Exact solution for the vibrations of an arbitrary plane curved pipe conveying fluid

In this paper, the response of an arbitrary plane curved pipe subjected to fluid flow is investigated analytically. The pipe cross-section is restricted to have a certain symmetry so that the pipe stays in its plane while under the effects of the fluid motion. Influence of fluid motion is considered in three terms. One is the inertial force due to the fluid mass which is assumed to be distributed uniformly along the length of the pipe. The inertial force naturally varies since the pipe has a variable curvature. The second one is due to the weight of the fluid and the last one is the friction force between the fluid and the pipe. These forces also vary along the length of the pipe. The general equations are given for any plane curved pipe and solved for a specific example using the method of power series. The equations are non-dimensionalised and the dynamic response of the pipe is plotted for a range of mass ratios between the fluid and the pipe material. (c) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinhei