弯曲波的变换弹性动力学和隐身
Transformation elastodynamics and cloaking for flexural waves
摘要：
本文讨论了弹性薄板中弯曲波的四阶偏微分方程的一个重要问题：隐式变换。它表明，在对比亥姆霍兹方程，偏微分方程的一般形式是不是不变的隐形变换。本文的重要成果是对转换方程的分析及其在预应力板线性理论框架下的解释。本文提供了一个正式的框架转换弹性动力学适用于弹性板。此外，提出了一种算法设计的弯曲波，它采用了正则化推出变换的方形斗篷。数值算例表明该算法具有较高的精度和效率。特别是，涉及由两个相干源产生的干涉图案的扰动的物理配置。它表明，由隐形缺陷产生的扰动是可以忽略不计的小，即使是这样一个微妙的干涉图案。
英文摘要：
The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general form of the partial differential equation is not invariant with respect to the cloaking transformation. The significant result of this paper is the analysis of the transformed equation and its interpretation in the framework of the linear theory of pre-stressed plates. The paper provides a formal framework for transformation elastodynamics as applied to elastic plates. Furthermore, an algorithm is proposed for designing a square cloak for flexural waves, which employs a regularised push-out transformation. Illustrative numerical examples show high accuracy and efficiency of the proposed cloaking algorithm. In particular, a physical configuration involving a perturbation of an interference pattern generated by two coherent sources is presented. It is demonstrated that the perturbation produced by a cloaked defect is negligibly small even for such a delicate interference pattern.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
