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

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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 to 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.

Original languageEnglish
Pages (from-to)1970-1981
Number of pages12
JournalJournal of the Mechanics and Physics of Solids
Issue number11
StatePublished - Nov 2012


  • Band-gap
  • Bloch-Floquet analysis
  • Composite
  • Dielectric elastomers
  • Finite deformations
  • Non-linear electroelasticity
  • Thickness vibrations
  • Wave propagation

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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