Analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic medium
Damped vibrations of elastic thin bodies, such as plates and circular cylindrical shells, embedded into a viscoelastic medium, the rheological features of which are described by fractional derivatives, are considered in the present article. Besides the forces of viscous friction, a thin body is subj...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2013-04-01
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| Series: | Journal of the Mechanical Behavior of Materials |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jmbm-2013-0002 |
| _version_ | 1818390922393550848 |
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| author | Rossikhin Yury A. Shitikova Marina V. |
| author_facet | Rossikhin Yury A. Shitikova Marina V. |
| author_sort | Rossikhin Yury A. |
| collection | DOAJ |
| description | Damped vibrations of elastic thin bodies, such as plates and circular cylindrical shells, embedded into a viscoelastic medium, the rheological features of which are described by fractional derivatives, are considered in the present article. Besides the forces of viscous friction, a thin body is subjected to the action of external forces dependent on the coordinates of the middle surface and time. The boundary conditions are proposed in such a way that the governing equations allow the Navier-type solution. The Laplace integral transform method and the method of expansion of all functions entering into the set of governing equations in terms of the eigenfunctions of the given problem are used as the methods of solution. It is shown that as a result of such a procedure, the systems of equations in the generalized coordinates could be reduced to infinite sets of uncoupled equations, each of which describes damped vibrations of a mechanical oscillator based on the fractional derivative Kelvin-Voigt model. |
| first_indexed | 2024-12-14T05:05:19Z |
| format | Article |
| id | doaj.art-c569bbb07ee7447aa330c8eb12353249 |
| institution | Directory Open Access Journal |
| issn | 0334-8938 2191-0243 |
| language | English |
| last_indexed | 2024-12-14T05:05:19Z |
| publishDate | 2013-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of the Mechanical Behavior of Materials |
| spelling | doaj.art-c569bbb07ee7447aa330c8eb123532492022-12-21T23:16:07ZengDe GruyterJournal of the Mechanical Behavior of Materials0334-89382191-02432013-04-01215-615515910.1515/jmbm-2013-0002Analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic mediumRossikhin Yury A.0Shitikova Marina V.1Research Center for Wave Dynamics in Solids and Structures, Voronezh State University of Architecture and Civil Engineering, 20-letijya Oktjabrja Street 84, Voronezh 394018, RussiaResearch Center for Wave Dynamics in Solids and Structures, Voronezh State University of Architecture and Civil Engineering, 20-letijya Oktjabrja Street 84, Voronezh 394018, RussiaDamped vibrations of elastic thin bodies, such as plates and circular cylindrical shells, embedded into a viscoelastic medium, the rheological features of which are described by fractional derivatives, are considered in the present article. Besides the forces of viscous friction, a thin body is subjected to the action of external forces dependent on the coordinates of the middle surface and time. The boundary conditions are proposed in such a way that the governing equations allow the Navier-type solution. The Laplace integral transform method and the method of expansion of all functions entering into the set of governing equations in terms of the eigenfunctions of the given problem are used as the methods of solution. It is shown that as a result of such a procedure, the systems of equations in the generalized coordinates could be reduced to infinite sets of uncoupled equations, each of which describes damped vibrations of a mechanical oscillator based on the fractional derivative Kelvin-Voigt model.https://doi.org/10.1515/jmbm-2013-0002cylindrical shelldamped vibrationsfractional derivative viscoelasticityfractional oscillatorthin plate |
| spellingShingle | Rossikhin Yury A. Shitikova Marina V. Analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic medium Journal of the Mechanical Behavior of Materials cylindrical shell damped vibrations fractional derivative viscoelasticity fractional oscillator thin plate |
| title | Analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic medium |
| title_full | Analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic medium |
| title_fullStr | Analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic medium |
| title_full_unstemmed | Analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic medium |
| title_short | Analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic medium |
| title_sort | analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic medium |
| topic | cylindrical shell damped vibrations fractional derivative viscoelasticity fractional oscillator thin plate |
| url | https://doi.org/10.1515/jmbm-2013-0002 |
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