Wavenumber domain analyses of vibro-acoustic decoupling and noise attenuation in a plate-cavity system enclosed by an acoustic black hole plate.

The acoustic black hole (ABH) effect is realized in thin plate structures with a decreasing thickness according to a power-law function, and offers potential applications for structure vibration damping enhancement and free-field noise radiation suppression. In this paper, a wavenumber domain method (WNDM) is proposed for the analysis of vibro-acoustic coupling and internal noise reduction mechanism of a pentahedral cavity enclosed by a flexible plate with a two-dimensional ABH indentation, subject to a point force excitation. The system response of the ABH plate-cavity is computed by a validated finite element model. The relationship between the space-averaged sound energy inside the cavity and the spectra of the structural displacement and the acoustic mode of the cavity is established. This allows revealing a dual physical mechanism behind the observed noise reduction: amplitude reduction and mismatching between the wavenumber spectra of the plate displacement and the acoustic field, which results in a weakened vibro-acoustic coupling. An additional configuration with an ABH embedded in an irregular pentagonal wall of the cavity is examined. Despite the increasing complexity in the geometry of the coupling interface and its coupling with the cavity, numerical analyses confirm the generality of the observed physical phenomena and the applicability of the proposed WNDM to more complex system configurations.