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Article

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Title

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

Authors

[ 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

2023

Published in

Materials

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

Article type

scientific article

Publication language

english

Keywords
EN
  • 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
Abstract

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

DOI

10.3390/ma16247527

URL

https://www.mdpi.com/1996-1944/16/24/7527

Comments

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

140

Impact Factor

3,4 [List 2022]

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