几乎掩盖了弹性波场
Nearly cloaking the elastic wave fields
摘要：
在这项工作中，我们开发了一个通用的数学框架，通过变换弹性动力学的方法由Lamé系统的弹性波的正则化近似隐形。我们的研究相当全面。我们首先提供了一个严格的理由转换弹性动力学。基于爆破点构造，导出了理想斗篷的弹性材料张量，并证明了其具有奇异性。为了避免奇异结构，我们提出将爆破点构造正则化为爆破小区域构造。然而，它示出，如果没有纳入一个合适的损耗层，正则化的建设将失败，由于谐振夹杂物。为了克服无损结构的失效，在正则化隐身结构中引入了一个合理设计的有损层。我们得到尖锐的渐近估计在评估隐身性能。所提出的隐形方案能够以高精度几乎隐形任意内容。
英文摘要：
In this work, we develop a general mathematical framework on regularized approximate cloaking of elastic waves governed by the Lamé system via the approach of transformation elastodynamics. Our study is rather comprehensive. We first provide a rigorous justification of the transformation elastodynamics. Based on the blow-up-a-point construction, elastic material tensors for a perfect cloak are derived and shown to possess singularities. In order to avoid the singular structure, we propose to regularize the blow-up-a-point construction to be the blow-up-a-small-region construction. However, it is shown that without incorporating a suitable lossy layer, the regularized construction would fail due to resonant inclusions. In order to defeat the failure of the lossless construction, a properly designed lossy layer is introduced into the regularized cloaking construction . We derive sharp asymptotic estimates in assessing the cloaking performance. The proposed cloaking scheme is capable of nearly cloaking an arbitrary content with a high accuracy.
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