Ring-shaped acoustic black holes for broadband vibration isolation in plates

Acoustic black holes (ABHs) in plates have shown great potential in a variety of applications that range from passive noise and vibration reduction, to energy harvesting thanks to localization, or to unusual flexural wave manipulation like lensing, or negative refraction and bi-refraction. The ABH effect can be typically achieved in plates by embedding regular arrays of circular cuneate indentations, with power-law profile. In this paper, we suggest new ring-shaped ABH designs that may be used for vibration isolation. Many common situations in the vibroacoustics of built-up structures involve wave propagation in plates excited at a small source area. This could be the case, for instance, of a beam/plate connection. It is herein proposed to surround the plate excitation region by means of ring-shaped ABHs to prevent the transmission of vibrations outside them. Several configurations of ABHs are tested, from concentric annular ABHs in different number and sizes to traditional circular ABHs in a ring arrangement. The inclusion of stiffeners to prevent excessive structural plate weakness due to the ABH indentations is also addressed. The performance of the ABH designs are analyzed by means of a semi-analytical approach that uses two-dimensional Gaussian functions to approximate the plate flexural displacement field, in the framework of the Rayleigh-Ritz method. The annular ABHs are shown to exhibit remarkable good isolation for the whole frequency range. An explanation is provided for their behavior.