Dynamic Analysis of Single-Layered Graphene Nano-Ribbons (SLGNRs) with Variable Cross-Section Resting on Elastic Foundation

Abstract

AbstractThis article deals with free vibration of the variable cross-section (non-uniform) single-layered graphene nano-ribbons (SLGNRs) resting on Winkler elastic foundation using the Differential Quadrature Method (DQM). Here characteristic width of the cross-section is varied exponentially along the length of the nano-ribbon while the thickness of the cross section is kept constant. Euler–Bernoulli beam theory in conjunction with Eringen nonlocal elasticity theory is considered in this study. The numerical as well as graphical results are reported by using MATLAB codes developed by authors. Convergence of present method is explored and our results are compared with known results available in literature showing excellent agreement. Further, effects various parameters on frequency parameters are studied comprehensively.