A great deal of study has been done on the dynamics of straight pipes conveying fluid. In contrast, only a few studies have been devoted to the dynamics of curved pipe conveying fluid. In this paper, a theoretical and experimental investigation was conducted into out-of-plane vibration of a curved pipe for the case that the fluid flow contains a small time-dependent harmonic component. The nonlinear out-of plane vibrations of a curved pipe, which is hanging horizontally and is supported at both ends, are examined when the frequency of the pulsating fluid flow is near twice the fundamental natural frequency of out-of-plane vibration. The main purpose of this paper is to investigate the nonlinear interactions between the in-plane and the out-of-plane vibrations analytically and experimentally. The partial differential equations of out-of-plane motions are reduced into a set of ordinary differential equations, which govern the amplitude and phase of out-of-plane vibration, using the method of Lyapnov-Schmidt reduction. It is clarified that the excitation of the in-plane vibration produces significant responses in the out-of-plane vibrations. Finally, the experiments were conducted with a silicon rubber pipe conveying water. The typical features of out-of-plane vibration are confirmed qualitatively by experiment.

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