Design of elastic metasurfaces for controlling shear vertical waves using uniaxial scaling transformation method

Abstract

Controlling wave propagation is a popular research field; however, progress with regard to the study of elastic waves is slow because of the coupling of different types of waves. In this paper, we report a novel approach to design elastic metasurfaces for controlling elastic shear vertical (SV) waves in solids. The metasurface is composed of separate parallel thin plates connected at both ends to half-space solids. The elastic SV-waves in solids were controlled by manipulating the induced flexural waves in the thin plates of the metasurface. Based on the form invariance of the governing equation for flexural waves in a thin plate under linear coordinate transformations, the uniaxial scaling transformation method (USTM) has been put forward to alter the material to constitute the thin plates of the metasurface. The transformed material is transversely isotropic, which greatly reduces implementation difficulties. To tune the traveling times of the flexural waves in the thin plates, different values of the scaling parameter α and plate thickness h were assigned for different thin plates based on the Kirchhoff plate theory. By combining the plate thickness variation approach with the USTM, the plate length of the metasurface could be effectively controlled to be smaller than the wavelength at the working frequency. To demonstrate the performance of the proposed approach, two designs of elastic metasurfaces for wave focusing and abnormal refraction were described in detail, and full numerical simulations were conducted. The present approach opens a promising avenue toward the realization of metasurfaces for controlling elastic waves.