Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity

Ansari, R.; Arash, Behrouz; Rouhi, H.

doi:10.1016/j.compstruct.2011.04.006

Cited by 146 publications

(37 citation statements)

References 59 publications

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“…The use of nonlocal elasticity in the mechanical analysis of nanostructures is extensively reported in the literature. 13,[16][17][18][19][20][21][22][23][24][25][26][27][28][29] Magnetic field effects in nanotubes and nanoplates (graphene) are important for exciting potential applications in nanotechnology such as in nanoelectromechanical systems (NEMS), microelectromechanical systems (MEMS), nanosensors, spintronics, and nanocomposites. In recent years, research interest has grown on studying the magnetic properties of nanotubes and behaviour of nanotubes within a magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal elasticity based magnetic field affected vibration response of double single-walled carbon nanotube systems

Murmu

McCarthy

Adhikari

2012

Journal of Applied Physics

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The behaviour of carbon nanotubes in a magnetic field has attracted considerable attention in the scientific community. This paper reports the effects of a longitudinal magnetic field on the vibration of a magnetically sensitive double single-walled carbon nanotube system (DSWNTS). The two nanotubes of the DSWNTS are coupled by an elastic medium. The dynamical equations of the DSWNTS are derived using nonlocal elasticity theory. The two nanotubes are defined as an equivalent nonlocal double-Euler-Bernoulli beam system. Governing equations for nonlocal bending-vibration of the DSWNTS under a longitudinal magnetic field are derived considering the Lorentz magnetic force obtained from Maxwell's relation. An analytical method is proposed to obtain nonlocal natural frequencies of the DSWNTS. The influence of (i) nanoscale effects and (ii) strength of longitudinal magnetic field on the synchronous and asynchronous vibration phase of the DSWNTS is examined. Nonlocal effects with and without the effect of magnetic field are illustrated. Results reveal the difference (quantitatively) by which the longitudinal magnetic field affects the nonlocal frequency in the synchronous and asynchronous vibration modes of a DSWNTS. V C 2012 American Institute of Physics. [http://dx

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Section: Introductionmentioning

confidence: 99%

Nonlocal elasticity based magnetic field affected vibration response of double single-walled carbon nanotube systems

Murmu

McCarthy

Adhikari

2012

Journal of Applied Physics

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“…Numerous studies investigated the linear free and vibration and wave propagation of CNTs [6][7][8][9]. Thongyothee et al [6] investigated the free vibration problem of CNTs including the effect of nonlocal elasticity to study the effect of their chirality and various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Thongyothee et al [6] investigated the free vibration problem of CNTs including the effect of nonlocal elasticity to study the effect of their chirality and various boundary conditions. Ansari et al [7] investigated the free vibration of double-walled carbon nanotubes (DWCNTs) using the Eringen's nonlocal elastic model along with the Donnell shell model. They accounted for the van der Waals forces between the inner and outer nanotubes.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal modeling of a Carbon Nanotube actuated by an electrostatic force

2016

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Abstract. Carbon nanotubes (CNTs) are promising mechanical structures at the nano-scale which have attracted increasing attention due to their amazing mechanical, chemical, thermal, and electrical properties. To take into account size dependence of such small sized structures, the use of nonlocal continuum theory is proposed where intrinsic length scales is taken into account. Based on the Eringen theory, a nonlinear nonlocal model of a clamped-clamped CNT is developed in this study. Static and free vibration responses are simulated and analyzed. The main objective of this work is to study the influence of CNT size and length scale parameter on the static and free vibration response to better understand their effect on the general behavior of the CNT. It has been found that the nonlocal effect can largely influence the performance of the CNT and change qualitatively its nonlinear response.

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“…All of these models were based on Kirchhoff plate theory 8,12,[14][15][16][17][18][19][22][23][24][25][26][27] , Mindlin plate theory 9,11,20,[28][29][30] , and Reddy plate theory 10,13,31 . It should be noted that the Kirchhoff plate theory (KPT) is only applicable for thin plates.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the nonlocal elasticity theory, a number of paper have been published in the last four years, attempting to develop nonlocal plate models and apply them to analyze the bending [8][9][10][11][12] , buckling [13][14][15][16][17][18][19][20][21] , and vibration [22][23][24][25][26][27][28][29][30][31] responses of nanoplates. All of these models were based on Kirchhoff plate theory 8,12,[14][15][16][17][18][19][22][23][24][25][26][27] , Mindlin plate theory 9,11,20,[28][29][30] , and Reddy plate theory 10,13,31 .…”

Section: Introductionmentioning

confidence: 99%

A nonlocal sinusoidal plate model for micro/nanoscale plates

Thai

Nguyen

et al. 2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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A nonlocal sinusoidal plate model for micro/nanoscale plates is developed based on Eringen's nonlocal elasticity theory and sinusoidal shear deformation plate theory. The small scale effect is considered in the former theory while the transverse shear deformation effect is included in the latter theory. The proposed model accounts for sinusoidal variations of transverse shear strains through the thickness of the plate, and satisfies the stress-free boundary conditions on the plate surfaces, thus a shear correction factor is not required. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions for bending, buckling, and vibration of simply supported plates are presented, and the obtained results are compared with the existing solutions. The effects of small scale and shear deformation on the responses of the micro/nanoscale plates are investigated.

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Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity

Cited by 146 publications

References 59 publications

Nonlocal elasticity based magnetic field affected vibration response of double single-walled carbon nanotube systems

Nonlocal elasticity based magnetic field affected vibration response of double single-walled carbon nanotube systems

Nonlocal modeling of a Carbon Nanotube actuated by an electrostatic force

A nonlocal sinusoidal plate model for micro/nanoscale plates

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