The time-domain propagation of scalar waves across a periodic row of inclusions is considered in 2D. As the typical wavelength within the background medium is assumed to be much larger than the spacing between inclusions and the row width, the physical configuration considered is in the low-frequency homogenization regime. Furthermore, a high contrast between one of the constitutive moduli of the inclusions and of the background medium is also assumed. So the wavelength within the inclusions is of the order of their typical size, which can further induce local resonances within the microstructure. In Pham et al. (J. Mech. Phys. Solids 106:80–94, 2017), two-scale homogenization techniques and matched-asymptotic expansions have been employed to derive, in the harmonic regime, effective jump conditions on an equivalent interface. This homogenized model is frequency-dependent due to the resonant behavior of the inclusions. In this context, the present article aims at investigating, directly in the time-domain, the scattering of waves by such a periodic row of resonant scatterers. Its effective behavior is first derived in the time-domain and some energy properties of the resulting homogenized model are analyzed. Time-domain numerical simulations are then performed to illustrate the main features of the effective interface model obtained and to assess its relevance in comparison with full-field simulations.

中文翻译：

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高对比度夹杂物周期性行的波散射时域中的有效共振模型和模拟

在二维中考虑标量波在周期性包裹体行上的时域传播。由于假设背景介质中的典型波长远大于夹杂物之间的间距和行宽，因此所考虑的物理配置处于低频均化状态。此外，还假定夹杂物的本构模量之一与背景介质的本构模量之间存在高对比度。因此，夹杂物内的波长与其典型尺寸的数量级相同，这可以进一步引起微观结构内的局部共振。在范等人。(J. Mech. Phys. Solids 106:80–94, 2017)，两尺度均匀化技术和匹配渐近扩展已被用于在调和状态下推导出等效界面上的有效跳跃条件。由于夹杂物的共振行为，这种均质模型与频率有关。在这种情况下，本文旨在直接在时域中研究这样一排周期性共振散射体对波的散射。它的有效行为首先在时域中导出，并分析了所得均质模型的一些能量特性。然后进行时域数值模拟，以说明获得的有效界面模型的主要特征，并与全场模拟比较评估其相关性。它的有效行为首先在时域中导出，并分析了所得均质模型的一些能量特性。然后进行时域数值模拟，以说明获得的有效界面模型的主要特征，并与全场模拟比较评估其相关性。它的有效行为首先在时域中导出，并分析了所得均质模型的一些能量特性。然后进行时域数值模拟，以说明获得的有效界面模型的主要特征，并与全场模拟比较评估其相关性。