A semi-analytical method for the vibration of cylindrical shells with embedded acoustic black holes

Embedding acoustic black holes (ABHs) on beams and plates has revealed as an appealing passive method for noise and vibration reduction. However, most ABH designs to date have only concerned straight beams and flat plates, while cylindrical structures are commonly found in the aeronautical and naval sectors. Therefore, it is worth exploring how the ABH concept applies to them. In this work, we suggest a semi-analytical method to compute the vibration field of a cylinder with an annular ABH indentation, using Gaussian functions as basis in the framework of the Rayleigh-Ritz method. The displacements in the three directions are forced to satisfy continuous periodic conditions. The proposed Gaussian expansion method (GEM) for the cylindrical shell is validated against a detailed finite element (FEM) model, showing high precision at a low computational cost. After that, the mean square velocity of the ABH shell under a point external excitation is compared to that of a uniform shell, in the 50-1000 Hz frequency range. Noticeable vibration reduction is achieved.