Vibration of a metaplate made of an acoustic black hole and local resonators

In recent years, acoustic black holes (ABHs) have revealed as a very efficient means of reducing vibrations in the mid-high frequency range. However, below the cut-on frequency an ABH fails to work. Besides, locally resonant acoustic metamaterials can generate stopbands and reduce vibrations at a subwavelength scale. In this paper we combine the advantages of metamaterials and ABHs to diminish the vibrations of a plate covering the whole frequency range, from low to high frequencies. The proposed solution, the MMABH plate, consists of a uniform plate with an embedded ABH such that the removed material from the indentation is used to build the resonators and the total weight remains constant. To characterize the MMABH performance, a Gaussian expansion component mode synthesis (GECMS) method is used, based on the modal coupling between the resonators and the ABH plate. The bandgaps of an infinite periodic MMABH plate as well as the modes of a finite one can be accurately predicted with the GECMS. Numerical results show that the low-frequency peaks of an ABH plate can be substantially suppressed when resonators with proper loss factors are attached to it, and tuned at their first resonant frequency. The proposed MMABH shows great potential as a light-weight option to achieve broadband vibration reduction in structures.