Dynamic stiffness of nonlocal damped nano-beams on elastic foundation

Adhikari, Sondipon; Karlicic, Danilo; Liu, X.

doi:10.1016/j.euromechsol.2020.104144

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Dynamic stiffness of nonlocal damped nano-beams on elastic foundation

Sondipon Adhikari, Danilo Karlicic

, X. Liu

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...

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Published in:	European Journal of Mechanics - A/Solids
ISSN:	0997-7538
Published:	Elsevier BV 2021
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URI:	https://cronfa.swan.ac.uk/Record/cronfa55483
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first_indexed	2020-10-22T13:00:04Z
last_indexed	2020-12-11T04:19:46Z
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spelling	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
author_id_fullname_str_mv	4ea84d67c4e414f5ccbd7593a40f04d3_*_Sondipon Adhikari d99ee591771c238aab350833247c8eb9_*_Danilo Karlicic
author	Sondipon Adhikari Danilo Karlicic
author2	Sondipon Adhikari Danilo Karlicic X. Liu
format	Journal article
container_title	European Journal of Mechanics - A/Solids
container_volume	86
container_start_page	104144
publishDate	2021
institution	Swansea University
issn	0997-7538
doi_str_mv	10.1016/j.euromechsol.2020.104144
publisher	Elsevier BV
college_str	Faculty of Science and Engineering
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hierarchy_top_title	Faculty of Science and Engineering
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department_str	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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score	11.012678

Dynamic stiffness of nonlocal damped nano-beams on elastic foundation

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