Transmission loss limitations of embedded acoustic black holes

Acoustic black hole (ABH) indentations in beams and plates are known to reduce vibrations and sound radiation above their cut-on frequency, $f_{\mathrm{cut-on}}$. However, their effect on transmission loss between cavities has not been fully explored. This study presents a two-dimensional model, representative of a three-dimensional case, that demonstrates that when the ABH cut-on frequency $f_{\mathrm{cut-on}}$ is lower than the plate’s critical frequency $f_{\mathrm{crit}}$, an ABH beam can underperform a uniform one in the frequency range $f_{\mathrm{cut-on}}<f<f_{\mathrm{crit}}$, leading to lower transmission loss. It is demonstrated that this counterintuitive behavior is linked to the excitation of different types of global modes in the coupled system (Source cavity - ABH beam - Receiver cavity) and to low-frequency non-resonant modes in the ABH beam, which lie in the radiation domain and inhibit the ABH effect. As a result, the acoustic pressure in the receiver cavity becomes higher compared to that for a uniform beam partition. The two-dimensional model is analyzed using a Rayleigh–Ritz formulation that couples the beam’s bending displacement to the acoustic particle displacement in the cavities. Natural boundary and traction continuity conditions are imposed weakly, while essential and displacement continuity conditions are enforced using the nullspace method, thus avoiding explicit coupling matrices.