Dielectric elastomers are active materials capable of large deformations. They are made of a thin elastomer membrane (typically silicone), sandwiched between two flexible electrodes (for example conductive carbon grease). When a voltage is applied between the electrodes, the membrane thins down, and because of the elastomer incompressibility this results in an area increase. This phenomenon can be exploited to create a displacement normal to the membrane when it is inflated over a cavity.

Loudspeakers using this electro-activation principle have been studied and tested by several research groups. Sound radiation over the whole audible frequency range has been demonstrated, and good efficiency has been reached. Models of the electro-activation principle have also been developed and used to study the dynamics of dielectric-elastomer membranes. However, no complete model taking in account the different physics that matter for a use as a loudspeaker has been presented. Any advanced optimisation of the different parameters of such a device (geometry, material parameters, inflation pressure, etc...) requires a validated model.

In the present research, a complete finite element model is set-up. First the non-linear static equilibrium that results from the applied inflation pressure and static voltage is computed. Then the linear dynamics around this pre-stressed equilibrium are computed. FreeFem++ is used to build the stiffness and mass matrices. Acoustics inside the cavity on which the membrane is inflated, free-field acoustics, electro-statics and membrane dynamics are computed by a fully coupled model. The transfer function between the applied electric voltage and the radiated pressure in any direction is computed, the directivity is predicted. Acoustic radiation in free-field is computed using Perfectly Matched Layers (PMLs) on the exterior boundary of the computation domain. Heavy fluid effects that arise because of the membrane light weight are studied. The model is validated by an experimental study of the dynamics and of the sound radiation of this device.

This model is capable of predicting the sound radiation of the dielectric elastomer membrane when a given voltage is applied to the electrodes. It can therefore be used to optimise dielectric elastomer loudspeakers.