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

Abstract

Although the nonlinear dynamics of hanging cantilevered pipes conveying fluid have been extensively scrutinized, there is limited research on the nonlinear behavior of standing ones. Hence, the objective of this study is to examine the geometrically exact nonlinear static and dynamic responses of cantilevered pipes conveying fluid in a standing position. The geometrically exact rotation-based model, combined with the shooting method and the 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 through either 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 due to 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 across four distinct scenarios, which vary based on the gravity parameter and mass ratio. Notably, only one of these scenarios is analogous to the situation that comes to pass for the hanging case.