Periodic additive acoustic black holes to absorb vibrations from plates

Abstract

This paper first suggests a composite structure with periodic additive acoustic black holes (ABH) to absorb vibrations from plates. Different from conventional embedded ABHs, this additive configuration no longer compromises structural integrity. The suggested periodic structure forms a compact acoustic functional material. To analyze the vibration behavior of this coupled structure, we establish a theoretical model employing the Gaussian expansion method (GEM) and the nullspace method (NSM), and it is validated through finite element simulations. Subsequently, we develop a two-dimensional wave and Rayleigh–Ritz method (WRRM) to compute complex dispersion curves, with the imaginary part predicting absorption capability. Our findings reveal that the local resonance eigenmodes of the ABH plate with high loss factors dominate the damping effect, overshadowing the role of Bragg scattering. Furthermore, the introduction of a damping layer proves highly effective in absorbing local vibrations across a wide frequency band. Moreover, we then conduct parametric analyses on various aspects, including ABH order, central thickness, ABH plate thickness, and ABH radius. Notably, the latter two parameters exert a significant influence on damping performance, primarily due to the added mass they introduce. Finally, we examine a finite plate consisting of a 4 × 4 cell arrangement. This composite structure demonstrates substantial modal loss factors when local modes are activated. Moreover, in forced vibration tests, the additive ABHs prove highly effective in mitigating vibrations within the host plate.