Coupled vibro-acoustic modeling of a dielectric elastomer loudspeaker

Abstract

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.

A multi-domain dynamical model for cone-shaped dielectric elastomer loudspeakers

“…Here, we do not account for the effect of the radiated sound pressure on the DE diaphragm dynamics, i.e., we neglect the effect of the acoustic impedance due to the fluid motion. 13 This contribution might be not negligible in DE loudspeakers made of thin lightweight membranes, 13 and will be thus included in the future.…”

“…Notice that, using the coordinates of the equilibrium point q 0 to evaluate n k (Eq. (12)) and the Green function (13), relationship (11) between p a and the DE nodes velocity is linear, and can be easily reformulated in the frequency-domain. 9 Figure.…”

“…12 In spite of these experimental proofs-of-concept, modelling and numerical analysis of DE speakers have been scarcely investigated. Recently, Garnell et al 9,13 investigated for the first time the complex electro-elastoacoustic interactions occurring in pneumatically-biased DE speakers. With the aim of weighting the effect of coupled elasto-acoustic interactions, they used a linear modelling approach, which proved very effective in predicting the DE loudspeaker frequency response, still without considering the effect of DEAs' nonlinear dynamics on the harmonic distortions.…”

“…17 Attention is restricted to axial-symmetrical deformations, which are expected to provide the most significant contribution to the radiated pressure. 13 The presented formulation lends itself to analytical studies of the modal shape and frequency response of the system. Thanks to the lagrangian formulation, the model is able to capture the essential features of a DE loudspeaker dynamics even with a coarse discretisation of the domain, potentially requiring lower computational cost compared with off-the-shelf finite element codes.…”

“…Compared with previously available models of the cone DEA, 15 our model is able to predict high-order complex mode shapes. Compared with available DEA speaker models, 13 this model accounts for the DEA nonlinear response, hence enabling the analysis of acoustic harmonic distortions.…”