Three-dimensional nonlinear dynamics of imperfectly supported pipes conveying fluid

This paper examines the effects of support imperfections on the dynamics and stability of pipes conveying fluid. The three-dimensional equations of motion for an imperfectly supported pipe conveying fluid are obtained using the extended Hamilton's principle. The support imperfection at the upstream end is modelled by cubic rotational springs. The partial differential equations governing the dynamics of the pipe are discretized in space via the Galerkin method. Numerical results including two-/three-dimensional motion maps and bifurcation diagrams show that the dynamics of the system is generally affected by the support imperfection. In particular, depending on the mass ratio and the level of imperfections, the critical flow velocity may be decreased or increased compared to the pipe with no support imperfections (i.e. cantilevered pipe). In addition, quasi-periodic oscillations may occur in the post-critical flow regime while they do not occur for cantilevered pipes. Also, the amplitude of oscillations are generally higher, and two-or three-dimensional motions may occur following a sequence different from that for cantilevered pipes.