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Periodic, quasi-periodic, and chaotic geometrically nonlinear forced vibrations of a shallow cantilever shell

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Abstract

Geometrically nonlinear forced vibrations of a cantilever shallow shell are analyzed. A finite degree of freedom nonlinear dynamical system is derived using the assumed mode method. The Neimark–Sacker bifurcations are detected close to the first principal resonance. The quasi-periodic vibrations, which originate from these bifurcations, are investigated numerically. These vibrations are transformed into chaotic motions as a result of the forcing frequency variation. Sub-harmonic vibrations with large amplitudes are analyzed in a wide forcing frequency range close to the second principal resonance.

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Author information

Authors and Affiliations

  1. Department of Vibrations, Podgorny Institute for Mechanical Engineering, National Academy of Science of Ukraine, 2/10 Dm. Pozharskogo St., Kharkiv, 61046, Ukraine

    K. V. Avramov

  2. Department of Continuum Mechanics, National Technical University “KhPI”, Frunze St. 21, Kharkiv, 61002, Ukraine

    K. V. Avramov & S. E. Malyshev

Authors
  1. K. V. Avramov
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  2. S. E. Malyshev
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Correspondence to K. V. Avramov.

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Avramov, K.V., Malyshev, S.E. Periodic, quasi-periodic, and chaotic geometrically nonlinear forced vibrations of a shallow cantilever shell. Acta Mech 229, 1579–1595 (2018). https://doi.org/10.1007/s00707-017-2087-x

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  • DOI: https://doi.org/10.1007/s00707-017-2087-x

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