Stability and nonlinear vibration of carbon nanotubes-reinforced composite pipes conveying fluid

This paper focuses on the stability and nonlinear vibration characteristics of carbon nanotubes-reinforced composite pipes conveying fluid, and the mechanism of the combined effects of multiple factors. Based on the assumption of Euler beam and Von-karman nonlinear stress-strain relationship, the dynamic governing equations and generalized boundary conditions of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) pipes are established by Hamiltonian variational principle. Firstly, the modal function suitable for generalized boundary conditions is derived by Galerkin method. The stability of FG-CNTRC pipes system and the relationship between natural frequency and flow velocity are analyzed in this paper. The effect of flow velocity on the natural frequency of pipelines is examined under various carbon nanomaterial distribution patterns and wall thicknesses in this research. Then, the nonlinear vibration characteristics of FG-CNTRC pipes are analyzed by multi-scale method. The method of deducing nonlinear frequency through high-order partial differential equations is also extended in nonlinear analysis. The results show that, in the case of uniform distribution of carbon nanotubes, increasing the wall thickness can improve the stability of the pipe system. The influence of amplitude on the nonlinear frequency is more obvious at the second-order frequency.