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Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers

The main motivation of this work was to present a semi-analytical extension of the correspondence principle in stochastic dynamics. It is demonstrated for the stochastic structural free vibrations of Kirchhoff–Love elastic, isotropic and rectangular plates supported by viscoelastic generalized Maxwe...

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Autores principales: Kamiński, Marcin, Lenartowicz, Agnieszka, Guminiak, Michał, Przychodzki, Maciej
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9573046/
https://www.ncbi.nlm.nih.gov/pubmed/36234154
http://dx.doi.org/10.3390/ma15196811
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author Kamiński, Marcin
Lenartowicz, Agnieszka
Guminiak, Michał
Przychodzki, Maciej
author_facet Kamiński, Marcin
Lenartowicz, Agnieszka
Guminiak, Michał
Przychodzki, Maciej
author_sort Kamiński, Marcin
collection PubMed
description The main motivation of this work was to present a semi-analytical extension of the correspondence principle in stochastic dynamics. It is demonstrated for the stochastic structural free vibrations of Kirchhoff–Love elastic, isotropic and rectangular plates supported by viscoelastic generalized Maxwell dampers. The ambient temperature of the plate affects the dampers only and is included in a mathematical model using the frequency–temperature correspondence principle. The free vibration problem of the plate–viscoelastic damper system is solved using the continuation method and also the Finite Element Method (FEM). The stochastic approach begins with an initial deterministic sensitivity analysis to detect the most influential parameters and numerical FEM recovery of the polynomial representation for lower eigenfrequencies versus these parameters. A final symbolic integration leads to the first four basic probabilistic characteristics, all delivered as functions of the input uncertainties.
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spelling pubmed-95730462022-10-17 Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers Kamiński, Marcin Lenartowicz, Agnieszka Guminiak, Michał Przychodzki, Maciej Materials (Basel) Article The main motivation of this work was to present a semi-analytical extension of the correspondence principle in stochastic dynamics. It is demonstrated for the stochastic structural free vibrations of Kirchhoff–Love elastic, isotropic and rectangular plates supported by viscoelastic generalized Maxwell dampers. The ambient temperature of the plate affects the dampers only and is included in a mathematical model using the frequency–temperature correspondence principle. The free vibration problem of the plate–viscoelastic damper system is solved using the continuation method and also the Finite Element Method (FEM). The stochastic approach begins with an initial deterministic sensitivity analysis to detect the most influential parameters and numerical FEM recovery of the polynomial representation for lower eigenfrequencies versus these parameters. A final symbolic integration leads to the first four basic probabilistic characteristics, all delivered as functions of the input uncertainties. MDPI 2022-09-30 /pmc/articles/PMC9573046/ /pubmed/36234154 http://dx.doi.org/10.3390/ma15196811 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Kamiński, Marcin
Lenartowicz, Agnieszka
Guminiak, Michał
Przychodzki, Maciej
Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers
title Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers
title_full Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers
title_fullStr Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers
title_full_unstemmed Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers
title_short Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers
title_sort selected problems of random free vibrations of rectangular thin plates with viscoelastic dampers
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9573046/
https://www.ncbi.nlm.nih.gov/pubmed/36234154
http://dx.doi.org/10.3390/ma15196811
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