Local bifurcations in the motion of spinning discs

The nonlinear equations of motion governing the dynamics of a spinning disc are examined. The flexible disc is assumed to be clamped near the center, free at the outer edge, and rotates with a time-varying spin rate. A 2-DOF system of ordinary differential equations is obtained which governs the dynamic variation of the amplitudes of the traveling waves associated with the dominant mode of the transverse motion. The equations are averaged using the method of averaging, and the corresponding local dynamics is examined in paper. In this paper, stability boundaries are obtained, along with the existence of single- and mixed-mode equilibrium solutions. The local bifurcation behavior associated with codimension-one and -two bifurcation varieties are examined using conventional techniques as well as ideas of symmetry analysis.