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The nonlinear character of the primary bifurcation is investigated for the flow around a flexibly mounted circular cylinder. We have considered the cases in which the cylinder can oscillate in the transverse direction only and in both transverse and in-line directions. Low and high values of mass ratio (
and 50) were studied, and reduced velocity (
) values are chosen inside (
) and outside (
) the lock-in range for low Reynolds numbers. For each combination of
, a global linear stability analysis was applied to find the critical Reynolds number
of the fluid–structure system. For
in the lock-in range, the values of
were noticeably less than the critical Reynolds number of the flow around a fixed circular cylinder (
). On the other hand, for
outside the lock-in range, the values of
were close to
. Next, nonlinear analyses were performed in the vicinity of
for each case. Subcritical character (with hysteresis) was observed for
in the lock-in range, while for
outside the lock-in region the bifurcations were found to be supercritical (without hysteresis). This shows that when the coupling between the structure and flow is strong, due to the proximity of the natural frequencies of the isolated systems, it significantly changes both the linear and nonlinear responses observed.
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