College

Buchtel College of Arts and Sciences

Date of Last Revision

2021-04-25 16:06:08

Major

Applied Mathematics

Honors Course

Master's Thesis

Number of Credits

3

Degree Name

Bachelor of Science

Date of Expected Graduation

Spring 2021

Abstract

In this paper we study a model of the buckling of a sheet of graphene between two rigid substrates. We seek to understand the buckling of the sheet as the substrate separation is varied with a fixed load on each end of the sheet. We write down the expression for total energy of the system and from it derive a 2-point nonlinear boundary-value problem whose solutions are equilibrium configurations of the sheet. We cannot get an explicit solution. Instead, we perform a bifurcation analysis by using asymptotics to approximate solutions on the bifurcating branches near the bifurcation points. The bifurcating parameter is the separation between the rigid substrates. We find that the bifurcations are supercritical or subcritical pitchfork bifurcations. We perform a parametric study to understand how the nature of the bifurcations is influenced by other physical parameters in the problem. This leads to insight on the orientation of the buckled graphene sheet depending on substrate separation.

Research Sponsor

J. Patrick Wilber

First Reader

Alexander Hoover

Second Reader

Dmitry Golovaty

Honors Faculty Advisor

Curtis B. Clemons

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