Mikhasev G I, Botogova M G, Eremeyev V A
Faculty of Mechanics and Mathematics, Belarusian State University, Nezavisimosty Ave. 4, 220030 Minsk, Belarus.
Department of Civil and Environmental Engineering and Architecture (DICAAR), University of Cagliari, Via Marengo 2, 09123 Cagliari, Italy.
Philos Trans A Math Phys Eng Sci. 2022 Sep 5;380(2231):20210373. doi: 10.1098/rsta.2021.0373. Epub 2022 Jul 18.
We consider anti-plane motions of an elastic plate taking into account surface energy within the linear Gurtin-Murdoch surface elasticity. Two boundary-value problems are considered that describe complete shear dynamics of a plate with free faces or with free and clamped faces, respectively. These problems correspond to anti-plane dynamics of an elastic film perfectly or non-perfectly attached to a rigid substrate. Detailed analysis of dispersion relations is provided. In particular, the influence of the ratio of a plate thickness to characteristic length on the dispersion curves is analysed. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.
我们考虑线性古尔廷-默多克表面弹性理论中包含表面能的弹性板的反平面运动。研究了两个边值问题，分别描述了具有自由表面或自由与夹紧表面的板的完全剪切动力学。这些问题分别对应于完美或不完美附着在刚性基底上的弹性薄膜的反平面动力学。给出了色散关系的详细分析。特别分析了板厚度与特征长度之比对色散曲线的影响。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播（第1部分）”的一部分。
