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Nonlinear vibrations of a circular cylindrical shell with multiple internal resonances under multi-harmonic excitation

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Abstract

The nonlinear response of a water-filled, thin circular cylindrical shell, simply supported at the edges, to multi-harmonic excitation is studied. The shell has opportune dimensions so that the natural frequencies of the two modes (driven and companion) with three circumferential waves are practically double than the natural frequencies of the two modes (driven and companion) with two circumferential waves. This introduces a one-to-one-to-two-to-two internal resonance in the presence of harmonic excitation in the spectral neighbourhood of the natural frequency of the mode with two circumferential waves. Since the system is excited by a multi-harmonic point-load excitation composed by first and second harmonics, very complex nonlinear dynamics is obtained around the resonance of the fundamental mode. In fact, at this frequency, both modes with two and three circumferential waves are driven to resonance and each one is in a one-to-one internal resonance with its companion mode. The nonlinear dynamics is explored by using bifurcation diagrams of Poincaré maps and time responses.

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Acknowledgements

The second author acknowledges the financial support of the NSERC Discovery Grant, Canada Research Chairs and CFI grant of Canada.

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Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, QC, H3A 0C3, Canada

    Ivan D. Breslavsky & Marco Amabili

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  1. Ivan D. Breslavsky
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  2. Marco Amabili
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Correspondence to Marco Amabili.

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Breslavsky, I.D., Amabili, M. Nonlinear vibrations of a circular cylindrical shell with multiple internal resonances under multi-harmonic excitation. Nonlinear Dyn 93, 53–62 (2018). https://doi.org/10.1007/s11071-017-3983-2

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  • DOI: https://doi.org/10.1007/s11071-017-3983-2

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