Theoretical analysis and experimental verification of effective properties and wave-manipulation capabilities in hollow rectangular acoustic metamaterials

Abstract Acoustic metamaterials have attracted considerable attention because of their ability to manipulate sound waves in unconventional ways. In this study, a hollow rectangular acoustic metamaterial embedded in an air background medium was proposed to explore its capability for acoustic-wave convergence. A theoretical model was developed to calculate the equivalent parameters of the structure based on equivalent medium theory and scattering acoustics theory. To validate the accuracy and reliability of the derived formulas, parametric studies were conducted by adjusting the geometric configuration of unit cells and comparing the results with theoretical predictions. Furthermore, finite element analysis was employed to simulate the acoustic wave propagation and to extract the sound speed distributions, providing additional verification of the theoretical model. Using the established formulas, the dimensional parameters of each layered unit were designed according to a predefined refractive index profile, and the full metamaterial structure was modeled accordingly. In the air background field, the sound pressure at the center of the structure is significantly higher than that in the regions on both sides, with a pressure level difference of approximately 6 dB between the center and the sides. Moreover, the designed structure exhibits pronounced acoustic wave convergence within the frequency range of 1500 Hz to 3600 Hz. In contrast, a control experiment conducted in pure air showed no convergence within this range, further confirming the structure’s ability to precisely control and guide sound waves within a defined frequency band.To further validate the design, an experimental setup for acoustic energy harvesting was constructed by integrating the metamaterial with piezoelectric energy conversion technology. The experimental results showed that the sound wave amplitude measured at the central point reached its maximum, while the amplitudes at adjacent points were significantly lower. This focusing effect is in good agreement with both theoretical predictions and simulation results.This study provides a solid foundation for the design of acoustic metamaterials capable of achieving sound wave convergence.