  We investigate the effect of shape and orientation for a horizontally
oscillating intruder on its vertical dynamics in a granular medium via Discrete
Element Method (DEM) simulations. Five distinct intruder shapes were considered
in this study: a disk (OS1), a square (OS2), two rectangles with aspect ratio >
1 (OS3) and < 1 (OS4) respectively, and an equilateral triangle (OS5). The
vertical velocity of the oscillating object was observed to be a function of
amplitude and frequency (f) (inverse of time period (T)) of oscillation, and
the shape of the object. The dynamics of the motion are modelled with the help
of a cavity based model which can empirically produce the regimes observed by
incorporating the free fall of the particles filling the cavity.The cavity
based model assumes that there is a point on the surface of each oscillating
object unique to its shape that any grain crossing it will irreversibly reach
the bottom of the cavity. This leads to the creation of bed of particles at the
bottom of the cavity which increases intruder's elevation as it oscillates,
leading to its vertical rise in the granular medium. When an intruder
oscillates much faster than the falling rate of the grains, the intruder cannot
rise up and thus sinks due to energy provided by the oscillation to the bottom
layer. On the contrary, if the intruder oscillates too slow, the cavity gets
completely filled much before it returns. The maximum rise rate is thus
observed at the oscillation time period where the cavity filling time is equal
to the half time period of oscillation. In addition, we observed a minimum
amplitude (Amin) below which the vertical position of the IO remains unaltered
for various T. We have also presented the time-averaged pressure P, velocity V,
and area fraction {\phi} fields around the intruder shapes.
