Root
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Conference Proceedings
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6th EUROMECH Nonlinear Dynamics Conference (ENOC 2008)
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The Chelomei Problem: High or Low Frequency Stabilization?
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The possibility to increase the stability of elastic systems by

means of vibrations was originally pointed out by V.N. Chelomei

in 1956. In particular, he arrived at the conclusion that an

elastic rod compressed by a periodic longitudinal force, whose

constant part is greater than the

critical Euler's value, can be stabilized by high-frequency

longitudinal vibrations applied to the rod end. In this study,

formulas for the upper and lower critical frequencies of rod

stabilization are derived and analyzed. It is shown that,

in contrast to the case of high-frequency stabilization of

an inverted pendulum with a vibrating suspension point, the

rod is stabilized at excitation frequencies of the order of

the natural frequency of transverse oscillations belonging to a certain interval.

means of vibrations was originally pointed out by V.N. Chelomei

in 1956. In particular, he arrived at the conclusion that an

elastic rod compressed by a periodic longitudinal force, whose

constant part is greater than the

critical Euler's value, can be stabilized by high-frequency

longitudinal vibrations applied to the rod end. In this study,

formulas for the upper and lower critical frequencies of rod

stabilization are derived and analyzed. It is shown that,

in contrast to the case of high-frequency stabilization of

an inverted pendulum with a vibrating suspension point, the

rod is stabilized at excitation frequencies of the order of

the natural frequency of transverse oscillations belonging to a certain interval.