Metasurface constituted by thin composite beams to steer flexural waves in thin plates

We report a novel approach to control flexural waves in thin plates using metasurfaces constituted of an array of parallel arranged composite beams with their neutral planes the same as that of the host plate. The composite beams are composed of two connecting parts made of different materials, and have a thickness identical to that of the host plate. To steer flexural waves in thin plates, a rectangular zone is subtracted from the thin plate and is then filled with the designed metasurface. The time delay of flexural waves in each composite beam of the metasurface is tuned through the varying length of the two connecting components, while keeping the total length fixed. To quantitatively evaluate the time delay in each composite beam, a theoretical model for analyzing the phase of the transmitted flexural waves is developed based on both Mindlin plate theory and Timoshenko beam theory. To control the flexural waves at will, each composite beam in the metasurface is delicately designed according to the proposed theoretical model. For illustrative purposes, the refracted and focusing metasurfaces are designed and numerically validated.