  Using continuum simulations, we show that under a sinusoidal electric field,
liquid crystal skyrmions undergo periodic shape oscillations which produce
controlled directed motion. The speed of the skyrmion is non-monotonic in the
frequency of the applied field, and exhibits multiple reversals of the motion
as a function of changing frequency. We map out the dynamical regime diagram of
the forward and reverse motion for two superimposed ac driving frequencies, and
show that the reversals and directed motion can occur even when only a single
ac driving frequency is present. Using pulsed ac driving, we demonstrate that
the motion arises due to an asymmetry in the relaxation times of the skyrmion
shape. We discuss the connection between our results and ratchet effects
observed in systems without asymmetric substrates.
