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The long-term behaviour of solutions to a model for acoustic-structureinteractions is addressed; the system is comprised of coupled semilinear wave(3D) and plate equations with nonlinear damping and critical sources. Thequestions of interest are: existence of a global attractor for the dynamicsgenerated by this composite system, as well as dimensionality and regularity ofthe attractor. A distinct and challenging feature of the problem is thegeometrically restricted dissipation on the wave component of the system. It isshown that the existence of a global attractor of finite fractal dimension --established in a previous work by Bucci, Chueshov and Lasiecka (Comm. PureAppl. Anal., 2007) only in the presence of full interior acoustic damping --holds even in the case of localised dissipation. This nontrivial generalizationis inspired by and consistent with the recent advances in the study of waveequations with nonlinear localised damping.

Finite dimensional attractor for a composite system of wave/plate equations with localised damping