth of the dissipation the instability zone shrinks. Then the frequency-amplitude curve becomes unambiguous, and the instability zone is completely degenerated. In this case the Sommerfeld effect also disappears.
Conclusions
Near the resonance the rotor is substantially influenced by the pair of forces acting from the vibrating base. The average value of this moment is a definite value proportional to quadrate of the amplitude of vibrations of the base. Therefore, near the resonance some increase in the angular velocity of the engine is experienced. This leads to the phenomenon of ‘pulling’ hesitation, despite the fact that the elastic properties of the base are linear. Together with the growth of dissipation the zone of the Sommerfeld instability narrows down to its complete disappearance. This leads to the idea of efficiency of utilizing vibration absorbers to stabilize the motion of electromechanical systems.
Acknowledgments
The work was supported in part by the RFBR grant (project 09-02-97053-р поволжье).
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[1] It should be noted that the characteristic polynomial coefficients are calculated with a somewhat inflated for the first-order approximation accuracy. In fact, it is easy to prove by series expansion in the small parameter. However, the coefficients in the truncated form are such that again lead to a transcendental equation. Therefore, the value of such asymptotics is small.