Free Vibration Analysis of Variable Cross-Section Single-Layered Graphene Nano-Ribbons (SLGNRs) Using Differential Quadrature Method - Jena, Subrat Kumar; Chakraverty, Snehashish (Frontiers in Built Environment, 2018)
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.