Free Vibration Analysis of Variable Cross-Section Single-Layered Graphene Nano-Ribbons (SLGNRs) Using Differential Quadrature Method

Subrat Kumar Jena,Snehashish Chakraverty

doi:10.3389/fbuil.2018.00063

Abstract

In this article, free vibration of variable cross-section (non-uniform) single layered graphene nano-ribbons (SLGNRs) is investigated by using Differential Quadrature Method (DQM). Here characteristic width of the cross section is assumed to vary exponentially along the length of the nano-ribbon while the thickness of the cross section is kept constant. Euler–Bernoulli beam theory is considered in conjunction with the nonlocal elasticity theory of Eringen. Step by step procedure is included and MATLAB code has been developed to obtain the numerical results for different scaling parameters as well as for four types of edge conditions. Convergence study is carried out to illustrate the efficiency of the method and obtained results are validated with known results in special cases showing good agreement. Further, numerical as well as graphical results are depicted to show the effects of nonuniform parameter, nonlocal parameter, aspect ratio and edge conditions on the frequency parameters.

Highlights

Application of nanomaterials has expanded in the area of physics, chemistry, engineering, and nanotechnology because of their special properties like mechanical, electrical and electronic (Dai et al, 1996)
For validation of present method, we consider a nanobeam with uniform cross-section viz. results of fundamental frequency parameter (λ) are compared with (Reddy, 2007; Aydogdu, 2009; Eltaher et al, 2013) for different nonlocal parameters (μ) which are presented in Tables 1, 2
With the increase in non-uniform parameter, frequency parameters decrease for all mode of CS edge whereas this is exactly opposite in case of CC nanoribbons

Summary

Introduction

Application of nanomaterials has expanded in the area of physics, chemistry, engineering, and nanotechnology because of their special properties like mechanical, electrical and electronic (Dai et al, 1996). To the best of the present authors’ knowledge, this article provides first time the frequency parameters of the variable crosssection (non-uniform) single-layered graphene nano-ribbons (SLGNRs) by using Differential Quadrature Method (DQM).

Results

Conclusion