**Abstract**

Acoustic black holes (ABHs) achieved by progressively diminishing structural thickness have been proved a very efficient approach for wideband vibration reduction, sound suppression, energy harvesting, and wave manipulation. In this chapter, the focus is placed on mitigating the sound emitted from cylindrical shells with embedded ABHs. In the applications of aeronautics, astronautics, and underwater vehicles, cylindrical shells are very common yet the vibroacoustic problems in such structures are very challenging. Even the researches on ABHs for straight beams and flat plates are boosting in recent years, the ABH effect is unclear for curved structures thus it deserves further investigations to push forward their applications. Since cylindrical shells are usually long in, for example, airplanes and rockets, periodic ABHs are designed to alleviate the acoustic emission from them. The Gaussian expansion method (GEM) is employed to recover the vibration field on the cylinder and, based on that, the sound radiation model is developed to determine the emitted sound power level (SWL). The band gaps (BGs) are shown for infinite periodic ABH shells, followed by the vibroacoustic level for a finite periodic shell. Particularly, axial stiffeners are introduced and the influences of their quantity and width are carried out.

**Keywords:** acoustic black holes, acoustic radiation, cylindrical shells, band gaps, stiffeners
