Abstract
A Duffing oscillator frictionally interacting with a moving belt under a quasiperiodic load is studied. The multiple-scales method is used to derive a system of two nonautonomous equations with small parameters, which describes the modulation of vibrations. It is shown that the system of modulation equations has a heteroclinic structure. Melnikov functions are used to analyze the domain of heteroclinic chaos
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K. V. Avramov, “Bifurcation of almost periodically excited frictional vibrations,” Dop. NAN Ukrainy, 9, 40–43 (2004).
K. V. Avramov, “Bifurcations at combination resonance and quasiperiodic vibrations of flexible beams,” Int. Appl. Mech., 39, No. 8, 976–982 (2003).
A. A. Alifov and K. V. Frolov, Interaction of Nonlinear Vibrating Systems with Energy Sources [in Russian], Nauka, Moscow (1985).
A. A. Andronov, A. A. Vitt, and S. E. Khaikin, Theory of Oscillators, Dover, New York (1987).
J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York (1983).
J. P. Den-Hartog, Mechanical Vibrations, McGraw-Hill, New York (1956).
V. H. Kauderer, Nichtlineare Mechanik, Springer-Verlag, Berlin (1958).
V. O. Kononenko, Vibrating Systems with a Limited Power Supply, Iliffe Books, London (1969).
I. V. Kragel’sknii and N. V. Gitis, Self-Excited Frictional Vibrations [in Russian], Nauka, Moscow (1987).
V. K. Mel’nikov, “On the stability of the center for time periodic perturbation,” Trans. Moscow Math. Soc., 12(1), 1–57 (1964).
A. H. Nayfeh, Perturbation Methods, Wiley, New York (1973).
K. V. Avramov, “Bifurcations of parametric oscillations of beams with three equilibriums,” Acta Mechanica, 164, 115–138 (2003).
K. V. Avramov and Yu. V. Mikhlin, “Damping of free elastic vibrations in linear systems,” Int. Appl. Mech., 41, No. 2, 203–209 (2005).
B. Feeny, A. Guran, N. Hinrichs, and K. Popp, “A historical review on friction in nonlinear dynamics,” Appl. Mech. Rev., 51, No. 5, 321–341 (1998).
A. A. Martynyuk and N. V. Nikitina, “Complex oscillations revisited,” Int. Appl. Mech., 41, No. 2, 179–186 (2005).
A. A. Martynyuk and N. V. Nikitina, “Complex behavior of a trajectory in single-and double-frequency systems,” Int. Appl. Mech., 41, No. 3, 315–323 (2005).
A. A. Martynyuk and N. V. Nikitina, “Nonlinear oscillations in a system with dry friction,” Int. Appl. Mech., 41, No. 4, 435–440 (2005).
Yu. V. Mikhlin and S. N. Reshetnikova, “Dynamic analysis of a two-mass system with essentially nonlinear vibration damping,” Int. Appl. Mech., 41, No. 1, 77–84 (2005).
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 127–133, September 2006.
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Avramov, K.V. Chaotic frictional vibrations excited by a quasiperiodic load. Int Appl Mech 42, 1071–1076 (2006). https://doi.org/10.1007/s10778-006-0178-9
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DOI: https://doi.org/10.1007/s10778-006-0178-9