Chaotic dynamics of two coaxially-nested cylindrical shells reinforced by two beams

J. Awrejcewicz, A. V. Krysko, O. A. Saltykova, S. S. Vetsel, V. A. Krysko

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Non-linear dynamics and contact interactions of beam-shell structures composed of two closed cylindrical shells which are coaxially nested and reinforced by two beams located symmetrically on the shell external perimeter is studied. In the present work, clearances between the mentioned structural members are taken into account, two beams are subjected to harmonic loads, and the dissipation factors are neglected. 3D PDEs governing non-linear dynamics of beams and shells within the geometric theory of Novozhilov are employed, whereas the contact pressure is defined through Kantor's model. PDEs are reduced to ODEs by means of the FEM (finite element method), and the solution convergence is validated through different numbers of finite elements located along the structural members thickness and by employment of the Runge principle with respect to spatial coordinates. The Cauchy problem is solved by the explicit integration (Euler method), which allows one to carry out the computation without the need to define solutions in a few initial points. Analysis of vibrations, including contact interactions, is realized with the use of methods of non-linear dynamics and the qualitative theory of differential equations, time histories/signals, phase portraits, Poincarè sections, Fourier spectra, wavelet-based analysis as well as the Lyapunov exponents.

Original languageEnglish
Pages (from-to)339-351
Number of pages13
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume62
DOIs
Publication statusPublished - 1 Sep 2018

Fingerprint

Cylindrical Shell
Chaotic Dynamics
Structural members
Nonlinear Dynamics
Contact
Shell
Fourier Spectrum
Shell Structure
Euler's method
Phase Portrait
Differential equations
Perimeter
Clearance
Interaction
Lyapunov Exponent
Finite element method
Dissipation
Cauchy Problem
Wavelets
Vibration

Keywords

  • 3D problem
  • Beams
  • Chaos
  • Clearance
  • Shells

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Chaotic dynamics of two coaxially-nested cylindrical shells reinforced by two beams. / Awrejcewicz, J.; Krysko, A. V.; Saltykova, O. A.; Vetsel, S. S.; Krysko, V. A.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 62, 01.09.2018, p. 339-351.

Research output: Contribution to journalArticle

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