Dynamic response and localization in strongly damaged waveguides
Dynamic response and localization in strongly damaged waveguides
复制标题
DOI：
10.1098/rspa.2014.0136
复制
发表时间：
2014-07-08
影响因子：
3.5
通讯作者：
Movchan, A. B.
中科院分区：
文献类型：
--
作者：
Carta, G.;Brun, M.;Movchan, A. B.
在本文中，我们研究了带隙的形成和局部化现象的弹性带几乎崩解的横向裂纹阵列。本文以具有周期性损伤的无限长条的传播带为参考，分析了有限强损伤细长固体的本征频率。随后，我们通过使用低维模型解析确定无限条的带隙，该模型由周期性损伤的梁表示，其中裂缝之间的小韧带被建模为“弹性连接”。通过随机渐近分析，得到了弹性结点的有效转动刚度和平动刚度。结果表明，在有限的频率范围内，简化光束模型的色散曲线与二维弹性条的数值色散曲线一致。详细讨论了强损伤系统中的指数局域化、边界层和驻波。
In this paper, we investigate the formation of band-gaps and localization phenomena in an elastic strip nearly disintegrated by an array of transverse cracks. We analyse the eigenfrequencies of finite, strongly damaged, elongated solids with reference to the propagation bands of an infinite strip with a periodic damage. Subsequently, we determine analytically the band-gaps of the infinite strip by using a lower-dimensional model, represented by a periodically damaged beam in which the small ligaments between cracks are modelled as 'elastic junctions'. The effective rotational and translational stiffnesses of the elastic junctions are obtained from an ad hoc asymptotic analysis. We show that, for a finite frequency range, the dispersion curves for the reduced beam model agree with the dispersion data determined numerically for the two-dimensional elastic strip. Exponential localization, boundary layers and standing waves in strongly damaged systems are discussed in detail.