Resonance modes for exterior vibro-acoustic problems, application to a dielectric elastomer loudspeaker

Modal expansion techniques are efficient order reduction tools for bounded problems, but their use for exterior problems is less investigated. In the present article a simple vibrating structure embedded in a heavy exterior acoustic fluid is studied. Using a coupled finite element model, with perfectly matched layers (PMLs) to insure the Sommerfeld boundary condition, we show that the coupled fluid-structure modes can be obtained by solving a linear eigenvalue problem. The full basis comprising the fluid loaded structural modes and numerical PML modes is then used to expand the structural displacement and the radiated acoustic pressure, providing good accuracy. It is shown that the displacement potential appears to be a more natural variable than the acoustic pressure to describe the fluid state. This modal approach is then applied in a real case where a dielectric elastomer loudspeaker is studied, and validated by measurements.