Dynamics and sound radiation of a dielectric elastomer membrane

This paper investigates sound radiation by an inflated dielectric elastomer membrane. The constitutive equations of the coupled electromechanical system are derived from general mechanical equilibrium equations, from Maxwell's equations, and from thermodynamic considerations. A finite deformation model featuring a hyperelastic constitutive law is written for the case of a thin membrane. The static finite deformation obtained when the membrane is inflated and when a voltage is applied is computed. The linear dynamics around this equilibrium are studied on the modal basis: the mode shapes and eigenfrequencies are computed, as well as the modal forces created by the voltage applied on the electrodes. The radiated acoustic pressure is estimated using a modified Rayleigh integral to take into account curvature effects. All numerical calculations are validated against measurements. The model is shown to be able to predict the linear vibrations, as well as the radiated pressure. The effect of the volume of the cavity on which the membrane is inflated is taken into account in the model. This model can therefore be used to optimize the design of dielectric loudspeakers, in terms of spectral balance for example.