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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Variation of Response Amplitude in Parametrically Driven Single Duffing Oscillator and Unidirectionally Coupled Duffing Oscillators

Journal of Applied Nonlinear Dynamics 6(1) (2017) 121--129 | DOI:10.5890/JAND.2017.03.009

S. Rajamani; S. Rajasekar

School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, India

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Abstract

We present our investigation on the effect of parametric force on the response amplitude in the single Duffing oscillator and unidirectionally coupled n Duffing oscillators. In the single oscillator parametric perturbation is of the form f xsinωt. Parametric perturbation induced oscillatory motion is found for values of f above a critical value. In the oscillatory motion the dominant frequency is found to be ω/2. A(ω/2), the amplitude of oscillation at the frequency ω/2, is found to vary linearly with ω. We consider unidirectionally coupled n oscillators with first oscillator alone driven by a parametric force and the other oscillators are nonlinearly or linearly coupled but one-way only. Depending upon the values of the coupling strength δ the oscillators, after first several oscillators, exhibit damped or undamped signal propagation. In the nonlinearly coupled oscillators the dominant frequency of oscillation is ω/2. In the linearly coupled system the frequency ω/2 is absent. The oscillators other than the first oscillator exhibiting oscillatory motions have frequencies ω or 2ω or both depending upon the values of the coupling strength.

Acknowledgments

S. Rajamani expresses her gratitude to University Grants Commission (U.G.C.), Government of India for financial support in the form of U.G.C. meritorious fellowship.

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