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Eigenvibrations of Kirchhoff Rectangular Random Plates on Time-Fractional Viscoelastic Supports via the Stochastic Finite Element Method


[ 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


Journal year: 2023 | Journal volume: vol. 16 | Journal number: iss. 24

Article type

scientific article

Publication language


  • stochastic finite element method
  • free damped vibrations
  • Kirchhoff–Love plates
  • viscoelastic dampers
  • fractional derivatives
  • continuation method
  • semi-analytical probabilistic technique
  • stochastic perturbation technique
  • Monte-Carlo simulations
  • probabilistic relative entropy
  • reliability analysis

EN The present work’s main objective is to investigate the natural vibrations of the thin (Kirchhoff–Love) plate resting on time-fractional viscoelastic supports in terms of the Stochastic Finite Element Method (SFEM). The behavior of the supports is described by the fractional order derivatives of the Riemann–Liouville type. The subspace iteration method, in conjunction with the continuation method, is used as a tool to solve the non-linear eigenproblem. A deterministic core for solving structural eigenvibrations is the Finite Element Method. The probabilistic analysis includes the Monte-Carlo simulation and the semi-analytical approach, as well as the iterative generalized stochastic perturbation method. Probabilistic structural response in the form of up to the second-order characteristics is investigated numerically in addition to the input uncertainty level. Finally, the probabilistic relative entropy and the safety measure are estimated. The presented investigations can be applied to the dynamics of foundation plates resting on viscoelastic soil.

Pages (from - to)

7527-1 - 7527-32





Article Number: 7527

License type

CC BY (attribution alone)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

at the time of publication

Ministry points / journal


Impact Factor

3,4 [List 2022]

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