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Article

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Title

Comprehensive sensitivity analysis of repeated eigenvalues and eigenvectors for structures with viscoelastic elements

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

2024

Published in

Acta Mechanica

Journal year: 2024 | Journal volume: vol. 235 | Journal number: iss. 8

Article type

scientific article

Publication language

english

Keywords
EN
  • design sensitivity analysis
  • repeated eigenvalues
  • viscoelastic elements
  • fractional derivatives
Abstract

EN The paper discusses systems with viscoelastic elements that exhibit repeated eigenvalues in the eigenvalue problem. The mechanical behavior of viscoelastic elements can be described using classical rheological models as well as models that involve fractional derivatives. Formulas have been derived to calculate first- and second-order sensitivities of repeated eigenvalues and their corresponding eigenvectors. A specific case was also examined, where the first derivatives of eigenvalues are repeated. Calculating derivatives of eigenvectors associated with repeated eigenvalues is complex because they are not unique. To compute their derivatives, it is necessary to identify appropriate adjacent eigenvectors to ensure stable control of eigenvector changes. The derivatives of eigenvectors are obtained by dividing them into particular and homogeneous solutions. Additionally, in the paper, a special factor in the coefficient matrix has been introduced to reduce its condition number. The provided examples validate the correctness of the derived formulas and offer a more detailed analysis of structural behavior for structures with viscoelastic elements when altering a single design parameter or simultaneously changing multiple parameters.

Date of online publication

08.06.2024

Pages (from - to)

5213 - 5238

DOI

10.1007/s00707-024-03967-2

URL

https://link.springer.com/article/10.1007/s00707-024-03967-2

License type

CC BY (attribution alone)

Open Access Mode

czasopismo hybrydowe

Open Access Text Version

final published version

Date of Open Access to the publication

in press

Ministry points / journal

100

Impact Factor

2,3 [List 2023]

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