A nonlocal finite element method for torsional statics and dynamics of circular nanostructures

Lim, C.W.; Islam, Md. Zahurul; Zhang, G.

doi:10.1016/j.ijmecsci.2015.03.002

Cited by 32 publications

(17 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 and 2 illustrate the variation of the rst three frequencies and damping ratios as a function of ∆µl s =l s −μ 0 for CF-CF/FS-FS and CF-FS boundary conditions, respectively. Whenμ 0 is close tol s , the solution is computed based the equation of motion (33). For the particular case whereμ 0 =l s , the solution is computed based on the equation of motion (46) and is shown with the symbol • in Figs.…”

Section: Equations Of Motion Of Size-dependent Rodsmentioning

confidence: 99%

“…Lim et al [32] obtained analytical solutions for the free torsional vibration of nanorods and concluded that the nonlocal parameter induces higher torsional stiness which in turn increases the vibration frequency. In another study, Lim et al [33] utilized the nite element method and the integral form of the nonlocal theory to study the torsional static and dynamic response of circular nanostructures. Demir and Civalek [34] developed a nite element model to investigate the torsional and axial vibration response of a microtube.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

El-Borgi

Rajendran

Friswell

et al. 2018

Composite Structures

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…For example, Xu and Deng 16 presented the nonlocal and surface effects in the adsorption-induced resonance of nanobeams using the nonlocal theory and they also revealed the influence of the adsorption density. To solve the derived integral nonlocal governing equation, Lim et al 17 developed a new nonlocal finite element method to investigate the torsional statics and dynamics of circular nanotubes/nanorods subjected to concentrated and distributed torques, respectively. Yang et al 18 investigated the nonlinear coupling effects of thermal loading and surface stress on pull-in instability of electrically actuated circular nanoplates based on the nonlocal theory.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Axially Moving Functionally Graded Nanoplates Based on the Nonlocal Strain Gradient Theory

Li¹,

Wang²,

Luo³

et al. 2020

The International Journal of Acoustics and Vibration

View full text Add to dashboard Cite

Using the nonlocal strain gradient theory, we explore vibration behaviours of initially bidirectional tensioned functionally graded nanoplates with axial speed. The governing equation of motion can be obtained based on the differential type of nonlocal strain gradient constitutive relation, which characters the dynamics of nanostructures containing kinematic relation. The simply supported boundary constraints on four sides are considered and subsequently the numerical results are determined. It shows that natural frequencies of axially moving nanoplates decrease when increasing the axial speed and the nonlocal parameter. Hence the nonlocal and kinematic factors cause the natural frequencies to decrease or, weaken the equivalent bending rigidity. On the other hand, natural frequencies increase with an increase in the axial tension and material characteristic scale. Hence the strain gradient and tensile stress factors cause the natural frequencies to increase or, strengthen the equivalent bending rigidity. In addition, the natural frequencies get higher with a larger aspect ratio of the functionally graded nanoplate. The larger one between the nonlocal parameter and the material characteristic scale plays a dominant role in the softening and stiffening mechanisms of the nonlocal strain gradient effect. In case of the same magnitude of the nonlocal parameter and the material characteristic scale, the softening and hardening phenomena disappear. The equivalent bending rigidity neither increases nor decreases in such a situation, and its value degenerates to the classical one.

show abstract

“…Analysis and assessment of size-effects in nano-structures is currently a topic of major interest in the scientific community [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Torsional deformations can frequently occur in structural elements of NEMS, and therefore, various size-dependent elasticity theories have been exploited in literature [21][22][23][24][25][26][27][28][29][30][31][32], as comprehensively discussed in review contributions [33,34].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

et al. 2019

View full text Add to dashboard Cite

Nonlocal strain gradient continuum mechanics is a methodology widely employed in literature to assess size effects in nanostructures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems.In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation.The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest.Both elastostatic torsional responses and torsional free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviours of structures involved in modern Nano-Electro-Mechanical-Systems (NEMS). KeywordsTorsion; nano-beams; nonlocal strain gradient model; strain gradient elasticity; integral elasticity; size effects; analytical modelling; NEMS. d J J dx J J dx J

show abstract

A nonlocal finite element method for torsional statics and dynamics of circular nanostructures

Cited by 32 publications

References 48 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

Free Vibration of Axially Moving Functionally Graded Nanoplates Based on the Nonlocal Strain Gradient Theory

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

Contact Info

Product

Resources

About