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Chaotic motions of a Duffing oscillator subjected to combined parametric and quasiperiodic excitation. (English) Zbl 1072.34509
Summary: The forced response of a Mathieu-Duffing oscillator subjected to a two-frequency quasiperiodic excitation is examined in the context when the ratio of the excitation frequencies is large. Numerical results are obtained by the spectral balance method and compared with those predicted by direct numerical integrations. Characteristics of the response as a frequency parameter is tuned, are investigated in terms of the time histories, frequency spectra, Poincaré sections and Lyapunov exponents. It is observed that routes to chaotic motions are different for frequency ranges near the natural frequency of the linear system and near the parametric resonance frequency. It is also shown that the contribution of the small frequency component is important in the prediction of chaotic motions.

MSC:
34C28 Complex behavior and chaotic systems of ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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References:
[1] DOI: 10.1109/TCS.1981.1084921 · Zbl 0484.93027 · doi:10.1109/TCS.1981.1084921
[2] DOI: 10.1109/TCS.1984.1085584 · Zbl 0548.94036 · doi:10.1109/TCS.1984.1085584
[3] DOI: 10.1006/jsvi.1997.1221 · doi:10.1006/jsvi.1997.1221
[4] Kim Y.B., ASME Journal of Applied Mechanics 58 pp 543– (1991)
[5] DOI: 10.1006/jsvi.1996.0220 · Zbl 1232.70024 · doi:10.1006/jsvi.1996.0220
[6] DOI: 10.1115/1.2893802 · doi:10.1115/1.2893802
[7] Zounes R.S., DE- 91 pp 1– (1996)
[8] DOI: 10.1115/1.2899422 · Zbl 0761.73067 · doi:10.1115/1.2899422
[9] DOI: 10.1006/jsvi.1995.0236 · Zbl 1055.74537 · doi:10.1006/jsvi.1995.0236
[10] DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[11] DOI: 10.1016/0167-2789(89)90071-7 · doi:10.1016/0167-2789(89)90071-7
[12] DOI: 10.1016/0020-7462(89)90010-3 · Zbl 0666.70030 · doi:10.1016/0020-7462(89)90010-3
[13] DOI: 10.1016/S0020-7462(98)00087-0 · Zbl 1068.70526 · doi:10.1016/S0020-7462(98)00087-0
[14] DOI: 10.1115/1.3171822 · Zbl 0597.73063 · doi:10.1115/1.3171822
[15] Moon F.C., Journal of Vibration 65 pp 276– (1979)
[16] DOI: 10.1115/1.3153746 · doi:10.1115/1.3153746
[17] DOI: 10.1016/0022-460X(82)90259-0 · doi:10.1016/0022-460X(82)90259-0
[18] Wiggins S, Physics 124 pp 138– (1987)
[19] DOI: 10.1103/RevModPhys.57.617 · Zbl 0989.37516 · doi:10.1103/RevModPhys.57.617
[20] DOI: 10.1016/0020-7462(89)90001-2 · doi:10.1016/0020-7462(89)90001-2
[21] DOI: 10.1063/1.459996 · doi:10.1063/1.459996
[22] Curry J., Springer Notes in Mathematics 668 pp 48– (1977)
[23] DOI: 10.1109/TCS.1987.1086135 · Zbl 0637.94019 · doi:10.1109/TCS.1987.1086135
[24] DOI: 10.1103/PhysRevLett.49.132 · doi:10.1103/PhysRevLett.49.132
[25] Landau L.D, Dokl. Akad. Nauk SSSR 44 pp 339– (1944)
[26] DOI: 10.1007/BF01646553 · Zbl 0223.76041 · doi:10.1007/BF01646553
[27] DOI: 10.1007/BF01197757 · doi:10.1007/BF01197757
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