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.

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The dynamics of a straight chain of cylindrical neodymium magnets is considered. We showed this system exhibits a behavior which is similar to that of a beam where the elastic rigidity acts like a restoring force. By using a Lagrangian approach, a linear model, accounting for different sets of boundary conditions, is derived. Specifying to the clamped-free case eigenfrequencies and eigenmodes are determined. These theoretical results are compared to experiments. A good agreement is found, the discrepancies being attributed to the accumulation of defaults in the contact surface between the magnets. In the last part of the article, the equivalent beam behavior is sought for by defining an equivalent flexural rigidity induced by magnetic dipoles interactions.