Finite element modelling of the vibro-acoustic response in dielectric elastomer membranes

This paper focuses on the characterisation of the vibroacoustic response of dielectric elastomer (DE) membranes. We set our attention on a circular DE membrane, deformed three-dimensionally and mounted in between fixed frames, which is able to generate sound with no need for any elastic or pneumatic biasing element. We present a finite element model of the system entirely based on commercial software Comsol Multiphysics. The model combines: 1) a mechanical model of the DE membrane, which makes use of suitably defined energy functions that account for electro-elastic coupling; and 2) an acoustic model of the domain surrounding the DE. The model implements a bi-directional coupling between the DE and the acoustic domain. In particular, it accounts for the effect of the acoustic pressure loads applied on the DE membrane, which, given the small thickness and low density of the membrane, play a significant role in the system dynamics. We validate the model against experimental measurements of the DE surface velocity and the sound pressure level (SPL) in the surroundings of the membrane. Despite relying on strong simplifications in the geometry of the system and the viscous response of the material, the model is able to describe the main trends in the device frequency response, and how the SPL varies as a function of the mechanical pre-load and the voltage applied on the membrane.