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Transformation method and wave control

ISSN号：0567-7718
期刊名称：Acta Mechanica Sinica
时间：0
页码：889-898
分类：O441[理学—电磁学;理学—物理] TP311[自动化与计算机技术—计算机软件与理论;自动化与计算机技术—计算机科学与技术]
作者机构：[1]School of Aerospace Engineering,Beijing Institute of Technology, 100081 Beijing,China, [2]School of Information and Electronics, Beijing Institute of Technology,100081 Beijing,China
相关基金：supported by the National Natural Science Foundation of China（10832002）; the National Basic Research Program of China（2006CB601204）.
相关项目：电磁波/声波超材料物理力学理论与多功能设计原理

关键词：控制框架, 变换方法, 弹性动力学方程, 电磁波方程, 转化关系, 变换关系, 转化过程, 物理过程, Wave control, Elastic wave, Acoustic wave Electromagnetic wave, Local affine transformation

中文摘要：

转变方法提供一个有效方法由材料控制波浪繁殖。为地和材料的转变关系在转变期间是必要的完成这个方法。我们建议一个系统的方法为一个一般药品过程导出转变关系，限制条件被在印射期间考虑几何、物理的限制获得。建议方法为电磁波为 elastodynamics，为声学的波浪的 Helmholtzs 方程和马方程被用于 Naviers 方程，相应转变关系被导出，它能为波浪控制在转变方法的框架被使用。我们证明与电磁波相反，转变关系不为有弹性的波浪和声学的波浪是特别地坚定的，因此我们有自由不同地选择他们。用获得的转变关系，我们也为设备设计，为有弹性的波浪的一个选矿厂，为声学的幻想的设备和幻想提供一些例子光学被数字模拟构思并且验证。

英文摘要：

Transformation method provides an efficient way to control wave propagation by materials.The transformed relations for field and material during a transformation are essential to fulfill this method.We propose a systematic method to derive the transformed relations for a general physic process,the constraint conditions are obtained by considering geometrical and physical constraint during a mapping. The proposed method is applied to Navier＇s equation for elastodynamics,Helmholtz＇s equation for acoustic wave and Maxwell＇s equation for electromagnetic wave,the corresponding transformed relations are derived,which can be used in the framework of transformation method for wave control.We show that contrary to electromagnetic wave,the transformed relations are not uniquely determined for elastic wave and acoustic wave,so we have a freedom to choose them differently.Using the obtained transformed relations,we also provide some examples for device design,a concentrator for elastic wave,devices for illusion acoustic and illusion optics are conceived and validated by numerical simulations.

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