  The thickness vibrations of a finitely deformed infinite periodic laminate
made out of two layers of dielectric elastomers is studied. The laminate is
pre-stretched by inducing a bias electric field perpendicular the the layers.
Incremental time-harmonic fields superimposed on the initial finite deformation
are considered next. Utilizing the Bloch-Floquet theorem along with the
transfer matrix method we determine the dispersion relation which relates the
incremental fields frequency and the phase velocity.
  Ranges of frequencies at which waves cannot propagate are identified whenever
the Bloch-parameter is complex. These band-gaps depend on the phases
properties, their volume fraction, and most importantly on the electric bias
field. Our analysis reveals how these band-gaps can be shifted and their width
can be modified by changing the bias electric field. This implies that by
controlling the electrostatic bias field desired frequencies can be filtered
out. Representative examples of laminates with different combinations of
commercially available dielectric elastomers are examined.
