Nonlinear Out-of-Plane Vibration of a Curved Pipe Due to Pulsating Flow

A great deal of study has been done on the dynamics of straight pipes conveying fluid. Relatively less effort has been directed towards the examination of the dynamics of curved pipes. In this paper, out-of-plane vibrations of a curved pipe due to the pulsating fluid flow are examined. The pipe is hanging horizontally and is supported at both ends. The main purpose of this paper is to investigate the nonlinear interaction between the in-plane and the out-of-plane vibrations analytically and experimentally. First, from the physical discussion of the equation for the spatial motion, the parametric excitation of the out-of-plane vibration and the forced excitation of the in-plane vibration most likely occur by the presence of pulsating fluid flow. Second, the complex amplitude equation of the out-of-plane pipe vibration in the case of the principal parametric resonance, is derived. The out-of-plane vibration is excited by the pulsating fluid flow and the nonlinear interaction between in-plane and out-of-plane vibrations. From the nonlinear analysis, it was clarified that the nonlinear interaction between in-plane and out-of-plane vibrations greatly affects the out-of-plane vibration. Third, the experiments were conducted with a silicon rubber pipe. The deflections of the pipe were measured with increasing the frequency of the pulsating flow gradually. In order to observe the principal parametric resonance, the frequency of the pulsating flow was determined as near twice the natural frequency of the out-of-plane vibration for the first mode. We confirm that the in-plane vibration affects the out-of-plane vibration, qualitatively.