Critical velocity and supercritical natural frequencies of fluid-conveying pipes with retaining clips

Although retaining clips are widely used to constrain high-velocity fluid-conveying pipes, there are few studies on the influence of retaining clips on the supercritical vibration characteristics of the pipes. In this study, the vibration characteristics of the fluid-conveying pipe with retaining clip are firstly presented in the supercritical regime. According to the generalized Hamiltonian principle, the governing equation of the fluid-conveying pipe with the retaining clip is derived. When the flow velocity exceeds the critical velocity, the equilibrium configuration of the pipe becomes the non-trivial static equilibrium configuration. By coordinate transformation, the governing equation of the supercritical pipe around the non-trivial static equilibrium configuration is obtained. Emphasis is put on the effects of the clip stiffness and position on the critical flow velocity, equilibrium configuration and natural frequencies. It is found that variations in the retaining clip stiffness can cause different types of non-trivial equilibrium configurations. The natural frequencies will not be monotonic with the increasing clip stiffness in the supercritical flow. Furthermore, the two-span model of the pipe with the clip is obtained for verification. In conclusion, this work lays a foundation for the study of the dynamic response of the supercritical fluid-conveying pipe with retaining clip and can provide a reference for the analysis of the vibration characteristics of the clips and pipes system in engineering.