Effective Resonant Model and Simulations in the Time-Domain of Wave Scattering from a Periodic Row of Highly-Contrasted Inclusions
Effective Resonant Model and Simulations in the Time-Domain of Wave Scattering from a Periodic Row of Highly-Contrasted Inclusions
复制标题
DOI：
10.1007/s10659-020-09789-2
复制
发表时间：
2020-08-24
影响因子：
2
通讯作者：
Bellis, Cedric
中科院分区：
文献类型：
--
作者：
Touboul, Marie;Pham, Kim;Bellis, Cedric
以二维方式考虑标量波穿过周期性包裹体行的时域传播。由于假设背景介质内的典型波长远大于夹杂物之间的间距和行宽度，因此所考虑的物理配置处于低频均匀化状态。此外，还假定夹杂物和背景介质的本构模量之一之间存在高对比度。因此，夹杂物内的波长与其典型尺寸相当，这可以进一步诱发微观结构内的局部共振。在范等人。 (J. Mech. Phys. Solids 106:80-94,2017)，两尺度均质化技术和匹配渐近展开已被用来在调和状态下导出等效界面上的有效跳跃条件。由于夹杂物的共振行为，该均质化模型与频率相关。在这种情况下，本文旨在直接在时域中研究这种周期性的共振散射体行对波的散射。首先在时域中推导其有效行为，并分析所得均质化模型的一些能量特性。然后进行时域数值模拟，以说明所获得的有效界面模型的主要特征，并评估其与全场模拟的相关性。
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.