Nonlinear analysis of the buckling and vibration of a rotating elasticum (Q1339458)

We investigate the static and dynamic behaviour of an elasticum which is clamped radially to the inside of a rotating ring and carries a mass at the free end. A nonlinear model for buckling and vibration of the structure in the plane of the ring is established, and a subsequent Galerkin procedure leads to a system of two first order ODEs, accessible to a bifurcation and phase plane analysis. More adequate results are obtained by a Poincaré-Lindstedt perturbation method. The analysis shows the existence of a supercritical bifurcation for any length of the elasticum. Finally, the case of out-of-plane buckling is shortly investigated, with the result that no buckling occurs for a sufficiently long elasticum.