Negative Schoch displacement of two-dimensional acoustic metamaterials with near-zero refractive index

Abstract

In this paper, the Schoch displacement at the interface between different two-dimensional triangular phononic crystal metamaterial and natural material is studied by using finite element software. As is well known, the Schoch displacement is highly dependent on the surface wave and leakage wave excited at the interface between different materials. So, the negative Schoch displacement can be more easily obtained by adding a suitable thickness of covering layer at the interface between metamaterial material and natural material. The numerical results show that when the negative Schoch displacement happens, the effective parameters of metamaterials are close to zero. It means that the effective refraction index is near to zero and the reduced frequency of the incident acoustic wave is correlated with the reduced frequency of the band gap. It is also found from the results that the reduced frequency of the incident acoustic wave is located at the edge of the band gap when the negative Schoch displacement occurs. The maximum of the metamaterial effective impedance and the maximum of the reflection coefficient are almost at the same frequency. The phase of the imaginary part of the reflection coefficient has a phase mutation in π rad at the corresponding frequency. The frequency of negative Schoch displacement is located in the first band gap of <i>MK</i> direction and near the upper boundary. The Schoch displacement at the interface between conventional materials is usually positive and negligible in previous reports. In this paper, the negative Schoch displacement is obtained by using the near-zero refraction index metamaterials. This not only enriches the physics contents of Schoch effect but also provides a theoretical reference for designing the acoustic devices based on acoustic wave displacement at the interface.