Nonlinear Dynamics of a Fluid–Structure Coupling Model for Vortex-Induced Vibration

This paper presents a fluid–structure coupling model to investigate the vortex-induced vibration of a circular cylinder subjected to a uniform cross-flow. A modified van der Pol nonlinear equation is employed to represent the fluctuating nature of vortex shedding. The wake oscillator is coupled with the motion equation of the cylinder by applying coupling terms in modeling the fluid–structure interaction. The transient responses of the fluid–structure coupled model are presented and discussed by numerical simulations. The results demonstrate the main features of the vortex-induced vibration, such as lock-in phenomenon, i.e. resonant oscillation of the cylinder occurs when the vortex shedding frequency is near to the natural frequency of the cylinder. The resonant responses of the fluid–structure coupled model in the lock-in region are determined by the multiple scales method. The accuracy of the asymptotic solution by the multiple scales method is verified by comparing with the numerical solution from the motion equation. The effects of different parameters on the steady state amplitude of oscillation are investigated for a given set of parameters. Frequency–response curves obtained from the modulation equation demonstrate the existence of jump phenomena.