Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis

Holmes, P. J. and J. E. Marsden

Automatica, 14, (1978), 367-384

Abstract:

We outline the application of center manifold theory to a problem of flow-induced vibrations in which bifurcations occur under the action of control parameters. Using these techniques, the governing nonlinear partial differential equation (PDE) can be replaced locally by a vector field on a low dimensional manifold. The bifurcations thus detected, including "global" bifurcations, yield a useful description of the qualitative dynamics of the original PDE.