Simple and fast determination of band structure and level repulsion in a mixed-mode metamaterial

Acoustic metamaterials are designed to manipulate sound waves for applications such as military acoustic cloaking and sound insulation. To apply metamaterials, properties derived from the band structure have to be understood. Discrete order models can predict the band structure of longitudinal or shear wave branches, but in mixed-mode metamaterials this is more challenging. A team of mechanical engineers have developed a rigorous analysis of level repulsion within a mixed-mode resonator array, which can be applied to other metamaterials with similar unit cell structure.

Amirkhizi et al. designed an easily 3D printable mixed-mode metamaterial unit cell that includes a T-shaped cantilever beam resonator and hollow frame as the cell. The team then used the finite element method to calculate the mixed longitudinal and shear wave branches at very low frequency, and produced dispersion diagrams and mode shapes. They used a novel reduced order analytical treatment to discretize the repeating unit cell into a small number of structural elements and degrees of freedom based on physical expectations.

“We showed that a good reduced order model is capable of providing band structure almost as well as full field simulation. It includes all the physics of interest and allows us to identify level repulsion in the band structure versus crossing of the branches with high accuracy and resolution,” said co-author Alireza Amirkhizi. “It’s also very simple and computationally efficient to use for oblique angles of propagation.”

They are now trying to understand how level repulsion and presence of exceptional points in the complex domain may affect the scattering of acoustic and stress waves in real-world systems. “We want to utilize these microstructured media for technological applications, such as improving sensing and source localization,” said Amirkhizi.

Source: “Reduced order derivation of the two-dimensional band structure of a mixed-mode resonator array,” by Alireza V. Amirkhizi and Weidi Wang, Journal of Applied Physics (2018). The article can be accessed at https://doi.org/10.1063/1.5057707 .