Modulated flexural edge waves in a plate with its free edge structured by an array of grooves

A flexural edge wave (FEW) is a guided wave propagating along the free edge of a semi-infinite isotropic elastic thin plate. Here, we investigate the FEW in a plate with its free edge structured by an array of grooves, revealing the essence of a kind of modulated FEW. We analytically solve the dispersion relation of the modulated FEW by developing the coupled mode theory (usually used in diffraction optics and acoustics) that couples diffraction modes and high-order flexural waveguide modes, and discuss the propagation characteristics of the first- and second-order modulated FEWs (symmetric and antisymmetric modes, respectively). Based on the features of the dispersion curves corresponding to the unit cells of the plate with grooves of graded depths, we numerically and experimentally realize the rainbow trapping of the first-order modulated FEW and the mode conversion of the second-order modulated FEW to the bulk wave. Our work provides new ideas for the manipulation of flexural waves and has the potential to develop corresponding acoustic devices based on the FEW.