ON THE INSTABILITY OF A SPRING-MOUNTED CIRCULAR CYLINDER IN A VISCOUS FLOW AT LOW REYNOLDS NUMBERS

The first instability of a spring-mounted, damped, rigid circular cylinder, immersed in a viscous flow and free to move in a direction orthogonal to the unperturbed flow, is investigated by a global stability analysis. The flow is modelled by the full Navier–Stokes equations. For low ratios of the fluid density to the structure density, the von Karman mode is always the critical one and the critical Reynolds number, about 47, is nearly the same as for a stationary cylinder. In this case, for low structural damping, two complex modes are active and chaos is possible near the bifurcation. For higher density ratios, the critical Reynolds number decreases to less than the half the critical Reynolds number for a stationary structure. In this case, only a complex mode is active and chaotic behaviour does not seem to be possible near the bifurcation threshold.