2011
DOI: 10.1007/s00419-011-0574-4
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Synchronization and sommerfeld effect as typical resonant patterns

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 base be linear one. As the measure of energy dissipation increases, the effect of bifurcated oscillations can disappear. The latter circums… Show more

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Cited by 24 publications
(4 citation statements)
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“…ultra-low frequencies: 0 ω < 30 rad/s; 2. low frequencies: 30 ω < 50 rad/s; 3. medium frequencies: 50 ω < 70 rad/s; 4. high frequencies: 70 ω < 100 rad/s; 5. superior frequencies: ω 100 rad/s. At frequency ω ≈ 125 rad/s the Sommerfeld effect (Sommerfeld, 1902;Blekhman, 1988;Dimentberg et al, 1997;Blekhman and Fradkov, 2004;Kovriguine, 2012;Cvetićanin and Zukovic, 2015) manifests itself; the frequencies in this range and the upper one have not been experimentally studied in (Andrievsky et al, 2019;Fradkov et al, 2021) and are not considered in the present study. The control laws for frequency stabilization along with the prescribed phase shift between the rotors angular positions are proposed and experimentally studied on the mechatronic vibration setup SV-2M.…”
Section: Description Of Experimental Mechatronic Setupmentioning
confidence: 94%
“…ultra-low frequencies: 0 ω < 30 rad/s; 2. low frequencies: 30 ω < 50 rad/s; 3. medium frequencies: 50 ω < 70 rad/s; 4. high frequencies: 70 ω < 100 rad/s; 5. superior frequencies: ω 100 rad/s. At frequency ω ≈ 125 rad/s the Sommerfeld effect (Sommerfeld, 1902;Blekhman, 1988;Dimentberg et al, 1997;Blekhman and Fradkov, 2004;Kovriguine, 2012;Cvetićanin and Zukovic, 2015) manifests itself; the frequencies in this range and the upper one have not been experimentally studied in (Andrievsky et al, 2019;Fradkov et al, 2021) and are not considered in the present study. The control laws for frequency stabilization along with the prescribed phase shift between the rotors angular positions are proposed and experimentally studied on the mechatronic vibration setup SV-2M.…”
Section: Description Of Experimental Mechatronic Setupmentioning
confidence: 94%
“…It is a very fast dynamics which produces no obvious change in the response except slowing down the simulations due to large differences in time constants. Moreover, motor armature inductance is small enough to influence the mechanical system's transient response [33][34][35]. Thus it has been dropped from the model.…”
Section: Integrated Modelmentioning
confidence: 99%
“…[9][10][11] Meanwhile, Balthazar et al gave some short comments on synchronization in pre-resonance and resonance region between DC motors coupling with a flexible strut structure, and ''sommerfeld effect'' of self-synchronization of the proposed system is also analyzed by numerical simulations, 12,13 and then Kovriguine used theoretical and experimental calculation to demonstrate the synchronous rotations of motors, which are almost deenergized and do not need any high-powered energy set in the proposed mode. 14 Djanan et al focused on three motors operated in the common and opposite direction on a same plate, the synchronous rotation between the rotors is depended on frequency of the motors and structure parameter of the plate. 15,16 Sperling et al presented a two-plane automatic balancing device for equilibration of rigid-rotor unbalance, and it not only derives dynamic equations for the considered system but also gives the discussion of numerical computation, as well as determines the synchronous condition according to an analytical approximation.…”
Section: Introductionmentioning
confidence: 99%
“…gave some short comments on synchronization in pre-resonance and resonance region between DC motors coupling with a flexible strut structure, and “sommerfeld effect” of self-synchronization of the proposed system is also analyzed by numerical simulations, 12,13 and then Kovriguine used theoretical and experimental calculation to demonstrate the synchronous rotations of motors, which are almost deenergized and do not need any high-powered energy set in the proposed mode. 14 Djanan et al. focused on three motors operated in the common and opposite direction on a same plate, the synchronous rotation between the rotors is depended on frequency of the motors and structure parameter of the plate.…”
Section: Introductionmentioning
confidence: 99%