English

Three-dimensional Elastic Scattering Coefficients and Enhancement of the Elastic Near Cloaking

Mathematical Physics 2020-12-08 v2 Analysis of PDEs math.MP

Abstract

This paper is concerned with the elastic near cloaking for the Lam\'e system in three-dimensions using the notion of elastic scattering coefficients (ESC). Accordingly, the ESC of arbitrary three-dimensional objects are designed and some of their properties are discussed using elements of the elastic layer potential theory. Then, near-cloaking structures, coined as ESC-vanishing-structures, are constructed for the elastic cloaking at a fixed frequency or a band of frequencies. These multi-layered structures are designed so that their first few significant ESC vanish ahead of transformation-elastodynamics. The invisibility effect is achieved as the arbitrary elastic object inside the cloak has a near-zero scattering cross-section for a band of frequencies. The cloaking effect for the Lam\'e system is significantly enhanced by the proposed near-cloaking structures.

Keywords

Cite

@article{arxiv.2003.10725,
  title  = {Three-dimensional Elastic Scattering Coefficients and Enhancement of the Elastic Near Cloaking},
  author = {Hongyu Liu and Wing Yan Tsui and Abdul Wahab and Xianchao Wang},
  journal= {arXiv preprint arXiv:2003.10725},
  year   = {2020}
}

Comments

41 pages, 4 figures