Abstract:By virtue of the code for the aeroelastic problems based on the loosely coupled method worked out by the authors,vortex induced vibration (VIV) for typical cylinders,including circular and square cylinders are simulated. Computational results show that there exist two lock in states for the VIV of the two dimensional cylinders:one is streamwise lock in at lower reduced velocity and the other is lateral lock in at higher reduced velocity.With the increase of the reduced velocity,the vortex shedding mode could be changed from out of phase 2S(2single) to in phase 2S,and at the same time,the phase difference between the aerodynamic force and the displacement could be changed from 0 to π,which is the so called phase switch phenomenon.By analyzing the phase switch phenomenon,the mechanism for the limited amplitude of the VIV is studied.