Natural Vibration of Critical Double-Span Functionally Graded Pipe Conveying Fluid Reinforced by Graphene Platelets

Background: Graphene platelet (GPL) has garnered substantial attention in recent years due to its excellent mechanical properties. Methods: In this paper, the reinforced effect of GPL on natural vibration characteristics of the double-span functionally graded pipe before and after critical velocity is analyzed for the first time. The nonlinear transverse vibration governing equation of GPL reinforced functionally graded pipe is derived. The critical velocity, natural frequency, mode, and non-trivial static equilibrium configuration are calculated. Furthermore, the influence of GPL and clip parameters on the natural vibration characteristics of the double-span pipe are analyzed. Results: Adding a few GPLs to the matrix material significantly enhances the bending stiffness of the pipe, thereby increasing the critical velocity. The GPL can raise the ceiling of the ability for clip stiffness increasing the double-span pipe critical velocity. Notably, the natural frequency shows a positive correlation with the GPL weight fraction and the clip stiffness at subcritical velocity, whereas exhibits a negative correlation at supercritical velocity. Moreover, the clip has a significant adjustment effect on the natural frequency before and after the critical velocity. Conclusion: The utilization of GPL and clip to regulate the fluid-conveying pipe holds significant engineering value in avoiding resonance.