A perturbation solution for non-linear vibration of uniformly curved pipes conveying fluid

The first-order non-linear interactions between the pipe structure and the flowing fluid are considered to formulate the governing equations of motion for the in-plane vibration of a circular-arc pipe containing flowing fluid. The forces and moments induced in a pipe element by the flowing fluid are analyzed as functions of the instantaneous local curvature of the pipe. The flow field is assumed to be one-dimensional, incompressible and of uniform flow, and to remain independent of pipe motion. For a fixed-end circular-arc pipe with arbitrary arc angle, the non-linear governing equations are solved by the method of multiple scales in conjunction with the Bubnov-Galerkin method. The non-linear solutions indicate that the vibrational behavior of the system can differ substantially from that predicted by a linear analysis.