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Supercritical and Subcritical Pitchfork Bifurcations in a Buckling Problem for a Graphene Sheet between 2 Rigid Substrates

Grdadolnik, Jake Matthew
http://rave.ohiolink.edu/etdc/view?acc_num=akron1618585173630134

Abstract Details

2021, Master of Science, University of Akron, Applied Mathematics.
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.
Dr. J. Patrick Wilber (Advisor)
Dr. Dmitry Golovaty (Committee Member)
Dr. Alexander Hoover (Committee Member)
102 p.
Applied Mathematics
bifurcation; graphene; asymptotics

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Citations

  • Grdadolnik, J. M. (2021). Supercritical and Subcritical Pitchfork Bifurcations in a Buckling Problem for a Graphene Sheet between 2 Rigid Substrates [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1618585173630134

    APA Style (7th edition)

  • Grdadolnik, Jake. Supercritical and Subcritical Pitchfork Bifurcations in a Buckling Problem for a Graphene Sheet between 2 Rigid Substrates. 2021. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1618585173630134.

    MLA Style (8th edition)

  • Grdadolnik, Jake. "Supercritical and Subcritical Pitchfork Bifurcations in a Buckling Problem for a Graphene Sheet between 2 Rigid Substrates." Master's thesis, University of Akron, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=akron1618585173630134

    Chicago Manual of Style (17th edition)

akron1618585173630134
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This open access ETD is published by University of Akron and OhioLINK.