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 journalArticle

5 Citations (Scopus)

Abstract

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
Volume91
Issue number4
DOIs
Publication statusAccepted/In press - 10 Jan 2018

Fingerprint

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

Keywords

  • 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

Cite this

Krysko, A. V., Awrejcewicz, J., Zakharova, A. A., Papkova, I. V., & Krysko, V. A. (Accepted/In press). 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.

In: Nonlinear Dynamics, Vol. 91, No. 4, 10.01.2018, p. 1-21.

Research output: Contribution to journalArticle

Krysko, AV, Awrejcewicz, J, Zakharova, AA, Papkova, IV & Krysko, VA 2018, 'Chaotic vibrations of flexible shallow axially symmetric shells', Nonlinear Dynamics, vol. 91, no. 4, pp. 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. In: Nonlinear Dynamics. 2018 ; Vol. 91, No. 4. pp. 1-21.
@article{a3da0ee312694e388d6a4e2943a734b9,
title = "Chaotic vibrations of flexible shallow axially symmetric shells",
abstract = "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.",
keywords = "Axially symmetric spherical shells, Boundary conditions, Chaos, Dents, Lyapunov exponents, Solution convergence, Vibration modes",
author = "Krysko, {A. V.} and J. Awrejcewicz and Zakharova, {A. A.} and Papkova, {I. V.} and Krysko, {V. A.}",
year = "2018",
month = "1",
day = "10",
doi = "10.1007/s11071-017-4013-0",
language = "English",
volume = "91",
pages = "1--21",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Netherlands",
number = "4",

}

TY - JOUR

T1 - Chaotic vibrations of flexible shallow axially symmetric shells

AU - Krysko, A. V.

AU - Awrejcewicz, J.

AU - Zakharova, A. A.

AU - Papkova, I. V.

AU - Krysko, V. A.

PY - 2018/1/10

Y1 - 2018/1/10

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.

AB - 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.

KW - Axially symmetric spherical shells

KW - Boundary conditions

KW - Chaos

KW - Dents

KW - Lyapunov exponents

KW - Solution convergence

KW - Vibration modes

UR - http://www.scopus.com/inward/record.url?scp=85040363346&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040363346&partnerID=8YFLogxK

U2 - 10.1007/s11071-017-4013-0

DO - 10.1007/s11071-017-4013-0

M3 - Article

VL - 91

SP - 1

EP - 21

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 4

ER -