Underwater sound radiation from a Mindlin plate with an acoustic black hole

Acoustic black holes (ABHs) have been shown very efficient to reduce sound radiation in the air. However, their underwater performance is not clear. In this paper, we consider a Mindlin plate with an embedded circular ABH indentation. The Gaussian expansion method is used to compute the rotations and bending displacement at the mid-surface, with boundary conditions imposed via the nullspace method. The interaction between the solid and fluid is accounted for by the work done by the sound pressure. The theoretical method is validated against FEM and hybrid BEM-FEM simulations. Results show that the ABH is very effective for suppressing the underwater sound power between the cut-on frequency and the critical frequency. Yet at higher frequencies, the advantage of the ABH is not significant. The underlying physics is revealed using modal loss factor (MLF) that is obtained by solving the eigenvalue problem with the Newton iteration method. It is found that beyond the critical frequency, the radiation damping is very high, because of energy transmission from the plate to the water. Observation on the non-negative intensity (NNI) demonstrates that at higher frequencies the radiation area moves from the plate corners to the force point.