Analytical Analysis of Nonlinear Vortex-Induced Vibration of Pipes Conveying Fluid

In this paper, the vortex-induced vibrations of a long flexible pipe conveying steady fluid are investigated via a two-mode discretization of the governing differential equations. The governing nonlinear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by applying the Galerkin’s method, which are then studied numerically for the pipe with primary resonances during lock-in for each of the first two modes. The method of multiple scales is utilized to obtain the steady-state responses of the coupled equations. It is found that the frequency-amplitude relationships present typical nonlinear phenomena, including jumping and multi-value. Numerical integrations are directly implemented in the vibration equations to verify the aforementioned analytical results. Furthermore, an analytical expression that predicts the lock-in phenomenon range of external fluid velocity is derived. The influences of the velocity of internal and external fluids on the dynamical characteristics are discussed in detail. It is shown that the values of the external fluid velocity triggering the start and stop of the lock-in phenomenon will change with the value of the internal fluid velocity of the pipe.