In a previous study (Marigo et al. in J. Mech. Phys. Solids 143:104029, 2020) we have studied the effect of a periodic array of subwavelength plates or beams over a semi-infinite elastic ground on the propagation of waves hitting the interface. The study was restricted to the low frequency regime where only flexural resonances take place. Here, we present a generalization to higher frequencies which allows us to account for both flexural and longitudinal resonances and to evaluate their interplay. An effective model is obtained using asymptotic analysis and homogenization techniques, which can be expressed in terms of the ground alone with an effective dynamic (frequency-dependent) boundary conditions of the Robin’s type. For an in-plane wave at oblique incidence, the scattered displacement fields and the reflection coefficients are obtained in closed forms and their effectiveness to reproduce the actual scattering is inspected by comparison with direct numerics in a two-dimensional setting.

在之前的一项研究中（Marigo 等人在 J. Mech. Phys. Solids 143:104029, 2020）中，我们研究了亚波长板或梁的周期性阵列在半无限弹性地面上对撞击波传播的影响界面。该研究仅限于仅发生弯曲共振的低频区域。在这里，我们对更高频率进行了概括，这使我们能够考虑弯曲和纵向共振并评估它们的相互作用。使用渐近分析和均匀化技术获得了一个有效模型，该模型可以单独根据具有 Robin 类型的有效动态（频率相关）边界条件的地面来表示。对于斜入射的面内波，