Size dependent dynamic analysis of nanoplates

Assadi, Abbas; Farshi, Behrooz; Alinia-ziazi, Ali

doi:10.1063/1.3437041

Cited by 68 publications

(19 citation statements)

References 17 publications

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“…Both residual surface stress and surface elasticity effects have been incorporated in the continuum mechanical modeling of nanostructures [18,19] by using the surface elastic model provided by Gurtin and Murdoch [20] and the generalized Young-Laplace equation. The surface elastic model and generalized Young-Laplace equation have been wieldy application in investigating the influence of surface effects on the mechanical responses of nanostructures, such as nanobeams [21][22][23][24] and nanoplates [25][26][27]. Recently, some researchers investigated the pull-in instability of nano-switches with consideration of surface effects, and found that surface effects made a major contribution to the pull-in instability of electrostatically actuated nanobeams [9,[28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

A general model for nano-cantilever switches with consideration of surface effects and nonlinear curvature

Wang

2015

Physica E: Low-dimensional Systems and Nanostructures

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Section: Introductionmentioning

confidence: 99%

A general model for nano-cantilever switches with consideration of surface effects and nonlinear curvature

Wang

2015

Physica E: Low-dimensional Systems and Nanostructures

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“…Based on the linear surface elasticity theory developed by Gurtin and Murdoch,11 the size-dependent properties of nanostructures originating from the surface effects have been widely investigated by the modified continuum models from both static and dynamic perspectives. [12][13][14][15][16][17][18][19][20] Recently, a more comprehensive and accurate model with the consideration of the effects of surface stress and surface elasticity was developed by Olsson and Park 21 to calculate the flexural rigidity of nanowires from three-dimensional elasticity theory. The distinguished feature of that model lies in the fact that it incorporates the heterogeneous nature of elasticity across the nanowire cross section.…”

Section: Introductionmentioning

confidence: 99%

Size effects on electromechanical coupling fields of a bending piezoelectric nanoplate due to surface effects and flexoelectricity

Zhang

Jiang

2014

Journal of Applied Physics

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Due to large surface to volume ratio and manifest strain gradients typically present in nanostructures, it is essential to incorporate both surface effects and flexoelectricity in studying the size-dependent electromechanical coupling behaviors of piezoelectric materials at the nano-scale. In the current work, a modified Kirchhoff plate model with the consideration of residual surface stress, surface elasticity, surface piezoelectricity, and flexoelectricity is developed to investigate the electroelastic responses and vibrational behaviors of a bending piezoelectric nanoplate (PNP). The governing equations and the corresponding boundary conditions accounting for both the surface effects and the flexoelectricity are derived by the variational principle. Ritz approximate solutions of the static bending and the free vibration indicate that these nano-scale features are more prominent for thinner plates with smaller thickness. The simulation results also reveal that the influence of the flexoelectricity and the surface effects upon the bending behaviors of the PNP depends on the applied electrical loading and the plate dimensions. Moreover, it is also observed that the frequency tuning of PNP-based nanoresonators by adjusting applied electrical load can be modified by both the flexoelectricity and the surface effects. The current work is expected to provide increased understanding on the theoretical basis for the design and applications of PNP-based nanodevices. V C 2014 AIP Publishing LLC. [http://dx.

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“…Lu et al [40] followed this approach to derive the generalized differential equations of static, dynamic, and stability of ultra thin films including surface effects. Assadi et al [41] modified the laminated plate theory to include the effects of surface properties and temperature on the dynamic behavior of rectangular nanoplates. Farshi et al [37] studied the size-dependent flexural vibration of nanotubes with consideration of surface effects using a modified beam theory.…”

Section: Surface Effects On Flexural Wave Propagation In Nanobeamsmentioning

confidence: 99%

Wave Propagation in 1D-Nanostructures: Nanobeams

Gopalakrishnan

Narendar

2013

Wave Propagation in Nanostructures

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Nanobeams are those which undergo flexural or transverse motion in lateral directions. The cross-sections of such nanostructures could be rectangular or circular. Some of the nano thin films, which find applications in Nano Electro Mechanical Systems (NEMS) is normally idealized as nanobeam with rectangular cross-section, while SWCNT undergoing transverse vibration, are normally idealized as nanobeams with circular cross-section. There are two different theories that describe the motion of beams. The first is the Euler-Bernoulli beam theory, which is also called the elementary beam theory. In this theory, rotation of the cross-section is derived from the transverse motion and the plane sections are assumed plane before and after bending. The second theory is called the Timoshenko beam theory, which is also called the First-order shear deformation Theory (FSDT). In this theory, the rotation of the cross-section is considered as independent motion and not derived from transverse deformation. Due to shear deformation effects, the plane sections do not remain plane after the bending of the section. The main aim of this chapter is to study the effect of nonlocal scale parameter on the transverse wave propagation in nanobeams. As before, we will use spectral analysis, outlined in Chap. 2, to perform this study. Some of the analysis performed in this chapter are the following:

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Size dependent dynamic analysis of nanoplates

Abstract: Articles you may be interested inSize effects on electromechanical coupling fields of a bending piezoelectric nanoplate due to surface effects and flexoelectricity

Cited by 68 publications

References 17 publications

A general model for nano-cantilever switches with consideration of surface effects and nonlinear curvature

A general model for nano-cantilever switches with consideration of surface effects and nonlinear curvature

Size effects on electromechanical coupling fields of a bending piezoelectric nanoplate due to surface effects and flexoelectricity

Wave Propagation in 1D-Nanostructures: Nanobeams

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