  In recent work, it was shown that elasticity theory can break down in
amorphous solids subjected to nonuniform {\em static} loads. The elastic fields
are screened by geometric dipoles; these stem from gradients of the quadrupole
field associated with plastic responses. Here we study the dynamical responses
induced by {\em oscillatory} loads. The required modification to classical
elasticity is described. Exact solutions for the displacement field in circular
geometry are presented, demonstrating that dipole screening results in
essential departures from the expected predictions of classical elasticity
theory. Numerical simulations are conducted to validate the theoretical
predictions and to delineate their range of validity.
