Nonlinear dynamics of extensible fluid-conveying pipes, supported at both ends

In this paper, the post-divergence behaviour of extensible fluid-conveying pipes supported at both ends is studied using the weakly nonlinear equations of motion of Semler, Li and Paidoussis. The two coupled nonlinear partial differential equations are discretized via Galerkin's method and the resulting set of ordinary differential equations is solved either by Houbolt's finite difference method or via AUTO. Typically, the pipe is stable at its original static equilibrium position up to the flow velocity where it loses stability by static divergence via a supercritical pitchfork bifurcation. The amplitude of the resultant buckling increases with increasing flow, but no secondary instability occurs beyond the pitchfork bifurcation. The effects of the system parameters on pipe behaviour as well as the possibility of a subcritical pitchfork bifurcation have also been studied. (C) 2008 Elsevier Ltd. All rights reserved.