圆柱形分层五模材料声学隐身衣的理论与数值分析

Theoretical and numerical analysis of layered cylindrical pentamode acoustic cloak

声学隐身衣物性参数分布的连续性对制备造成了很大困难,需要采用分层的方法进行近似.研究分层对隐身衣性能的影响具有重要意义.本文首先推导了圆柱形分层声学隐身衣散射声压场的理论解,然后通过数值算例验证了理论推导的正确性,最后针对层数、层厚分布对隐身衣性能的影响进行了计算研究.结果表明,选取恰当的层数和层厚分布可在不增加制备难度的同时改善隐身衣性能.

As a newly-developed method, acoustic cloak made of pentamode materials is on its speedway to the promising potential application. However, physical fabrication of pentamode cloak with continuously varying material parameters can be a tough work, if not totally impossible. Layering is a natural compromise to bypass this quandary. Researches on layering effects of inertial cloak are ample. However, researches on layering pentamode acoustic cloak are relatively limited. Among these researches Scandrett extends the effective bandwidth through optimization of material parame-ters[2010 J. Acoust. Soc. Am. 127 2856, 2011 Wave Motion. 48 505]. 〈br〉 The present work concerns the layering effects of pentamode acoustic cloak. By comparing with precedent results, the present paper has two major innovations： Firstly, cylinder is chosen to be the basic geometry. This is of obvious advantage since cylinder is the basic geometry of acoustic cloak’s important potential host. Secondly, effects of layers’ number and thickness distribution on the stealth effect are analyzed. The two are key parameters to be determined in the layering process. This paper is organized as follows： Firstly, analytical expression of the scattering pressure field of layered cloak is deduced by means of variables separation. In this process Fourier expansion plays a key role. And the harmonic assumption of the incident acoustic wave is made. Secondly, typical cases are calculated to verify the validation of the theoretical analysis. First let material parameters tend towards that of water, and compare the scattering field with that of the bare rigid object when the cloak is replaced by water. Second let the layering number goes to infinity, and compare the scattering field with that of the continuous cloak. Phenomena conforming with basic physical laws are observed. And validity of the theory and codes is confirmed. Thirdly, effects of layers’ number and thickness distribution on the stealth character are theoretically and numerically analyzed. One can easily see from the computational results that a critical number N exists. When layers’ number exceeds N , improvement of the stealth effect becomes less e？cient by further adding layers’ number. One can also see from the computational results that a wise distributional strategy that helps improve the stealth effect indeed exists. And the optimization iteration can be utilized to further improve it. 〈br〉 As a summary, the present paper concerns the layering process of cloaking. Qualitatively and quantitatively, several significant results are obtained. This paper offers a useful reference for future fabrication of realistic acoustic pentamode cloak.