Broadband locally resonant band gaps in periodic beam structures with embedded acoustic black holes

Abstract

The Acoustic Black Hole (ABH) effect can be used to effectively reduce structural vibrations by trapping flexural waves in a thin-walled structure with a power-law thickness variation. In the present study, we used a wavelet-decomposed energy method to investigate an Euler-Bernoulli beam embedded with multiple ABHs. Broadband transmission attenuation bands at relatively low frequencies are observed in a beam containing only a few ABH elements. To explain the underlying phenomena, an infinite structure with periodic ABH elements is analyzed. Numerical results show that the periodic boundary conditions in terms of displacement and rotational slope of a unit cell, based on the finite model, are sufficient to describe the band structures, without requiring full treatment of the entire infinite structure. This provides an efficient and flexible means to predict, and eventually optimize, the band structure based on a single element. Meanwhile, the ABH-induced locally resonant band gaps coincide with the attenuation bands observed in the finite beams. Because of the unique ABH feature, the proposed beam requires only a small number of elements to obtain broad attenuation bands, which offers great potential for vibrational isolation applications and wave filter designs in beam structures.