Geometrically exact post-buckling and post-flutter of standing cantilevered pipe conveying fluid

Abstract

Although the nonlinear dynamics of hanging cantilevered pipe conveying fluid have been extensively scrutinized, a few investigations exist about the nonlinear behavior of standing one. Hence, the objective of this study is to examine the geometrically exact nonlinear static and dynamic responses of standing cantilevered pipe conveying fluid. The geometrically exact rotation-based model, along with the shooting method and Galerkin technique is applied to assess the nonlinear static behavior of system and its stability characteristics. Moreover, to compute the nonlinear dynamics of system, the geometrically exact quaternion-based model, together with the Galerkin technique is employed. It is revealed that the system may undergo buckling via a supercritical or subcritical pitchfork bifurcation depending on the gravity parameter, which may give rise to extremely large-amplitude responses. The system may also experience flutter instability via a supercritical Hopf bifurcation, which brings about self-excited periodic oscillations. The generic behavior of system for a specific range of the gravity parameter is investigated for four distinct scenarios depending on the gravity parameter and mass ratio, which only one of them is similar to that comes to pass for the hanging case.