Dispersion and ellipticity of Rayleigh waves in a soil substrate supporting resonant beams and plates

The behavior of surface waves in a soil supporting an array of beams in three dimensions, or an array of plates in two dimensions, with compressional and flexural resonances is examined both theoretically and numerically. Our findings demonstrate that Love waves, characterized by displacements perpendicular to the sagittal plane, can propagate even without a homogeneous guiding layer, owing to the influence of flexural resonances in beams. Within the sagittal plane, hybridized Rayleigh waves exhibit a dispersion that is notably altered by the presence of the array, with their properties emerging from the interaction between flexural and compressional resonances. Notably, we uncover the coexistence of two Rayleigh waves with distinct wave numbers within specific frequency ranges, corresponding to prograde and retrograde motions. Additionally, both waves significantly amplify ground motion, either horizontally or vertically. Similar physics, yet quantitatively different, is demonstrated in the case of plate arrays.