College
Buchtel College of Arts and Sciences
Date of Last Revision
2023-05-04 07:14:37
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
Recommended Citation
Grdadolnik, Jake, "Supercritical and Subcritical Pitchfork Bifurcations in a Buckling Problem for a Graphene Sheet Between two Rigid Substrates" (2021). Williams Honors College, Honors Research Projects. 1269.
https://ideaexchange.uakron.edu/honors_research_projects/1269
Included in
Ordinary Differential Equations and Applied Dynamics Commons, Other Applied Mathematics Commons