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IssuesArchive of Issues2013-2pp.119-127

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L.D. Akulenko and S.V. Nesterov, "Parametric Vibrations of a Mechanical System and Their Stability for an Arbitrary Modulation Coefficient," Mech. Solids. 48 (2), 119-127 (2013)
Year 2013 Volume 48 Number 2 Pages 119-127
DOI 10.3103/S0025654413020015
Title Parametric Vibrations of a Mechanical System and Their Stability for an Arbitrary Modulation Coefficient
Author(s) L.D. Akulenko (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, gavrikov@ipmnet.ru)
S.V. Nesterov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia)
Abstract The natural frequencies and modes of parametric vibrations of a mechanical system are studied, by way of example, for a pendulum of variable length with modulation coefficient varying from arbitrarily small to maximum admissible values. Analytic and numerical methods are used to construct and study the boundaries of the resonance domains for the first four vibration modes, and the main qualitative properties of higher modes are found. The complete degeneration of modes with even numbers, i.e., the coincidence of the frequencies of symmetric and nonsymmetric natural modes for admissible values of the modulation parameter, is proved. The global picture of boundaries of stability domains for the lower equilibrium is constructed, and a significant difference from the Ince-Strutt diagram is shown. Specific properties of the natural modes are established.
Keywords pendulum, variable length, parametric vibrations, modulation coefficient, resonance domain, natural frequency, natural mode
References
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Received 08 September 2011
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