A metamaterial consisting of an acoustic black hole plate with local resonators for broadband vibration reduction

Acoustic black hole (ABH) indentations on plates are very efficient to reduce high frequency vibrations. However, when the wavelength of the impinging bending waves on the ABH is larger than its diameter, waves cannot be trapped and dissipated within the ABH and that becomes ineffective. Therefore, it would be highly desirable to extend the performance of ABH plates to lower frequencies. In this work, a method is proposed to accomplish that goal. It is suggested to design a metamaterial in which a set of periodic local resonators are attached to an ABH plate. On the one hand, the resonators are tuned to have a bandgap at the plate first eigenmode so as to suppress it. On the other hand, the resonators are also damped which substantially lowers the peaks of the remaining low-order eigenfrequencies. In combination with the ABH effect, such design, hereafter termed the MMABH plate, provides broadband vibration reduction covering the whole frequency range. To characterize the MMABH, the Gaussian expansion method (GEM) for determining the vibrations of the ABH plate is integrated with a component mode synthesis (CMS) approach, which allows one to link the resonators to the plate. That method is validated against finite element simulations. The MMABH is designed so that its overall mass (ABH plate plus resonators) equals that of the uniform plate without ABH indentation, to offer a light-weight solution. Theoretical explanations of the functioning of the MMABH plate are provided based on the analysis of the ABH effect, the dispersion curves and bandgaps of infinite periodic plates with local resonators and finally, the merging of both topics.