Acta Mechanica

, Volume 229, Issue 4, pp 1579–1595 | Cite as

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

  • K. V. Avramov
  • S. E. Malyshev
Original Paper


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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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Vibrations, Podgorny Institute for Mechanical EngineeringNational Academy of Science of UkraineKharkivUkraine
  2. 2.Department of Continuum MechanicsNational Technical University “KhPI”KharkivUkraine

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