Simulation study on characteristics of acoustic metamaterials based on Mie and Helmholtz resonance for low-frequency acoustic wave control

An increasing number of applications require a low-frequency acoustic source to achieve a high sound pressure level (SPL) in the far field; however, controlling low-frequency waves remains a challenge. Recently, phononic crystals have provided a new way to control acoustic waves. For example, the Mie resonant structure, which can reflect low-frequency acoustic waves effectively with its subwavelength size, has been used to realize an acoustic collimated beam. In this work, on the basis of the Mie resonant structure, we designed a Mie-Helmholtz structure (M-H structure) that can use the high sound pressure inside the central cavity to further enhance the far-field SPL and unidirectional directivity. The developed design consists of adding two shells on both sides of the maze-like structure and creating a hole in the middle of the upper shell. We used modal analysis, equivalent medium method to study the structure and obtained lumped parameter model, finding that the M-H structure has physical properties in the XY plane similar to those of the Mie structure while showing a Helmholtz amplification effect in the Z direction. To explore the effect of the new structure on realizing the directivity of low-frequency waves, we also compared the sound field between M-H structure and M-structure. The simulation results showed 8.4% enhancement of the far-field sound intensity and 61.9% enhancement of the directivity index (DI) in main lobe direction. We also provided an example of how this design can be applied to improve low-frequency loudspeaker directivity by adding 4M-H structures and found that the radiation power was restrained in the XY plane and showed better unidirectional directivity (DI ⩾4 dB) in the Z direction. The location of M-H structure for better unidirectional directivity (DI = 9.1 dB) have also been investigated. Finally, we studied the influence of different sizes on the resonance frequency and the SPL gain at the middle hole to explore a guidance for design.