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Dynamic stiffness of nonlocal damped nano-beams on elastic foundation
European Journal of Mechanics - A/Solids, Volume: 86, Start page: 104144
Swansea University Authors: Sondipon Adhikari, Danilo Karlicic
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DOI (Published version): 10.1016/j.euromechsol.2020.104144
Abstract
Free and forced bending vibration of damped nonlocal nano-beams resting on an elastic foundation is investigated. Two types of nonlocal damping models, namely, strain-rate-dependent viscous damping and velocity-dependent viscous damping are considered. A frequency-dependent dynamic finite element me...
Published in: | European Journal of Mechanics - A/Solids |
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ISSN: | 0997-7538 |
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Elsevier BV
2021
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URI: | https://cronfa.swan.ac.uk/Record/cronfa55483 |
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2020-12-10T14:25:06.1743548 v2 55483 2020-10-22 Dynamic stiffness of nonlocal damped nano-beams on elastic foundation 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false d99ee591771c238aab350833247c8eb9 0000-0002-7547-9293 Danilo Karlicic Danilo Karlicic true false 2020-10-22 FGSEN Free and forced bending vibration of damped nonlocal nano-beams resting on an elastic foundation is investigated. Two types of nonlocal damping models, namely, strain-rate-dependent viscous damping and velocity-dependent viscous damping are considered. A frequency-dependent dynamic finite element method is developed to obtain the forced vibration response. Frequency-adaptive complex-valued shape functions are used for the derivation of the dynamic stiffness matrix. It is shown that there are six unique coefficients which define the general dynamic stiffness matrix. These complex-valued coefficients are obtained exactly in closed-form and illustrated numerically as functions of the frequency. It is proved that the general dynamic stiffness matrix reduces to the well known special cases under different conditions. The stiffness and mass matrices of the nonlocal beam are also obtained using the conventional finite element method. A numerical algorithm to extract the eigenvalues from the dynamic stiffness matrix with a transcendental element for the special case when the system is undamped is suggested. Results from the dynamic finite element method and the conventional finite element method are compared. The application of the dynamic stiffness approach is shown through forced response analysis of a double-walled carbon nanotube in pinned-pinned and cantilever configurations. Explicit closed-form expressions of the dynamic response for both the cases have been obtained and the role of crucial system parameters such as, the damping factors, the nonlocal parameter and the foundation stiffness have been investigated. Journal Article European Journal of Mechanics - A/Solids 86 104144 Elsevier BV 0997-7538 Bending vibration; Nonlocal mechanics; Dynamic stiffness; Asymptotic analysis; Frequency response 1 3 2021 2021-03-01 10.1016/j.euromechsol.2020.104144 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2020-12-10T14:25:06.1743548 2020-10-22T13:54:00.9082962 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Sondipon Adhikari 1 Danilo Karlicic 0000-0002-7547-9293 2 X. Liu 3 55483__18481__593968236c7546f6839d3e58aaf7662f.pdf 55483.pdf 2020-10-23T09:14:31.5578048 Output 3085893 application/pdf Accepted Manuscript true 2021-10-17T00:00:00.0000000 © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license true eng http://creativecommons.org/licenses/by-nc-nd/4.0/ |
title |
Dynamic stiffness of nonlocal damped nano-beams on elastic foundation |
spellingShingle |
Dynamic stiffness of nonlocal damped nano-beams on elastic foundation Sondipon Adhikari Danilo Karlicic |
title_short |
Dynamic stiffness of nonlocal damped nano-beams on elastic foundation |
title_full |
Dynamic stiffness of nonlocal damped nano-beams on elastic foundation |
title_fullStr |
Dynamic stiffness of nonlocal damped nano-beams on elastic foundation |
title_full_unstemmed |
Dynamic stiffness of nonlocal damped nano-beams on elastic foundation |
title_sort |
Dynamic stiffness of nonlocal damped nano-beams on elastic foundation |
author_id_str_mv |
4ea84d67c4e414f5ccbd7593a40f04d3 d99ee591771c238aab350833247c8eb9 |
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4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari d99ee591771c238aab350833247c8eb9_***_Danilo Karlicic |
author |
Sondipon Adhikari Danilo Karlicic |
author2 |
Sondipon Adhikari Danilo Karlicic X. Liu |
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Journal article |
container_title |
European Journal of Mechanics - A/Solids |
container_volume |
86 |
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104144 |
publishDate |
2021 |
institution |
Swansea University |
issn |
0997-7538 |
doi_str_mv |
10.1016/j.euromechsol.2020.104144 |
publisher |
Elsevier BV |
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Faculty of Science and Engineering |
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School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised |
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description |
Free and forced bending vibration of damped nonlocal nano-beams resting on an elastic foundation is investigated. Two types of nonlocal damping models, namely, strain-rate-dependent viscous damping and velocity-dependent viscous damping are considered. A frequency-dependent dynamic finite element method is developed to obtain the forced vibration response. Frequency-adaptive complex-valued shape functions are used for the derivation of the dynamic stiffness matrix. It is shown that there are six unique coefficients which define the general dynamic stiffness matrix. These complex-valued coefficients are obtained exactly in closed-form and illustrated numerically as functions of the frequency. It is proved that the general dynamic stiffness matrix reduces to the well known special cases under different conditions. The stiffness and mass matrices of the nonlocal beam are also obtained using the conventional finite element method. A numerical algorithm to extract the eigenvalues from the dynamic stiffness matrix with a transcendental element for the special case when the system is undamped is suggested. Results from the dynamic finite element method and the conventional finite element method are compared. The application of the dynamic stiffness approach is shown through forced response analysis of a double-walled carbon nanotube in pinned-pinned and cantilever configurations. Explicit closed-form expressions of the dynamic response for both the cases have been obtained and the role of crucial system parameters such as, the damping factors, the nonlocal parameter and the foundation stiffness have been investigated. |
published_date |
2021-03-01T04:09:43Z |
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1763753678244675584 |
score |
11.036706 |