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Torsional Vibration of Size-dependent Viscoelastic Rods using Nonlocal Strain and Velocity Gradient Theory

S. El-Borgi, P. Rajendran, M.I. Friswell, M. Trabelssi, J.N. Reddy, Michael Friswell

Composite Structures

Swansea University Author: Michael Friswell

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DOI (Published version): 10.1016/j.compstruct.2017.12.002

Abstract

In this paper the torsional vibration of size-dependent viscoelastic nanorods embedded in an elastic medium with different boundary conditions is investigated. The novelty of this study consists of combining the nonlocal theory with the strain and velocity gradient theory to capture both softening a...

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Published in: Composite Structures
ISSN: 0263-8223
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa37347
first_indexed 2017-12-12T13:49:43Z
last_indexed 2018-02-09T05:30:41Z
id cronfa37347
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spelling 2017-12-07T09:55:11.1454107 v2 37347 2017-12-07 Torsional Vibration of Size-dependent Viscoelastic Rods using Nonlocal Strain and Velocity Gradient Theory 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2017-12-07 In this paper the torsional vibration of size-dependent viscoelastic nanorods embedded in an elastic medium with different boundary conditions is investigated. The novelty of this study consists of combining the nonlocal theory with the strain and velocity gradient theory to capture both softening and stiffening size-dependent behavior of the nanorods. The viscoelastic behavior is modelled using the so-called Kelvin–Voigt viscoelastic damping model. Three length-scale parameters are incorporated in this newly combined theory, namely, a nonlocal, a strain gradient, and a velocity gradient parameter. The governing equation of motion and its boundary conditions for the vibration analysis of nanorods are derived by employing Hamilton’s principle. It is shown that the expressions of the classical stress and the stress gradient resultants are only defined for different values of the nonlocal and strain gradient parameters. The case where these are equal may seem to result in an inconsistency to the general equation of motion and the related non-classical boundary conditions. A rigorous investigation is conducted to prove that that the proposed solution is consistent with physics. Damped eigenvalue solutions are obtained both analytically and numerically using a Locally adaptive Differential Quadrature Method (LaDQM). Analytical results of linear free vibration response are obtained for various length-scales and compared with LaDQM numerical results. Journal Article Composite Structures 0263-8223 Torsional nanorod; Nonlocal strain and velocity gradient theory; Viscoelasticity; Kelvin–Voigt model; Torsional vibration 31 12 2017 2017-12-31 10.1016/j.compstruct.2017.12.002 COLLEGE NANME COLLEGE CODE Swansea University 2017-12-07T09:55:11.1454107 2017-12-07T09:24:14.4746333 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised S. El-Borgi 1 P. Rajendran 2 M.I. Friswell 3 M. Trabelssi 4 J.N. Reddy 5 Michael Friswell 6 0037347-07122017092653.pdf el-borgi2017.pdf 2017-12-07T09:26:53.6630000 Output 1135555 application/pdf Accepted Manuscript true 2018-12-06T00:00:00.0000000 false eng
title Torsional Vibration of Size-dependent Viscoelastic Rods using Nonlocal Strain and Velocity Gradient Theory
spellingShingle Torsional Vibration of Size-dependent Viscoelastic Rods using Nonlocal Strain and Velocity Gradient Theory
Michael Friswell
title_short Torsional Vibration of Size-dependent Viscoelastic Rods using Nonlocal Strain and Velocity Gradient Theory
title_full Torsional Vibration of Size-dependent Viscoelastic Rods using Nonlocal Strain and Velocity Gradient Theory
title_fullStr Torsional Vibration of Size-dependent Viscoelastic Rods using Nonlocal Strain and Velocity Gradient Theory
title_full_unstemmed Torsional Vibration of Size-dependent Viscoelastic Rods using Nonlocal Strain and Velocity Gradient Theory
title_sort Torsional Vibration of Size-dependent Viscoelastic Rods using Nonlocal Strain and Velocity Gradient Theory
author_id_str_mv 5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv 5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
author Michael Friswell
author2 S. El-Borgi
P. Rajendran
M.I. Friswell
M. Trabelssi
J.N. Reddy
Michael Friswell
format Journal article
container_title Composite Structures
publishDate 2017
institution Swansea University
issn 0263-8223
doi_str_mv 10.1016/j.compstruct.2017.12.002
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 In this paper the torsional vibration of size-dependent viscoelastic nanorods embedded in an elastic medium with different boundary conditions is investigated. The novelty of this study consists of combining the nonlocal theory with the strain and velocity gradient theory to capture both softening and stiffening size-dependent behavior of the nanorods. The viscoelastic behavior is modelled using the so-called Kelvin–Voigt viscoelastic damping model. Three length-scale parameters are incorporated in this newly combined theory, namely, a nonlocal, a strain gradient, and a velocity gradient parameter. The governing equation of motion and its boundary conditions for the vibration analysis of nanorods are derived by employing Hamilton’s principle. It is shown that the expressions of the classical stress and the stress gradient resultants are only defined for different values of the nonlocal and strain gradient parameters. The case where these are equal may seem to result in an inconsistency to the general equation of motion and the related non-classical boundary conditions. A rigorous investigation is conducted to prove that that the proposed solution is consistent with physics. Damped eigenvalue solutions are obtained both analytically and numerically using a Locally adaptive Differential Quadrature Method (LaDQM). Analytical results of linear free vibration response are obtained for various length-scales and compared with LaDQM numerical results.
published_date 2017-12-31T13:24:02Z
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score 11.080252

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