Two-dimensional space-time finite-element simulations are carried out to study the effect of oscillator mass ratio, m* on free inline
and transverse vibrations of a rigid square cylinder. The effect of viscous damping or resistance is not considered and thus
cylinders of mass ratio 1, 5, 10 and 20 execute free undamped vibrations. Results are presented for 50≤Re≤250 where Re is the
Reynolds number. For m* = 1, synchronization between cylinder oscillation and vortex-shedding is 1:1 (periodic flow). Thus, the
Cl-Y phase portraits must be single looped closed curves. For m* = 5-20, synchronization is 1:1 (periodic flow) prior to galloping.
For m* = 5, the synchronization during galloping is quite different from 1:3. Along ‘increasing Re’, the entire galloping branch of
m* = 5 cylinder is quasi-periodic. However, along ‘decreasing Re’, it is mostly quasi-periodic and it is periodic for Re≤190. An
1:3 sub-harmonic synchronization is seen for the m* = 10 and 20 cylinders only in the periodic regime of galloping occurring at
higher Re. For m *= 1, only one kink is seen in the response curve signifying transition from initial to lower branch. Two kinks
are captured for m* = 5 cylinder. For m*= 10 and 20, an additional third kink is resolved in the galloping branch that signifies
transition from quasi-periodic flow/body motion to periodic flow/body motion.
© 2016 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the organizing committee of ICOVP 2015.
Keywords: Square cylinder, Free vibration, Mass ratio, Galloping, Wake modes, Synchronization