Large-amplitude vibrations of cantilevered pipe conveying fluid with arbitrary initial configuration in three-dimensional sense

Up to now, three-dimensional modeling for investigating the nonlinear dynamics of cantilevered pipes conveying fluid with arbitrary initial configurations is still unsolved. This study aims to establish a universal three-dimensional nonlinear dynamic model based on absolute node coordinate formulation (ANCF) and the generalized Lagrange equation. Through this three-dimensional model, static equilibrium configuration and stability analysis for a straight-curved planar pipe system are extensively explored. The results demonstrate that the static equilibrium configuration obtained by the three-dimensional ANCF is limited to the in-plane and hence, it is consistent with that predicted by the two-dimensional model. In terms of stability analysis, two critical flow velocities for flutter instability, namely, the in-plane and out-of-plane critical flow velocities are obtained. It is found that the out-of-plane critical flow velocity is much lower than its counterpart of the in-plane. Regarding on nonlinear dynamics, vibration shapes, time history curves and phase portraits are offered to display rich dynamical behaviors of the pipe system, which are strongly dependent on in-plane and out-of-plane initial conditions. The proposed nonlinear dynamic model in this study can deal with large-amplitude vibrations of pipes conveying fluid with arbitrary initial configurations in the three-dimensional sense, which provides a new thought for the dynamical analysis of nonconservative fluid-conveying pipe system.