Deep-subwavelength elastic metasurface with force-moment resonators for abnormally reflecting flexural waves

The elastic metasurface with compact design and easy fabrication has provided some insight into applications of solid wave-based field owing to its novel wavefront-shaping functionality; Yet, the deep-subwavelength design remains a challenge. In this research, we propose a new design of deep-subwavelength elastic metasurface (DEM) (1/49.5 of the incident wavelength), composed of gradient force-moment resonators, to abnormally reflect flexural waves. The force-moment resonator is implemented by stacking up a lead block atop silicone rubber block. The analytical solution of the reflection coefficient is obtained based on the transfer matrix method (TMM) to predict the phase shift (full 2π span) of the reflected flexural wave. Further, a theoretically simplified two degree-of-freedom (2DOF) mass-spring model considering the stretching and rotational resonance modes of the resonator and the dynamic stiffness method (DSM) to calculate the reflection coefficient are developed to reveal the deep-subwavelength physical mechanism. Both the analytical solution and the DSM have excellent consistency with the finite element (FE) simulation. By extending 2D force-moment resonators to 3D ones, the DEM is theoretically designed based on the generalized Snell's law (GSL). FE simulations and corresponding experiments well validate the abnormal reflection performance of the present DEM. The study shows that the DEM that does not damage and is easy to install on the host plate can be effectively used for flexural wave manipulation, which has potential applications in vibration control, wave absorption and energy harvesting.