Stability and nonlinear vibration analysis of fluid-conveying composite pipes with elastic boundary conditions

Considering geometric nonlinear deformation and elastic boundary conditions, this paper mainly investigates the stability and nonlinear vibration characteristics of fluid-conveying composite pipes. Based on Euler–Bernoulli Beam Theory and the effects of von Karman nonlinearity, using Kelvin–Voigt model and Hamilton variational principle, the dynamic governing equations and elastic boundary conditions of composite pipe are established. Firstly, the modal function suitable for elastic elastic boundary conditions is derived by Galerkin method, and the stability of fluid-conveying composite pipe system and the influence of elastic boundary conditions on the unstable critical velocity are analyzed. Then the Homotopy analysis method is used to solve the nonlinear vibration characteristics of the composite pipe system. The effects of viscoelastic coefficient, initial amplitude and fiber orientation on the nonlinear natural frequencies are given. The results show that the translation spring has little effect on the instability critical velocity, while the rotation spring will increase the instability critical velocity and make the system more stable. The increase of viscoelastic coefficient and fiber orientation will lead to the decrease of nonlinear frequency, the larger the initial amplitude, the larger the nonlinear frequency.