Abstract
A frictional self-oscillating system with an elastic force delay and external influence is considered while interacting with an energy source of limited power. The procedure for using direct linearization methods to calculate mixed forced oscillations and self-oscillations in a system with delay and limited excitation is described. Based on this procedure, equations of nonstationary and stationary motion are derived.
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REFERENCES
Kononenko, V.O., Kolebatel’nye sistemy s ogranichennym vozbuzhdeniem (Excitation Limited Oscillation Systems), Moscow: Nauka, 1964.
Kononenko, V.O., Vibrating Systems with Limited Power-Supply, London: Iliffe, 1969.
Frolov, K.V., Izbrannye trudy, T.1. Vibratsiya i tekhnika (Selected Works, Vol. 1: Vibration and Technology), Moscow: Nauka, 2007.
Kovriguine, D.A., Synchronization and Sommerfeld effect as typical resonant patterns, Arch. Appl. Mech., 2012, vol. 82, pp. 591–604.
Samantaray, A.K., Dasgupta, S.S., and Bhattacharyya, R., Sommerfeld effect in rotationally symmetric planar dynamical systems, Int. J. Eng. Sci., 2010, vol. 48, pp. 21–36. https://doi.org/10.1016/j.ijengsci.2009.06.005
Alifov, A.A., About calculation of self-oscillatory system delayed and limited excitation, in Measurement and Quality: Challenges, Perspectives, Proceedings of the International Conference, November 21–23,2018, Baku, Azerbaijan: AzTU, 2018, p. 289.
Rubanik, V.P., Kolebaniya kvazilineinykh sistem s zapazdyvaniem (Oscillations of Quasilinear Systems with Delay), Moscow: Nauka, 1969.
Butenin, N.V., Neimark, Yu.I., and Fufaev, N.A., Vvedenie v teoriyu nelineinykh kolebanii (Introduction to the Theory of Nonlinear Oscillations), Moscow: Nauka, 1976.
Astashev, V.K. and Gerts, M.E., Self-oscillations of a viscoelastic rod with limiters under the action of a delayed force, Mashinovedenie, 1973, no. 5, p. 3.
Zhirnov, B.M., On self-oscillations of a mechanical system with two degrees of freedom in the presence of delay, Prikl. Mekh., 1973, vol. 9, no. 10, p. 83.
Teoriya avtomaticheskogo upravleniya. Ch. I. Teoriya lineinykh sistem avtomaticheskogo upravleniya (Theory of Automatic Control. Part I. The Theory of Linear Automatic Control Systems), Voronov, A.A., Ed., Moscow: Vyssh. Shkola, 1986.
Bogolyubov, N.N. and Mitropol’skii, Yu.A., Asimptoticheskie metody v teorii nelineinykh kolebanii (Asymptotic Methods in the Theory of Nonlinear Oscillations), Moscow: Nauka, 1974; Boca Raton, FL: CRC, 1961.
Vibratsii v tekhnike: Spravochnik, T.5. Kolebaniya nelineinykh mekhanicheskikh sistem (Vibration in Technology, Vol. 5: Oscillations of Nonlinear Mechanical Systems), Chelomei, V.N. and Blekhman, I.I., Eds., Moscow: Mashinostroenie, 1979.
Alifov, A.A., Metody pryamoi linearizatsii dlya rascheta nelineinykh sistem (Direct Linearization Methods for Calculating Nonlinear Systems), Moscow, Izhevsk: RKhD, 2015, p. 74.
Alifov, A.A., Method of the direct linearization of mixed nonlinearities, J. Mach. Manuf. Reliab., 2017, vol. 46, no. 2, p. 128.
Alifov, A., Farzaliev, M.G., and Jafarov, E.N., Dynamics of a self-oscillatory system with an energy source, Russ. Eng. Res., 2018, vol. 38, no. 4, p. 260.
Alifov, A.A. and Frolov, K.V., Interaction of Nonlinear Oscillatory Systems with Energy Sources, New York: Hemisphere, 1990, p. 327.
Zhuravlev, V.F. and Klimov, D.M., Prikladnye metody v teorii kolebanii (Applied Methods in the Theory of Oscillations), Moscow: Nauka, 1988.
Bronovets, M.A. and Zhuravlev, V.F., On self-excited vibrations in friction force measurement systems, Mech. Solids, 2012, vol. 47, no. 3, p. 261.
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Translated by L. Trubitsyna
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Alifov, A.A. Calculating Mixed Forced and Self-Oscillations for Delayed Elastic Constraint and a Limited Power Energy Source. J. Mach. Manuf. Reliab. 49, 105–109 (2020). https://doi.org/10.3103/S1052618820020053
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DOI: https://doi.org/10.3103/S1052618820020053