Modeling, design, and optimization of a dielectric elastomer acoustic liner

The modeling, design, and optimization of an embedded dielectric elastomer (DE) membrane acoustic liner is considered. The acoustic impedance of the liner is modified when the DE is subjected to voltage, resulting in a reduction of the in-plane stress. A lumped element model of an embedded dielectric elastomer acoustic liner is derived and validated in a normal incidence impedance tube and is subsequently used to optimize its performance. The optimization cost functions include (1) maximization of the average absorption coefficient over a targeted frequency range, 400 - 1600 Hz and (2) maximization of the change in the liner fundamental resonance frequency when the membrane is activated. Good agreement between measured and predicted absorption is observed. Tuning of the resonant frequency requires a numerical solution for resonance using the imaginary part of the impedance, since a simple analytical expression for resonance cannot be derived due to the complex coupling between the acoustics of the liner and the electro-mechanics of the DE membrane. Nonetheless, resonant frequency shifts predicted with the lumped element model compare favorably to those measured with the activated liner sample, with a shift of 213 Hz.