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

Band-gaps in electrostatically controlled dielectric laminates subjected to incremental shear motions