Efficient absorption of flexural waves by a lossy coupled-mode meta-layer

Elastic metasurfaces offer a promising paradigm for wave manipulation with compact and lightweight structures. By placing a metasurface at the edge of a plate, total absorption of reflected waves has recently been achieved to exhibit strong potential for vibration control. However, in a general case, simultaneous suppression of both reflected and transmitted waves is fundamentally challenging, because a single-mode structure is inherently limited to a maximum absorption of 0.5. Here, we propose a lossy coupled-mode meta-layer (LCMM), which couples translational and rotational modes simultaneously, to totally absorb flexural waves when attached at an arbitrary position on the plate. A coupled-mode theoretical model is developed to reveal that the translational and rotational modes independently govern symmetric and antisymmetric scattering eigenchannels. It shows that total absorption is achieved when both modes satisfy respective critical conditions. Guided by the theoretical model, we design a lossy U-shaped cantilevered resonator as the unit cell of the LCMM, achieving an absorption coefficient of up to 0.99 with a characteristic dimension of approximately 0.5λ. The analysis is further extended to oblique incidence to determine the angle-dependent dual critical conditions revealing the origin of the LCMM's quasi-omnidirectional absorption. The meta-layer is further arranged into a closed-ring configuration to exploit its bidirectional absorption capability for suppressing structural vibrations induced by waves incident from both inside and outside. This work provides a generalizable paradigm for robust wave absorption, with significant implications for vibration control in plate-like structures.