  Recent experiments showed that standing acoustic waves could be exploited to
induce self-propulsion of rigid metallic particles in the direction
perpendicular to the acoustic wave. We propose in this paper a physical
mechanism for these observations based on the interplay between inertial forces
in the fluid and the geometrical asymmetry of the particle shape. We consider
an axisymmetric rigid near-sphere oscillating in a quiescent fluid along a
direction perpendicular to its symmetry axis. The kinematics of oscillations
can be either prescribed or can result dynamically from the presence of an
external oscillating velocity field. Steady streaming in the fluid, the
inertial rectification of the time-periodic oscillating flow, generates steady
stresses on the particle which, in general, do not average to zero, resulting
in a finite propulsion speed along the axis of the symmetry of the particle and
perpendicular to the oscillation direction. Our derivation of the propulsion
speed is obtained at leading order in the Reynolds number and the deviation of
the shape from that of a sphere. The results of our model are consistent with
the experimental measurements, and more generally explains how time periodic
forcing from an acoustic field can be harnessed to generate autonomous motion.
