Chaotic vibrations of flexible shallow axially symmetric shells

A. V. Krysko, J. Awrejcewicz, A. A. Zakharova, I. V. Papkova, V. A. Krysko

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


In this work, chaotic dynamics of flexible spherical axially symmetric shallow shells subjected to sinusoidal transverse load is studied with emphasis put on the vibration modes. Chaos reliability is verified and validated by solving the implemented mathematical model by partial nonlinear equations governing the dynamics of flexible spherical shells and by estimating the signs of the largest Lyapunov exponents with the help of qualitatively different approaches. It is shown how the scenario of transition of the investigated shells from regular to chaotic vibrations depends on the boundary condition. The following cases are considered: (1) movable and fixed simple supports along the shell contours, taking into account shell stiffness (Feigenbaum scenario) and shell damping (Ruelle–Takens–Newhouse scenario), and (2) movable clamping (regular shell vibrations). The presence of dents, the location and character of which essentially depend on the shell geometric parameters, boundary conditions, and the external load parameters, is detected in some regions of the shell surface and discussed.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalNonlinear Dynamics
Issue number4
Publication statusAccepted/In press - 10 Jan 2018


  • Axially symmetric spherical shells
  • Boundary conditions
  • Chaos
  • Dents
  • Lyapunov exponents
  • Solution convergence
  • Vibration modes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

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