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Multiple resonance and anti-resonance in coupled Duffing oscillators

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Abstract

We investigate the resonance behaviour in a system composed by n coupled Duffing oscillators where only the first oscillator is driven by a periodic force, assuming a nearest neighbour coupling. We have derived the frequency-response equations for a system composed of two coupled oscillators by using a theoretical approach. Interestingly, the frequency-response curve displays two resonance peaks and one anti-resonance. A theoretical prediction of the response amplitudes of two oscillators closely matches with the numerically computed amplitudes. We analyse the effect of the coupling strength on the resonance and anti-resonance frequencies and the response amplitudes at these frequencies. For the n coupled oscillators’ system, in general, there are n-resonant peaks and (\(n-1\)) anti-resonant peaks. For large values of n, except for the first resonance, other resonant peaks are weak due to linear damping. The resonance behaviours observed in the n coupled Duffing oscillators are also realized in an electronic analog circuit simulation of the equations. Understanding the role of coupling and system size has the potential applications in music, structural engineering, power systems, biological networks, electrical and electronic systems.

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Acknowledgments

The work of R.J. is supported by the University Grants Commission, Government of India in the form of Research Fellowship in Science for Meritorious Students. The work of K.T. forms a part of a Department of Science and Technology, Government of India sponsored project Grant No. SR/S2/HEP-015/2010. M.A.F.S. acknowledges the financial support by the Spanish Ministry of Economy and Competitivity under Project Number FIS2013-40653-P.

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Authors and Affiliations

  1. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli, Tamilnadu, 620 024, India

    R. Jothimurugan & K. Thamilmaran

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

    S. Rajasekar

  3. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tuliṕan s/n, 28933, Móstoles, Madrid, Spain

    M. A. F. Sanjuán

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  1. R. Jothimurugan
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  2. K. Thamilmaran
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  4. M. A. F. Sanjuán
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Correspondence to S. Rajasekar.

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Jothimurugan, R., Thamilmaran, K., Rajasekar, S. et al. Multiple resonance and anti-resonance in coupled Duffing oscillators. Nonlinear Dyn 83, 1803–1814 (2016). https://doi.org/10.1007/s11071-015-2447-9

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