Acoustic metamaterials with near-zero density effects for acoustic focusing

Acoustic focusing technology has demonstrated significant application prospects across multidisciplinary fields. Based on the principle of fractal self-similarity, this study proposes a novel fractal acoustic metamaterial. Calculations of equivalent acoustic parameters reveal that this structure exhibits near-zero density effects at frequencies of 2271 Hz and 3872 Hz. Further analysis elucidates the bandgap characteristics of the fractal unit, demonstrating that its formation mechanism stems from negative equivalent mass density induced by even-order resonance, thereby blocking sound wave propagation and generating bandgaps. Leveraging this principle, two types of near-zero-density acoustic focusing lenses were designed, achieving point focusing and line focusing functionalities, respectively. These lenses exhibit an acoustic diode effect, enabling asymmetric sound wave transmission. By reconfiguring the fractal structural units, the lens radius and aperture angle can be modified to achieve focal point positioning control. Subsequently, an analysis of the system robustness indicates that the designed acoustic focusing lenses possess commendable system robustness. Furthermore, a multi-directional focusing acoustic lens was designed, capable of focusing sound waves in different directions, thereby providing a design basis for omnidirectional acoustic focusing lenses. Finally, experimental measurements of the sound pressure field for Lens A were conducted. The measured results show close agreement with simulation analyses, confirming the structural effectiveness and computational accuracy.