Last modified: 2018-04-16

#### Abstract

Flow-induced transverse vibrations of an elastically mounted square cylinder are numerically studied for a cylinder mass ratio of *m** = 3.0, Reynolds number *Re *(=*U _{∞}D*/

*n*= 100 – 200) and reduced velocity

*U*(=

_{r }*U*/

_{∞}*f*= 1.0 - 30), where

_{n}D*D*is the cylinder width,

*U*is the free stream velocity,

_{∞ }*f*is the natural frequency of the cylinder system, and

_{n}*n*is the kinematic viscosity of the fluid. The focus is given on (i) identifying different branches of flow-induced vibrations, (ii) flow characteristics at different branches, and (iii) dependence of different branches on

*Re*. It is found that the dependence of Strouhal number

*St*on

*U*can distinguish different branches more appropriately than that of the vibration amplitude on

_{r}*U*. With increasing

_{r}*U*, the cylinder undergoes three response branches at

_{r}*Re*= 100: initial (

*U*< 4.5), lower (4.5 <

_{r}*U*< 10), and desynchronization (

_{r}*U*≥ 10). Akin to those at

_{r}*Re*=100, the initial and lower branches at

*Re*= 200 appear at

*U*< 12 while a galloping branch occurs at

_{r}*U*> 12. It is discovered that, in the galloping branch, the vibration response at 12 <

_{r}*U*< 24 involves the characteristic of both initial and lower branches while that at

_{r }*U*> 24, of both initial and desynchronization branches. The phase lag between force and displacement changes from 0° to 180° at the commencement of the lower branch. For

_{r }*Re*= 200 at

*U*= 5, force and displacement signals comprise two intermittent modes corresponding to high and low oscillation frequencies.

_{r }