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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...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2022
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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. |
format | Online Article Text |
id | pubmed-9573046 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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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