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

Abstract

In recent years, acoustic black holes (ABHs) exhibit fascinating damping effects at mid-to-high frequencies. However, flexural waves having long wavelength cannot be trapped in the ABH pit when there is a residual thickness at the ABH tip, therefore below the cut-on frequency the ABH effect fails to work. While locally resonant acoustic metamaterials allows mitigating vibrations in subwavelength scale, usually in a narrow band. In this paper we combine the advantages of the metamaterials and ABHs (MMABH) to control vibrations in the whole frequency band. The designed MMABH plate remains the same weight to the reference uniform plate. To characterize the MMABH performance, an artificial spring component mode synthesis (GECMS) method is suggested, based on the modal coupling between the resonators and the ABH plate via springs. The band gap for the infinite periodic MMABH and the modes for the finite MMABH have been accurately predicted with the GECMS, compared to a reference FEM model. Numerical results show that the low-frequency peaks of the ABH plate can be substantially suppressed when the resonators with proper loss factor are set at its first resonant frequency. The proposed MMABH shows great potentials for light-weight and whole-band vibration reduction.