This experimental study investigates the effect of imposed rotary oscillation on the flow-induced vibration of a sphere that is elastically mounted in the cross-flow direction, employing simultaneous displacement, force and vorticity measurements. The response is studied over a wide range of forcing parameters, including the frequency ratio
$f_{R}$
and velocity ratio
$\unicode[STIX]{x1D6FC}_{R}$
of the oscillatory forcing, which vary between
$0\leqslant f_{R}\leqslant 5$
and
$0\leqslant \unicode[STIX]{x1D6FC}_{R}\leqslant 2$
. The effect of another important flow parameter, the reduced velocity,
$U^{\ast }$
, is also investigated by varying it in small increments between
$0\leqslant U^{\ast }\leqslant 20$
, corresponding to the Reynolds number range of
$5000\lesssim Re\lesssim 30\,000$
. It has been found that when the forcing frequency of the imposed rotary oscillations,
$f_{r}$
, is close to the natural frequency of the system,
$f_{nw}$
, (so that
$f_{R}=f_{r}/f_{nw}\sim 1$
), the sphere vibrations lock on to
$f_{r}$
instead of
$f_{nw}$
. This inhibits the normal resonance or lock-in leading to a highly reduced vibration response amplitude. This phenomenon has been termed ‘rotary lock-on’, and occurs for only a narrow range of
$f_{R}$
in the vicinity of
$f_{R}=1$
. When rotary lock-on occurs, the phase difference between the total transverse force coefficient and the sphere displacement,
$\unicode[STIX]{x1D719}_{total}$
, jumps from
$0^{\circ }$
(in phase) to
$180^{\circ }$
(out of phase). A corresponding dip in the total transverse force coefficient
$C_{y\,(rms)}$
is also observed. Outside the lock-on boundaries, a highly modulated amplitude response is observed. Higher velocity ratios (
$\unicode[STIX]{x1D6FC}_{R}\geqslant 0.5$
) are more effective in reducing the vibration response of a sphere to much lower values. The mode I sphere vortex-induced vibration (VIV) response is found to resist suppression, requiring very high velocity ratios (
$\unicode[STIX]{x1D6FC}_{R}>1.5$
) to significantly suppress vibrations for the entire range of
$f_{R}$
tested. On the other hand, mode II and mode III are suppressed for
$\unicode[STIX]{x1D6FC}_{R}\geqslant 1$
. The width of the lock-on region increases with an increase in
$\unicode[STIX]{x1D6FC}_{R}$
. Interestingly, a reduction of VIV is also observed in non-lock-on regions for high
$f_{R}$
and
$\unicode[STIX]{x1D6FC}_{R}$
values. For a fixed
$\unicode[STIX]{x1D6FC}_{R}$
, when
$U^{\ast }$
is progressively increased, the response of the sphere is very rich, exhibiting characteristically different vibration responses for different
$f_{R}$
values. The phase difference between the imposed rotary oscillation and the sphere displacement
$\unicode[STIX]{x1D719}_{rot}$
is found to be crucial in determining the response. For selected
$f_{R}$
values, the vibration amplitude increases monotonically with an increase in flow velocity, reaching magnitudes much higher than the peak VIV response for a non-rotating sphere. For these cases, the vibrations are always locked to the forcing frequency, and there is a linear decrease in
$\unicode[STIX]{x1D719}_{rot}$
. Such vibrations have been termed ‘rotary-induced vibrations’. The wake measurements in the cross-plane
$1.5D$
downstream of the sphere position reveal that the sphere wake consists of vortex loops, similar to the wake of a sphere without any imposed rotation; however, there is a change in the timing of vortex formation. On the other hand, for high
$f_{R}$
values, there is a reduction in the streamwise vorticity, presumably leading to a decreased total transverse force acting on the sphere and resulting in a reduced response.