Coupled vibro-acoustic modeling of a dielectric elastomer loudspeaker

Dielectric elastomer membranes are soft electro-active materials capable of large deformations. When inflated over a cavity, the membrane radiates sound and can therefore be used as a loudspeaker. This type of device has been studied both experimentally and numerically. However, most studies on the dynamics of dielectric elastomer membranes either focus on the very low frequency behavior to analyse viscosity effects for example, or try to maximise the overall radiated sound pressure level. Here the mid-frequency range is analysed in detail, by setting up a fully coupled finite element model of an inflated dielectric elastomer membrane. Electrostatics, vibro-acoustics, free-field radiation, and pre-stressed linear dynamics are solved together, to find the fluid loaded resonance modes. The dynamics of the membrane and the sound radiation are then computed using this resonance mode basis. Perfectly matched layers are used to implement the Sommerfeld radiation boundary condition. The model is validated by a comparison with measurements of the pressure radiated by a prototype, and predicts accurately the radiated pressure and the directivity. This model should therefore help the development of optimized dielectric elastomer loudspeakers, with improved frequency responses and directivity.