In this talk, I will present two simple models of symmetry-breaking bifurcations. The first model is that of a structure with geometric nonlinearity under static load. The bifurcation is associated with the loss of stability leading to the failure of the structure. The second model is that of a periodically forced nonlinear oscillator. The periodic forcing is of the type known as “parametric excitation.” Similar bifurcations in other physical systems are shown with analysis and experimental demonstrations.
I will also briefly introduce the graduate program in Mechanical and Aerospace Engineering Department of University of Missouri.