DAMPED FLOW-INDUCED VIBRATIONS OF A SQUARE CYLINDER AT LOW REYNOLDS NUMBERS

Damped flow-induced bidirectional vibrations of a square cylinder are investigated using a stabilized space-time finite-element solver in two dimensions. The vibrations are computed for a mass ratio, m*, of 10 of the cylinder and the value of damping coefficient, ?, equals 0.044. The computations are performed over a Reynolds number, Re, range of 60-350 subject to the FN = 14.39/Re constraint where FN stands for the reduced natural frequency. Relative to the undamped bidirectional results, the damping is found to lower the maximum transverse displacement by a factor of 0.5 and also to delay the onset of galloping. With damped oscillations, the frequency and response characteristics near the lock-in resemble those obtained from undamped vibrations of oscillators of low m*, such as unity. It is found that apart from oscillation frequency, the frequency ratio is also very effective in locating the interbranch transitions. A kink is resolved in the response curve at Re = 220 that splits the galloping branch into two distinct parts. In the first part ahead of the kink, the building up of response and forcing is very steep. A flat or slower rise of the characteristic quantities is noted in the second part next to the kink. Both odd and even type synchronizations are resolved between cylinder oscillations and vortex shedding. In the galloping branch, the wake mode corresponding to 1:3 type odd synchronization is 2P+2S whereas a complex mode comprised of eight shed vortices form in 1:4 type even synchronization.