Nonlocal plate model for free vibrations of single-layered graphene sheets

Ansari, R.; Sahmani, S.; Arash, Behrouz

doi:10.1016/j.physleta.2010.10.028

Cited by 381 publications

(138 citation statements)

References 40 publications

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“…Ansari et al [51], and S.C. Pradhan et al [52] investigated the vibration analysis of SLGS by incorporating Eringen's nonlocal elasticity equation into the classical plate theory and the solutions are computed using a special numerical technique named the generalized differential quadrature (GDQ) method. B. Arash et al [53] studied wave propagation in graphene sheets using the nonlocal finite element (FE) method.…”

Section: Vibrationmentioning

confidence: 99%

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

Liew

Zhang

2017

Journal of Modeling in Mechanics and Materials

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Abstract:This paper presents a literature review of recent research studies on the applications of nonlocal elasticity theory in the modeling and simulation of graphene sheets (GSs). The history, development and excellent properties of GSs are introduced. The details of nonlocal elasticity theory are also presented. A systematic introduction to the application of nonlocal elasticity on linear modeling and nonlinear modeling for single-layer graphene sheets (SLGSs) and multilayered graphene sheets (MLGSs) is also provided. The necessity of determining mechanical parameters and nonlocal parameters is discussed. Recommendations for future work are particularly presented. This work is intended to review the development of GSs, give an introduction to the research studies on nonlocal elasticity theory in the modeling of GSs, and provide recommendations for future research.

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Section: Vibrationmentioning

confidence: 99%

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

Liew

Zhang

2017

Journal of Modeling in Mechanics and Materials

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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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“…More specifically, due to a complete lack of results about corrugated nanoplates, we here compare our results with those ones obtained for flat nanosheets. Among a large variety of possible approaches adopted in literature for the vibration study of graphene plates, the molecular dynamics and the non-local GDQ-based FSDT, as proposed in [36], have been here selected as efficient and accurate methods for comparative purposes.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Effect of Sinusoidal Corrugated Geometries on the Vibrational Response of Viscoelastic Nanoplates

2018

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Abstract:The vibrational behavior of viscoelastic nanoplates with a corrugated geometry is a key topic of practical interest. This problem is addressed here for wrinkled nanoplates with small corrugations related to incorrect manufacturing. To this end, a new One-Variable First-order Shear Deformation plate Theory (OVFSDT) is proposed in a combined form with a non-local strain gradient theory. The Kelvin-Voigt model is employed to describe the viscoelastic behavior of the nanoplate, whereby the frequency equations are solved numerically according to Navier's approach, for simply-supported nanostructures. A comparative evaluation between the proposed theory and other approaches in the literature is successfully performed. It follows a large parametric study of the vibration response for varying geometry corrugations and non-local parameters.

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Nonlocal plate model for free vibrations of single-layered graphene sheets

Cited by 381 publications

References 40 publications

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

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

Effect of Sinusoidal Corrugated Geometries on the Vibrational Response of Viscoelastic Nanoplates

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