  We perform numerical simulations of a two-dimensional bidisperse granular
packing subjected to both a static confining pressure and a sinusoidal dynamic
forcing applied by a wall on one edge of the packing. We measure the response
experienced by a wall on the opposite edge of the packing and obtain the
resonant frequency of the packing as the static or dynamic pressures are
varied. Under increasing static pressure, the resonant frequency increases,
indicating a velocity increase of elastic waves propagating through the
packing. In contrast, when the dynamic amplitude is increased for fixed static
pressure, the resonant frequency decreases, indicating a decrease in the wave
velocity. This occurs both for compressional and for shear dynamic forcing, and
is in agreement with experimental results. We find that the average contact
number $Z_c$ at the resonant frequency decreases with increasing dynamic
amplitude, indicating that the elastic softening of the packing is associated
with a reduced number of grain-grain contacts through which the elastic waves
can travel. We image the excitations created in the packing and show that there
are localized disturbances or soft spots that become more prevalent with
increasing dynamic amplitude. Our results are in agreement with experiments on
glass bead packings and earth materials such as sandstone and granite, and may
be relevant to the decrease in elastic wave velocities that has been observed
to occur near fault zones after strong earthquakes, in surficial sediments
during strong ground motion, and in structures during earthquake excitation.
