**4. Conclusions**

In the current chapter, the acoustic black hole (ABH) effect is concerned and applied to cylindrical structures. By reducing thickness following the power law, the wave velocity is substantially slowed and the wavenumber is increased when it propagates to the ABH center, where the damping layer is very efficient to consume vibrational energy. The focus is placed on reducing the sound emission from cylindrical shells, which can be found in many fields, via embedding periodic ABHs. First, the reconstructed Gaussian expansion method (GEM) is presented to characterize infinite periodic ABH shells. The band gaps (BGs), induced by the locally resonant effect in the ABH area, are investigated, together with the influence of the ABH parameters. Next, the sound radiation model for finite periodic cylindrical shells is developed. Numerical results show that the periodic ABHs can both reduce the vibration and sound power, relying on two mechanisms—(i) the BGs for

**Figure 12.**

*Surface sound pressure distributions at 340 Hz. (a) Uniform shell, (b) ABH shell without stiffener, (c1)-(c3) stiffened ABH shell with the different number of stiffeners of the same width, (d1)-(d3) stiffened ABH shell with 16 stiffeners having different widths. The red circles stand for the ring force.*

isolating vibrations and (ii) the damping effects for energy consumption. The inclusion of stiffeners not only strengthens the structural stiffness but also keeps the vibration and sound power level as the pure ABH one in the passbands.
