Chaotic vibrations of flexible shallow axially symmetric shells

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

Результат исследований: Материалы для журналаСтатья

5 Цитирования (Scopus)

Выдержка

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.

Язык оригиналаАнглийский
Страницы (с-по)1-21
Число страниц21
ЖурналNonlinear Dynamics
Том91
Номер выпуска4
DOI
СостояниеПринято/в печати - 10 янв 2018

Отпечаток

Shell
Vibration
Boundary conditions
Nonlinear equations
Chaos theory
Damping
Stiffness
Mathematical models
Scenarios
Shallow Shell
Largest Lyapunov Exponent
Spherical Shell
Chaotic Dynamics
Chaos
Nonlinear Equations
Transverse
Mathematical Model
Partial

ASJC Scopus subject areas

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

Цитировать

Krysko, A. V., Awrejcewicz, J., Zakharova, A. A., Papkova, I. V., & Krysko, V. A. (Принято в печать). Chaotic vibrations of flexible shallow axially symmetric shells. Nonlinear Dynamics, 91(4), 1-21. https://doi.org/10.1007/s11071-017-4013-0

Chaotic vibrations of flexible shallow axially symmetric shells. / Krysko, A. V.; Awrejcewicz, J.; Zakharova, A. A.; Papkova, I. V.; Krysko, V. A.

В: Nonlinear Dynamics, Том 91, № 4, 10.01.2018, стр. 1-21.

Результат исследований: Материалы для журналаСтатья

Krysko, AV, Awrejcewicz, J, Zakharova, AA, Papkova, IV & Krysko, VA 2018, 'Chaotic vibrations of flexible shallow axially symmetric shells', Nonlinear Dynamics, том. 91, № 4, стр. 1-21. https://doi.org/10.1007/s11071-017-4013-0
Krysko, A. V. ; Awrejcewicz, J. ; Zakharova, A. A. ; Papkova, I. V. ; Krysko, V. A. / Chaotic vibrations of flexible shallow axially symmetric shells. В: Nonlinear Dynamics. 2018 ; Том 91, № 4. стр. 1-21.
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AU - Zakharova, A. A.

AU - Papkova, I. V.

AU - Krysko, V. A.

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N2 - 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.

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