Multiscale Modeling &Simulation, Volume 22, Issue 2, Page 713-751, June 2024.
Abstract. This paper is devoted to establishing the resonant modal expansion of the low-frequency part of the scattered field for acoustic bubbles embedded in elastic materials. Due to the nanobubble with damping, the Minnaert resonance can be induced at certain discrete resonant frequencies, which forms the fundamental basis of effectively constructing elastic metamaterials via the composite material theory. There are two major contributions in this work. First, we ansatz a special form of the density, approximate the incident field with a finite number of modes, and then obtain an expansion with a finite number of modes for the acoustic-elastic wave scattering in the time-harmonic regime. Second, we show that the low-frequency part of the scattered field in the time domain can be well approximated by using the modal expansion with sharp error estimates. Interestingly, we find that the 0th mode is the main contribution to reconstruct the information of the low-frequency part of the scattered field.

中文翻译：

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弹性材料中纳米气泡时域弹性散射的共振模态近似

多尺度建模与仿真，第 22 卷，第 2 期，第 713-751 页，2024 年 6 月
。摘要。本文致力于建立嵌入弹性材料中的声气泡的散射场低频部分的共振模态展开。由于纳米气泡具有阻尼，可以在一定的离散共振频率下诱发明纳尔特共振，这为利用复合材料理论有效构建弹性超材料奠定了基础。这项工作有两个主要贡献。首先，我们提出一种特殊形式的密度，用有限数量的模式近似入射场，然后获得时谐状态下声弹性波散射的有限数量模式的展开。其次，我们表明，通过使用具有尖锐误差估计的模态展开，可以很好地近似时域中散射场的低频部分。有趣的是，我们发现第0模态对重建散射场低频部分的信息有主要贡献。