Torsional vibration of size-dependent viscoelastic rods using nonlocal strain and velocity gradient theory

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

Research output: Contribution to journalArticle

20 Citations (Scopus)

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 and stiffening size-dependent behavior of the nanorods. The viscoelastic behavior is modeled 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 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.

Original languageEnglish
Pages (from-to)274-292
Number of pages19
JournalComposite Structures
Volume186
DOIs
Publication statusPublished - 15 Feb 2018

Fingerprint

Nanorods
Boundary conditions
Equations of motion
Vibration analysis
Numerical methods
Physics
Damping

Keywords

  • Kelvin–Voigt model
  • Nonlocal strain and velocity gradient theory
  • Torsional nanorod
  • Torsional vibration
  • Viscoelasticity

ASJC Scopus subject areas

  • Ceramics and Composites
  • Civil and Structural Engineering

Cite this

Torsional vibration of size-dependent viscoelastic rods using nonlocal strain and velocity gradient theory. / El-Borgi, Sami; Rajendran, P.; Friswell, M. I.; Trabelssi, M.; Reddy, J. N.

In: Composite Structures, Vol. 186, 15.02.2018, p. 274-292.

Research output: Contribution to journalArticle

El-Borgi, Sami ; Rajendran, P. ; Friswell, M. I. ; Trabelssi, M. ; Reddy, J. N. / Torsional vibration of size-dependent viscoelastic rods using nonlocal strain and velocity gradient theory. In: Composite Structures. 2018 ; Vol. 186. pp. 274-292.
@article{35ee316afec14df8b80265ee6ed0f08a,
title = "Torsional vibration of size-dependent viscoelastic rods using nonlocal strain and velocity gradient theory",
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 and stiffening size-dependent behavior of the nanorods. The viscoelastic behavior is modeled 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 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.",
keywords = "Kelvin–Voigt model, Nonlocal strain and velocity gradient theory, Torsional nanorod, Torsional vibration, Viscoelasticity",
author = "Sami El-Borgi and P. Rajendran and Friswell, {M. I.} and M. Trabelssi and Reddy, {J. N.}",
year = "2018",
month = "2",
day = "15",
doi = "10.1016/j.compstruct.2017.12.002",
language = "English",
volume = "186",
pages = "274--292",
journal = "Composite Structures",
issn = "0263-8223",
publisher = "Elsevier BV",

}

TY - JOUR

T1 - Torsional vibration of size-dependent viscoelastic rods using nonlocal strain and velocity gradient theory

AU - El-Borgi, Sami

AU - Rajendran, P.

AU - Friswell, M. I.

AU - Trabelssi, M.

AU - Reddy, J. N.

PY - 2018/2/15

Y1 - 2018/2/15

N2 - 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 modeled 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 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.

AB - 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 modeled 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 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.

KW - Kelvin–Voigt model

KW - Nonlocal strain and velocity gradient theory

KW - Torsional nanorod

KW - Torsional vibration

KW - Viscoelasticity

UR - http://www.scopus.com/inward/record.url?scp=85038006676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038006676&partnerID=8YFLogxK

U2 - 10.1016/j.compstruct.2017.12.002

DO - 10.1016/j.compstruct.2017.12.002

M3 - Article

VL - 186

SP - 274

EP - 292

JO - Composite Structures

JF - Composite Structures

SN - 0263-8223

ER -