Compact and efficient elastic metasurface based on mass-stiffness relation for manipulation of flexural waves

Metasurfaces are a group of lower dimensional metamaterials. They have shown excellent capacities in precise and efficient manipulation of wavefront at-will. However, most of them suffer from low transmission performances since they only consider the control of phase but ignore the impedance that determines transmission behaviours. To optimize the behaviours of metasurface, we employ the mass-stiffness relation to realize efficient manipulation of flexural waves. We use external mass blocks (pillars) to tune the effective mass and cut grooves in connecting beams to release effective stiffness. The two degrees of freedom are used to control the two design targets: local phase shift and impedance. Based on the theoretical analysis and finite element simulations, a three-unit metasurface with high transmission performances and compact geometry is designed. From the comparisons with currently existed designs, we show that our proposed metasurface is much more efficient and compact. This research may play an important role in guidance of the design of highly efficient and compact metasurfaces for precise engineering of elastic wavefront.