Natural vibration of pipes conveying high-velocity fluids with multiple distributed retaining clips

Pipes are usually constrained by multiple distributed retaining clips (MRCs). In addition, piping fluids are always required for higher velocities. In this paper, the effect of MRCs distribution on the natural vibration of pipes conveying high-velocity fluids are investigated. The nonlinear dynamical model of multi-span pipes conveying fluids is established by the generalized Hamiltonian principle. The critical velocity of fluid-conveying pipes is obtained. Then, the supercritical static equilibrium bifurcation appears in the pipe conveying high-velocity fluids. Subsequently, the non-trivial static equilibrium configuration is solved by developing the iterative scheme. By coordinate transformation, the governing equation of the pipe constrained by MRCs is established in the supercritical regime. Some meaningful and interesting results are obtained. Results show that the critical velocity of a multi-span (more than two-span) pipe is not monotonous with the change of the clip location. For pipes with single clip and two or more clips, the critical velocity varies significantly with the trend of clip stiffness. With the increase of flow velocity, the modes of multi-span pipes change significantly. Moreover, the first-order natural frequency of the three-span pipe is not monotonous with the change of clip stiffness, number, and location in the supercritical regime. Therefore, as a common and important pipe form in engineering, more attention should be paid to pipes with multiple distributed retaining clips.