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Stochastic nonlinear eigenvibrations of thin elastic plates resting on time-fractional viscoelastic supports


[ 1 ] Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.7] Civil engineering, geodesy and transport

Year of publication


Published in

Probabilistic Engineering Mechanics

Journal year: 2023 | Journal volume: vol. 74

Article type

scientific article

Publication language


  • Stochastic finite element method
  • Free damped vibrations
  • Kirchhoff-love plates
  • Viscoelastic dampers
  • Fractional derivatives
  • Continuation method
  • Probabilistic relative entropy

EN The main objective of this work is to investigate natural vibrations of the thin (Kirchhoff-Love) plate resting on time-fractional viscoelastic supports using the Stochastic Finite Element Method (SFEM). The mechanical behavior of the supports is deterministic and is described by the fractional order derivatives of the Riemann-Liouville type. A subspace iteration method in conjunction with the continuation method is the basis of the numerical solution carried out using the displacement formulation of the Finite Element Method. The probabilistic analysis includes independent Monte-Carlo simulation, the semi-analytical approach, and the iterative generalized stochastic perturbation method of the first two probabilistic moments. Moreover, a corresponding relative entropy and the entropy-based reliability index are contrasted with the First Order Reliability Method (FORM). It has been found that the relative entropy for analyzed eigen-vibrations is some interesting alternative to the FORM methodology in reliability assessment.

Date of online publication


Pages (from - to)

103522-1 - 103522-4





Article Number: 103522

License type

CC BY-NC-ND (attribution - noncommercial - no derivatives)

Open Access Mode

czasopismo hybrydowe

Open Access Text Version

final published version

Date of Open Access to the publication

in press

Ministry points / journal


Impact Factor

2.6 [List 2022]

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