Flexural wave manipulation by deep-subwavelength beam-type elastic metasurface

The manipulation of flexural waves in thin plates using compact elastic metasurfaces is of fundamental interest in wave physics and structural dynamics. In this work, a deep-subwavelength beam-type elastic metasurface (BEM) is proposed for anomalous reflection of flexural waves. The metasurface consists of a periodic array of gradient beam-type resonators attached to a host plate, with a thickness of only 1/49.5 of the incident flexural wavelength. A theoretical model is developed based on the coupled flexural-longitudinal wave motion of the resonator-plate system, and the reflection coefficient is derived using the transfer matrix method. The analytical results show that the proposed beam-type resonator can provide an almost full 2π reflection phase span by tuning the resonator height while maintaining a high reflection amplitude over most of the investigated parameter range. Finite-element simulations are performed to validate the analytical predictions, showing good agreement in both reflection phase and amplitude. The two-dimensional beam-type resonator model is further extended to a practical three-dimensional metasurface configuration, and a phase-gradient supercell is designed according to the generalized Snell's law. Numerical simulations demonstrate that the designed metasurface can redirect normally and obliquely incident flexural-wave Gaussian beams toward prescribed anomalous reflection directions. The results reveal the wave-manipulation mechanism of the beam-type resonator and provide a compact route for deep-subwavelength control of flexural-wave reflection in plate structures.