Bifurcation and stability analysis of static equilibrium configuration of curved pipe conveying fluid

Abstract

We present bifurcation and stability analysis of static equilibrium configurations of a clamped-clamped curved pipe conveying fluid in this paper. To capture large deformations of the pipe, this pipe is modeled with an absolute nodal coordinate formulation (ANCF). A technique of parameter continuation is used to solve the equilibria of the governing equation of this pipe system. Effects of external force, flow velocity and arc angle on the nonlinear responses of the curved pipe conveying fluid are discussed in detail. In the case of the curved pipe without any external loadings, the system admits two stable equilibria and an unstable equilibrium when the flow velocity exceeds a critical value on which a saddle-node bifurcation occurs. This critical flow velocity that characterizes the onset of the multistability is increased as the arc angle of the pipe increases. In addition, a pitchfork bifurcation occurs along the branch of the unstable equilibria. When the curved pipe is subjected to a concentrated force at its midpoint, the pipe deforms only in symmetrical mode shapes and undergoes a snap-through buckling under variations in the concentrated force. In contrast, when the curved pipe is subject to a gravity and the arc angle of the pipe exceeds a critical value, a pitchfork bifurcation buckling is observed under variations in the gravity. Along the secondary branch of this pitchfork bifurcation, equilibria in asymmetric mode shapes are found. Finally, effects of system parameters on these critical buckling loads are carefully explored.