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A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation

Stepa Paunović, Milan Cajić, Danilo Karličić, Marina Mijalković, Danilo Karlicic Orcid Logo

Journal of Sound and Vibration, Volume: 463, Start page: 114955

Swansea University Author: Danilo Karlicic Orcid Logo

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DOI (Published version): 10.1016/j.jsv.2019.114955

Abstract

The Galerkin method is widely applied for finding approximate solutions to vibration problems of beam and plate structures and for estimating their dynamic behavior. Most studies employ the Galerkin method in the analysis of the undamped systems, or for simple structure models with viscous damping....

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Published in: Journal of Sound and Vibration
ISSN: 0022-460X
Published: 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa52355
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first_indexed 2019-10-07T14:22:55Z
last_indexed 2019-10-08T14:22:34Z
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spelling 2019-10-08T10:47:18.5907798 v2 52355 2019-10-07 A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation d99ee591771c238aab350833247c8eb9 0000-0002-7547-9293 Danilo Karlicic Danilo Karlicic true false 2019-10-07 EEN The Galerkin method is widely applied for finding approximate solutions to vibration problems of beam and plate structures and for estimating their dynamic behavior. Most studies employ the Galerkin method in the analysis of the undamped systems, or for simple structure models with viscous damping. In this paper, a novel approach of using the Galerkin method and Fourier transform to find the solution to the problem of vibration of fractionally damped beams with an arbitrary number of attached concentrated masses and base excitation is presented. The considered approach is novel and it lends itself to determination of the impulse response of the beam and leads to the solution of the system of coupled fractional order differential equations. The proposed approximate solution is validated against the exact solution for a special case with only one tip mass attached, as well as against the Finite Element Method Solution for a special case with classical viscous damping model. Numerical analysis is also given, including the examples of vibration analysis of viscoelastic beams with different fractional derivative orders, retardation times, and the number, weight and position of the attached masses. Journal Article Journal of Sound and Vibration 463 114955 0022-460X Galerkin method, Fractional viscoelasticity, Beam mass system, Base excitation, Impulse response 22 12 2019 2019-12-22 10.1016/j.jsv.2019.114955 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2019-10-08T10:47:18.5907798 2019-10-07T11:10:39.4551583 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Stepa Paunović 1 Milan Cajić 2 Danilo Karličić 3 Marina Mijalković 4 Danilo Karlicic 0000-0002-7547-9293 5 0052355-08102019104648.pdf paunovic2019.pdf 2019-10-08T10:46:48.3400000 Output 732193 application/pdf Accepted Manuscript true 2020-09-18T00:00:00.0000000 false eng
title A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation
spellingShingle A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation
Danilo Karlicic
title_short A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation
title_full A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation
title_fullStr A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation
title_full_unstemmed A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation
title_sort A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation
author_id_str_mv d99ee591771c238aab350833247c8eb9
author_id_fullname_str_mv d99ee591771c238aab350833247c8eb9_***_Danilo Karlicic
author Danilo Karlicic
author2 Stepa Paunović
Milan Cajić
Danilo Karličić
Marina Mijalković
Danilo Karlicic
format Journal article
container_title Journal of Sound and Vibration
container_volume 463
container_start_page 114955
publishDate 2019
institution Swansea University
issn 0022-460X
doi_str_mv 10.1016/j.jsv.2019.114955
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description The Galerkin method is widely applied for finding approximate solutions to vibration problems of beam and plate structures and for estimating their dynamic behavior. Most studies employ the Galerkin method in the analysis of the undamped systems, or for simple structure models with viscous damping. In this paper, a novel approach of using the Galerkin method and Fourier transform to find the solution to the problem of vibration of fractionally damped beams with an arbitrary number of attached concentrated masses and base excitation is presented. The considered approach is novel and it lends itself to determination of the impulse response of the beam and leads to the solution of the system of coupled fractional order differential equations. The proposed approximate solution is validated against the exact solution for a special case with only one tip mass attached, as well as against the Finite Element Method Solution for a special case with classical viscous damping model. Numerical analysis is also given, including the examples of vibration analysis of viscoelastic beams with different fractional derivative orders, retardation times, and the number, weight and position of the attached masses.
published_date 2019-12-22T04:04:40Z
_version_ 1763753360800874496
score 11.012678

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