Evanescent waves in a metabeam attached with lossy acoustic black hole pillars

In this paper, we suggest a metabeam having periodically distributed integrated acoustic black holes (IABHs). Compared to conventional embedded ABHs, the thickness of the base beam has not been modified, so it adapts well to application occasions with load-bearing requirements. The ABH pillars behave as dynamic vibration absorbers (DVAs) that not only provide abundant modes with high damping performance but also generate local resonance and Bragg scattering bandgaps to stop wave propagation. To characterize the evanescent waves, a wave and Rayleigh-Ritz method (WRRM) is proposed, based on the nullspace method (NSM) that assumes the response is constituted by the linear combination of the nullspace basis of the constraint matrix. The proposed WRRM is validated using numerical partial differential solutions. Analysis of the complex dispersion curves shows that multiple local resonance and Bragg scattering bandgaps take place in the whole frequency range of interest, and the damping effect can merge these bandgaps so as to form very wide attenuation bands. Not only that, remarkable evanescent waves are also observed in the passbands. The lattice constant and ABH length are studied parametrically. Results show that the larger the lattice constant, the more attenuation bands appear, and the longer ABH length can enhance the attenuation capability. Finally, the transmissibility and mean square velocity for a finite metabeam with 5 cells are investigated, indicating substantial wave damping in a broadband frequency range.