Nonlinear Interactions of Unstable Modes on a Self-excited Vibration of a Spring Supported Pipe Conveying Fluid

Abstract

Self-excited vibrations of a pipe conveying fluid have been studied as an essential problem of unstable phenomena on non-conservative continuous systems. In this system, double Hopf bifurcations can be produced in the range of certain parameters. In this study, we investigate the nonlinear interactions between two unstable modes. By using Lyapnov-Schmidt reduction method, we obtained the amplitude equations which govern the nonlinear interactions between two unstable modes. In this study, we explain mechanism of nonlinear interactions on amplitude equations. Furthermore, we conducted additional experimental results of non-planar mixed modal self-excited vibrations.