Use of loss limit approach to zero in scattering-based parameter retrieval of elastic micro-structured media
Use of loss limit approach to zero in scattering-based parameter retrieval of elastic micro-structured media
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DOI：
10.1016/j.ijsolstr.2020.05.010
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发表时间：
2020-09
影响因子：
3.6
通讯作者：
R. Abedi;A. Amirkhizi
中科院分区：
文献类型：
--
作者：
R. Abedi;A. Amirkhizi
采用基于散射数据的参数提取方法求取周期结构固体的动态本构参数。反演的波数和阻抗符号的实部存在固有的模糊性，尽管后者与能量流方向一一对应。此外，对于无损结构，可以存在满足作为频率函数的波数的无源性和连续性的多个解分支，从而导致对微结构介质的潜在的双正或双负(就密度和模数而言)的总体描述。利用有耗单元波数的连续性来明确地确定其本构参数，并在损耗趋于零时取极限值，从而确定无损微结构的稳定解分支。比较了非零阻尼型和复模量型两种损耗模型的能量损耗特性和恢复参数。这些模型被用在时间域和频域计算中。有耗解表明，在双负双正解中，只有后者是无耗一维单胞通带内的稳定解分支。用一个二维光子晶体的例子说明了波数在两个连续阻带之间的过渡点出现了不连续的跳跃，从而使现有的基于波数连续性的方法失效。相反，基于有损解取限的方法可以成功地确定这类介质的稳定的整体性质。最后讨论了半周期和全周期阻带的某些特性。
The parameter retrieval method based on scattering data is used to derive dynamic constitutive parameters of solids with periodic structure. There are inherent ambiguities in the real part of the retrieved wavenumber and the sign of impedance, though the latter has a one-to-one correspondence with the direction of energy flux. Moreover, for lossless structures there can be multiple solution branches that satisfy passivity and continuity of the wavenumber as a function of frequency, leading to potentially double positive or double negative (in terms of density and modulus) overall descriptions of the micro-structured medium. The continuity of wavenumber for lossy unit cells is used to unambiguously determine their constitutive parameters and by taking the limit when loss approaches zero, one can determine the stable solution branches of lossless micro-structures. The two loss models of nonzero damping and complex modulus are compared in terms of their energy loss characteristics and retrieved parameters. These models are employed in both time and frequency domain calculations. The lossy solutions demonstrate that from double-negative and double-positive solutions, only the latter is the stable solution branch in a pass-band of a lossless 1D unit cell. A 2D photonic crystal example is used to demonstrate that the wavenumber appears to jump, discontinuously, at the transition point between two consecutive stop-bands, hence rendering the existing methods based on continuity of wavenumber ineffective. In contrast, the proposed approach based on taking limit of lossy solutions can successfully be used to determine stable overall properties of such media. Finally, certain features of half- and full-cycle stop-bands are discussed.