Predicting the ultrasonically suppressive behavior of acoustic metasurfaces

Abstract

By combining the finite element method of thermoviscous acoustics and the temporal linear stability theory, a computational method (hereinafter referred to as FEM-LST) is proposed to predict the ultrasonically suppressive behavior of acoustic metasurfaces, especially for the ones with non-uniform cross sections. The impedance boundary condition is obtained from the FEM and then applied in the LST. The given number of collocation points and mesh configuration are verified through the dependency tests. In addition, the FEM-LST method shows its advantage in terms of convergence rate and is validated by the comparison with the direct numerical simulation data for the slot metasurface in the literature. Following the same base flow condition, more calculation examples are presented for a series of acoustic metasurfaces, including the slot, the v-slot, and the Helmholtz Resonator. The results indicate that the second mode growth rate evidently depends on both impedance magnitude and phase. For the slot metasurface, the local minimum of second mode growth rate mainly caused by phase cancellation is captured. The v-slot metasurface is found to be safe from the resonant mode near the corners over the range of cavity depth we considered. The region in which low growth rates occur is favorably broadened for the HR metasurface. Finally, from the disturbance field of second mode, it appears that the acoustic metasurfaces suppress the second mode in a way of decentralizing its energy content. Overall, the present work shows the capability of our FEM-LST method in predicting the ultrasonically suppressive behavior of acoustic metasurfaces.