Torsional Wave Propagation and Vibration of Circular Nanostructures Based on Nonlocal Elasticity Theory

Islam, Zakaria; Jia, Peng; Lim, C.W.

doi:10.1142/s1758825114500112

Cited by 51 publications

(12 citation statements)

References 58 publications

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“…However, the expressions for the classical stress and the stress gradient resultants given in non-dimensional form in Eqs. (36) and (37) are not dened whenμ 0 =l s . In this case, using Eqs.…”

Section: Equations Of Motion Of Size-dependent Rodsmentioning

confidence: 99%

“…Arda and Aydogdu [35] investigated analytically the static and free vibration response of a carbon nanotube (CNT) embedded in an elastic medium. Islam et al [36] obtained analytical solutions for the wave propagation problem of an innitely long torsional CNT rod. Li [37] developed two dierent nonlocal elasticity models to study the torsional vibration response of CNTs.…”

Section: Introductionmentioning

confidence: 99%

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

El-Borgi

Rajendran

Friswell

et al. 2018

Composite Structures

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In this paper the torsional vibration of size-dependent viscoelastic nanorods embedded in an elastic medium with dierent 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 stiening size-dependent behavior of the nanorods. The viscoelastic behavior is modelled using the so-called KelvinVoigt 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 dened for dierent 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 Dierential Quadrature Method (LaDQM). Analytical results of linear free vibration response are obtained for various length-scales and compared with LaDQM numerical results.

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Section: Equations Of Motion Of Size-dependent Rodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

El-Borgi

Rajendran

Friswell

et al. 2018

Composite Structures

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“…Gupta et al (2012a) pointed that in a homogeneous layer over a heterogeneous half-space torsional waves do exist. The commendable works by Islam et al (2014), Chattopadhyay et al (2012cChattopadhyay et al ( , 2013b, Kalyani et al (2008), Pal and Mandal (2014) in the study of seismic waves may be cited.…”

Section: Introductionmentioning

confidence: 99%

Effect of irregularity on torsional surface waves in an initially stressed anisotropic porous layer sandwiched between homogeneous and non-homogeneous half-space

et al. 2016

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The present paper is concerned with the propagation of torsional surface waves in an initially stressed anisotropic porous layer sandwiched between homogeneous and non-homogeneous half-space. We assume the quadratic inhomogeneity in rigidity and density in the lower half-space and irregularity is taken in the form of rectangle at the interface separating the layer from the lower half-space. The dispersion equation for torsional waves has been obtained in a closed form. Velocity equation is also obtained in the absence of irregularity. The study reveals that the presence of irregularity, initial stress, porosity, inhomogeneity and anisotropy factor in the dispersion equation approves the significant effect of these parameters in the propagation of torsional waves in porous medium. It has also been observed that for a uniform media, the velocity equation reduces to the classical result of Love wave.

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“…Islam et al studied the size effects on the torsional wave propagation properties of circular nanostructure. The effect of nanoscale on natural frequency for finite nanotube/nanorod is investigated based on the integral nonlocal constitutive relation and it was concluded that the torsional wave dispersion characteristics for a circular nanostructure was significantly different from the classical model [Islam et al, 2014].…”

Section: Introductionmentioning

confidence: 99%

Torsional Vibration of Cracked Nanobeam Based on Nonlocal Stress Theory with Various Boundary Conditions: An Analytical Study

Rahmani

Hosseini

Moghaddam

et al. 2015

Int. J. Appl. Mechanics

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In this paper, the torsional vibration of cracked nanobeam was studied based on a nonlocal elasticity theory. The location of the crack is simulated by a torsional spring which links segments of nanobeam together. Also, different boundary conditions, including clamped-free, clamped-clamped and clamped-torsional spring, were considered. Furthermore, a detailed parametric study was conducted to investigate the influence of crack location, nonlocal parameter, length of nanobeam, spring constant and end supports on the torsional vibration.

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Torsional Wave Propagation and Vibration of Circular Nanostructures Based on Nonlocal Elasticity Theory

Cited by 51 publications

References 58 publications

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

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

Effect of irregularity on torsional surface waves in an initially stressed anisotropic porous layer sandwiched between homogeneous and non-homogeneous half-space

Torsional Vibration of Cracked Nanobeam Based on Nonlocal Stress Theory with Various Boundary Conditions: An Analytical Study

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