Nonlinear forced vibrations of a slightly curved pipe conveying supercritical fluid

Vibrations of pipes caused by axially flowing fluids are very common in engineering applications. Due to material imperfections, guide misalignment, and improper supports, the installed pipes are prone to the initial curvature. Though small, the initial curvature can significantly change the dynamic characteristics of the slightly curved pipe system. This study investigates the non-linear forced vibration of a slightly curved pipe conveying supercritical fluid around the curved equilibrium, with the emphasis on amplitude-frequency responses around two asymmetric non-trivial equilibrium configurations. The governing equations for the forced vibration of a slightly curved pipe conveying supercritical fluids are derived using the generalized Hamilton principle. Then, the equations of motion are discretized into a set of coupled ordinary differential equations via the Galerkin truncation method and solved by the harmonic balance method combined with the pseudo-arc length technique. The approximate analytical results are verified by the numerical integration results. The obtained results demonstrate that the initial curvature has a significant effect on the dynamic characteristics of pipes conveying supercritical fluids, and can lead to significant differences in the dynamic response of the pipe system near different equilibrium configurations.