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

TL;DR

This paper investigates how electrostatic bias fields influence wave propagation in dielectric laminate structures, revealing tunable band-gaps that can be controlled for filtering specific frequencies.

Contribution

It introduces a method to analyze and control wave band-gaps in dielectric laminates using bias electric fields, combining Bloch-Floquet and transfer matrix techniques.

Findings

Band-gaps depend on electric bias, material properties, and volume fraction.

Bias electric field can shift and modify the width of band-gaps.

Wave propagation can be effectively filtered by adjusting the electrostatic bias.

Abstract

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.