  The dynamics of an oscillated sessile drop of incompressible liquid with the
focus on the contact line hysteresis is under theoretical consideration. The
solid substrate is subject to transverse oscillations, which are assumed small
amplitude and high frequency. The dynamic boundary condition that involves an
ambiguous dependence of the contact angle on the contact line velocity is
applied: the contact line starts to move only when the deviation of the contact
angle exceeds a certain critical value. As a result, the stick-slip dynamics
can be observed. The frequency response of surface oscillations on the
substrate and at the pole of the drop are analyzed. It is shown that novel
features such as the emergence of antiresonant frequency bands and nontrivial
competition of different resonances are caused by contact line hysteresis.
