NONLINEAR DYNAMICS OF A FLUID-CONVEYING CANTILEVERED PIPE WITH AN INTERMEDIATE SPRING SUPPORT

In this paper, the nonlinear planar dynamics of a vertical cantilevered pipe conveying fluid are explored, in the presence of an intermediate spring support, by means of a two-degree-of-freedom Galerkin discretization of the flexible system. The stability of the original equilibrium is examined first, and the regions in the parameter space where the system is stable or loses stability by divergence or flutter are determined. Then, by examining the nonlinear equations of motion, the stability of the other fixed points that emerge with increasing flow velocity is studied, for various system parameters, revealing a very rich bifurcational behaviour. The nonlinear dynamics is also studied in the vicinity of various bifurcations by means of centre manifold theory and normal form reduction, as well by numerical simulation, in the vicinity of picthfork, Hopf and double degeneracy bifurcations; local and global behaviour are explored. Finally, the dynamics in the presence of harmonic perturbations in the flow is investigated numerically in the neighbourhood of the double degeneracy, where heteroclinic orbits arise, and chaotic regions are shown to exist. © 1993 by Academic Press, Inc.