Broad band gaps for flexural wave manipulation in plates with embedded periodic strip acoustic black holes

Abstract

Abstract Acoustic black holes (ABHs) achieved by thinning structural thickness following a power-law profile have shown fantastic applications in vibration and noise suppression, energy harvesting, and wave manipulation. For the latter, many passband properties exemplified by self-collimation, focusing, and bi-refraction, have been reported on metamaterial plates with embedded circular ABHs in periodic arrangement. To date, however, band gaps (BGs), being the main feature for metamaterials, have not yet been observed in ABH plates. In this paper, we propose a new class of phononic crystal consisting in two crossed strip ABHs to open broad and complete BGs in plates, based on the dual benefit of local resonance and Bragg scattering effect. The dispersion curves of infinite strip ABHs are recovered by means of the Gaussian expansion method, then validated by a finite element model. The influences of ABH radius, ABH order and residual thickness, on the GBs have been carried out by parametric studies. The results show that the BGs can be modulated to very low frequencies via adjusting the ABH parameters, while maintaining the broadband characteristics. Finally, the wave propagation properties including isolation, guiding, and shielding, in plates with finite periodic arrays have been characterized, indicating that a small number of ABHs are very efficient to quarantine flexural waves. Experimental samples have been fabricated and tested, showing very close results compared to the BGs predicted by the GEM. Even though the proposed strip ABHs seems fragile in strength, peripheral frame can be adopted to partially alleviate this problem. The proposed PCs possess a great potential to broaden ABH applications in vibration control and wave manipulation in plates based on the highlighted BG feature.