Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method

It is well recognized that size dependency of materials characteristics, i.e. size-effect, often plays a significant role in the performance of nano-structures. Herein, strain gradient continuum theory is employed to investigate the size dependent pull-in instability of beam-type nano-electromechanical systems (NEMS). Two most common types of NEMS i.e. nano-bridge and nano-cantilever are considered. Effects of electrostatic field and dispersion forces i.e. Casimir and van der Waals (vdW) attractions have been considered in the nonlinear governing equations of the systems. Two different solution methods including numerical and Rayleigh-Ritz have been employed to solve the constitutive differential equations of the system. Effect of dispersion forces, the size dependency and the importance of coupling between them on the instability performance are discussed.

Section: Using Various Approachesmentioning

confidence: 99%

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Koochi

Sedighi

Abadyan

2014

“…The scale coefficients are assumed as Duan and Wang (2007) presented the constitutive relations of nonlocal elasticity theory for application in the analysis of circular graphene sheet. Recently, these values for the nonlocal parameter are used by many researchers (Farajpour et al 2011b;Danesh et al 2012;Farajpour et al 2012;Mohammadi et al 2013b). Properties of the orthotropic graphene sheet in this paper are considered same as mentioned in the reference .…”

Section: Validation Of Present Resultsmentioning

confidence: 99%

Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium

Mohammadi

Moradi

Ghayour

et al. 2014

In this paper, the effect of the temperature change on the vibration frequency of mono-layer graphene sheet embedded in an elastic medium are studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets. Using Levy and Navier solutions, analytical frequency equations for single-layered graphene sheets are obtained. Using Levy solution, the frequency equation and mode shapes of orthotropic rectangular nanoplate are considered for three cases of boundary conditions. The obtained results are subsequently compared with valid result reported in the literature. The effects of the small scale, temperature change, different boundary conditions, Winkler and Pasternak foundations, material properties and aspect ratios on natural frequencies are investigated. It has been shown that the non-dimensional frequency decreases with increasing temperature change. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the nanoplates.

“…There are various modified classical continuum theories which capture size effects such as couple stress theory (Zhou and Li 2001), strain gradient elasticity theory (Fleck and Hutchinson 1997;Akgöz and Civalek 2011), modified couple stress theory (Yang et al 2002;Akgöz and Civalek 2012) and nonlocal elasticity theory (Eringen and Edelen 1972;Eringen 1983). Among all size-dependent theories, the nonlocal elasticity theory has been commonly applied in the theoretical investigations of structures at small scale (Sudak 2003;Reddy 2007;Reddy and Pang 2008;Heireche et al 2008;Aydogdu 2009;Farajpour et al 2011a;Moosavi et al 2011;Danesh et al 2012;Mohammadi et al 2013). To overcome the drawbacks of local elasticity theory, Eringen introduced the nonlocal continuum mechanics in 1972.…”

Section: Introductionmentioning

confidence: 99%

A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory

Asemi

Mohammadi

Farajpour

2014

Recently, graphene sheets have shown significant potential for environmental engineering applications such as wastewater treatment. In the present work, the posbuckling response of orthotropic single-layered graphene sheet (SLGS) is investigated in a closedform analytical manner using the nonlocal theory of Eringen. Two opposite edges of the plate are subjected to normal stresses. The nonlocality and geometric nonlinearity are taken into consideration, which arises from the nanosized effects and mid-plane stretching, respectively. Nonlinear governing differential equations (nonlocal compatibility and equilibrium equations) are derived and presented for the aforementioned study. Galerkin method is used to solve the governing equations for simply supported boundary conditions. It is shown that the nonlocal effect plays a significant role in the nonlinear stability behavior of orthotropic nanoplates. Unlike first and second postbuckling modes, nonlocal effects decrease with the increase of lateral deflection at higher postbuckling modes. It is also observed that the nonlocality and nonlinearity is more pronounced for higher postbuckling modes.