Modal Analysis of Graphene Sheet

Abstract

The flat graphene sheet is analysed to obtained the mode shape and natural frequency. The flat graphene sheet is analysed using the molecular mechanics approach as well as continuum mechanics’ approach. In this project work basically Euler Bernoulli theorem is used for analysis. Analytical solutions of natural frequencies are obtained for various aspect ratio. In this work boundary condition is taken as clamped either from one side or from both side for analysis purpose. Modal analysis of the graphene sheet is also carried out for square plates with different mass location. Also, impact of mass on graphene resonator is studied in the present work. The vibrational characteristics of graphene sheet is investigated for cantilever and fixed-fixed boundary conditions for obtaining different natural frequency and mode shapes.

In continuum mechanic approach zigzag and armchair results got same in both cantilever and double clamped beams. From this project work natural frequency decrease as length between two carbon bond increase in continuum mechanical approach. These results obtain in both without mass and with mass analysis for zigzag and armchair. In addition, in molecular mechanics approach once a frequency of analysis decreases with applied mass increase. In molecular mechanic approach zigzag and armchair results got same in without mass cantilever and without mass double clamped beams.