Attenuation band splitting in a finite plate strip with two-dimensional acoustic black holes

Acoustic black holes (ABH) lattice is an effective way to realize the bandgaps (BGs) through lightweight design. The predicted BGs using infinitely large periodic structures are commonly believed to enable corresponding attenuation bands (ABs) even the structure only contains a limited number of unit cells. This paper reports an unusual splitting phenomenon in the ABs of a finite plate strip with two-dimensional (2D) ABHs. A wide AB predicted by BG is split into two ABs in the finite strip separated by a high resonance peak, which challenges the aforementioned common belief. Results show that the increasing number of periodic unit cells has a negligible effect on the frequency and amplitude of the resonance peak. Its underlying mechanism is clarified by investigating the relationship between the BGs and ABs, obtained from infinite and finite periodic plate strips with the same 2D ABHs respectively. Complex wavenumber analysis results show the existence of two flexural wave modes in the considered frequency range due to the finite width of the strip. Two types of BGs, in which one satisfies the Bragg condition, are found when both wave modes fail to propagate. Analysis of structural modes further uncover the physical reason for the emerging AB splitting: a certain natural frequency of the boundary portion of the 2D ABHs strip falling into the theoretical BG. Due to the boundary reflection and energy concentration, this structural portion can loosely be regarded as a clamped-free plate strip. It is demonstrated that the resonance peak splitting the AB becomes tunable via disrupting the structural details of finite ABH strips. In particular, extending the terminal end of a finite ABH strip allows the change in boundary portion, which is conducive to eliminating the splitting peak. The reported study is helpful for the design of finite periodic structures with broadband attenuation bandgap.