Sharma Basant Lal
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, India.
Philos Trans A Math Phys Eng Sci. 2022 Sep 5;380(2231):20210396. doi: 10.1098/rsta.2021.0396. Epub 2022 Jul 18.
For a triangular lattice of particles, with nearest neighbour interactions and a traction free boundary, there exists a surface wave band for out-of-plane motion. Interactions between such a surface wave and stationary crack tip in mode III are investigated. The discrete Helmholtz equation for scattered waves, that incorporates an anisotropy parameter for unequal spring constants in horizontal versus slant directions, is solved exactly. The coefficient of transmission from one crack face to another, as well as that owing to reflection on the same face, is obtained in a closed form; the same leads to an estimate of energy fraction of incident wave that is leaked at the crack tip via bulk waves. It is found, in terms of surface wave band, that the transmission coefficient attains its maximum magnitude above the mid-band while the energy leak is minimum at the upper-band limit. Besides surface wave propagation across crack tip, surface wave excitation due to incident bulk wave is also discussed. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.
对于具有最近邻相互作用和无牵引力边界的三角形粒子晶格，存在面外运动的表面波带。研究了这种表面波与III型静止裂纹尖端之间的相互作用。精确求解了包含水平与倾斜方向不等弹簧常数的各向异性参数的散射波离散亥姆霍兹方程。以封闭形式获得了从一个裂纹面到另一个裂纹面的透射系数以及由于在同一面上反射而产生的透射系数；这进而得出了通过体波在裂纹尖端泄漏的入射波能量分数的估计值。从表面波带的角度发现，透射系数在带中上方达到其最大值，而能量泄漏在上带极限处最小。除了表面波穿过裂纹尖端的传播外，还讨论了由入射体波引起的表面波激发。本文是主题为“多尺度复杂介质和结构化超材料中的波产生与传输（第1部分）”的一部分。
