On-off switching of vortex shedding and vortex-induced vibration in crossflow past a circular cylinder by locking or releasing a rotational nonlinear energy sink

We show how fully developed vortex-induced vibration (VIV) of a linearly sprung circular cylinder can be completely suppressed, i.e., driven to zero asymptotically in time, by release of a rotational nonlinear energy sink, consisting of a mass rotating about the axis of the cylinder and a dissipative element damping the rotational motion of the mass. (The nonlinear energy sink is located either inside the cylinder or beyond the spanwise extent of the flow, with which it thus interacts only through inertial coupling to the rectilinear motion of the cylinder.) We also show that VIV can be turned on by locking up the rotating mass. Once VIV is suppressed or turned on, no further action or energy input is required. Thus, this approach provides a true switch. Applications for flow control and for turning mixing on or off are discussed.

Figure 1

Linearly sprung cylinder in crossflow with rotational NES.

Figure 2

Effect of a rotational NES (with $\zeta =4/3$ and ${\overline{r}}_0=0.3$) on the stability of the steady, symmetric, motionless-cylinder solution for ${\varepsilon }_p{sin}^2{\theta }_s=0$ (green open circles), ${\varepsilon }_p{sin}^2{\theta }_s=0.15$ (orange open squares), ${\varepsilon }_p{sin}^2{\theta }_s=0.3$ (purple open triangles), and ${\varepsilon }_p{sin}^2{\theta }_s=0.6$ (pink open diamonds). The horizontal line at $\text{Re}=46.05$ is the critical value for the fixed cylinder.

Figure 3

Time series for $\text{Re}=24$ and $1/g_n^{*}=0.3$, where a rotational NES with ${\varepsilon }_p=0.3$ is released from ${\theta }_{\mathrm{release}}=\pi /2$ at $\tau =696.46$ (corresponding to ${\varphi }_{\mathrm{release}}=0.113\pi$) and locked at $\tau =1500$: (a) cylinder displacement, (b) NES angular displacement, (c) NES angular velocity, (d) lift coefficient, and (e) drag coefficient.

Figure 4

Time series for $\text{Re}=24$ and $1/g_n^{*}=0.3$, where a rotational NES with ${\varepsilon }_p=0.3$ is released from ${\theta }_{\mathrm{release}}=\pi /2$ at $\tau =698.57$ (corresponding to ${\varphi }_{\mathrm{release}}=0.65\pi$) and locked at $\tau =2000$: (a) cylinder displacement, (b) NES angular displacement, (c) NES angular velocity, (d) lift coefficient, and (e) drag coefficient.

Figure 5

Time series for maxima of cylinder displacement for $\text{Re}=24, 1/g_n^{*}=0.3, {\varepsilon }_p=0.3, {\theta }_{\mathrm{release}}=\pi /2$, and ${\varphi }_{\mathrm{release}}=0.112\pi$ (red circles), ${\varphi }_{\mathrm{release}}=0.5\pi$ (green squares), and ${\varphi }_{\mathrm{release}}=0.612\pi$ (blue triangles). Each symbol corresponds to a maximum of $y_1$. The lines connecting consecutive symbols merely facilitate visualization and should not be thought of as the result of interpolation between data points.