Non-symmetric forms of non-linear vibrations of flexible cylindrical panels and plates under longitudinal load and additive white noise

V. A. Krysko, J. Awrejcewicz, E. Yu Krylova, I. V. Papkova, A. V. Krysko

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Parametric non-linear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the second-order accuracy and the Runge-Kutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the Faedo-Galerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4th-order Runge-Kutta methods. The numerical experiment yielded, for a certain set of parameters, the non-symmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasi-periodicity, whereas the previously non-symmetric vibration modes are closer to symmetric ones.

Original languageEnglish
Pages (from-to)212-229
Number of pages18
JournalJournal of Sound and Vibration
Volume423
DOIs
Publication statusPublished - 9 Jun 2018

Fingerprint

White noise
white noise
Finite difference method
Runge-Kutta method
Runge Kutta methods
vibration
vibration mode
structural members
Cauchy problem
Structural members
Galerkin method
Galerkin methods
Ordinary differential equations
partial differential equations
Partial differential equations
periodic variations
differential equations
degrees of freedom
approximation
Experiments

Keywords

  • Finite difference method
  • Non-symmetric modes
  • Parametric vibrations
  • Transitional processes
  • White noise

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Non-symmetric forms of non-linear vibrations of flexible cylindrical panels and plates under longitudinal load and additive white noise. / Krysko, V. A.; Awrejcewicz, J.; Krylova, E. Yu; Papkova, I. V.; Krysko, A. V.

In: Journal of Sound and Vibration, Vol. 423, 09.06.2018, p. 212-229.

Research output: Contribution to journalArticle

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AU - Papkova, I. V.

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