Bifurcations to divergence and flutter in flow-induced oscillations: A finite dimensional analysis

摘要: Abstract The behaviours of a pipe conveying fluid and loaded panel are studied from the viewpoint differentiable dynamics. Non-linear terms included it is shown how partial differential equation motion can be recast, by Galerkin's method modal truncation, in form an ordinary Euclidean n -space. This evolution then analysed qualitatively, attention being paid to bifurcations which occur as control parameters axial force flow velocity varied. Bifurcations fixed points when at least one eigenvalues linearized crosses imaginary axis complex plane. In this situation, centre manifold theory used extract low dimensional subsystem completely captures local bifurcational behaviour. Such essential models enable onset divergence flutter relatively simply inclusion non-linear permits global study post-bifurcational general approach illustrated analysis two mode some important omissions previous treatments linear undamped systems discussed.