Khusnutdinova K R, Tranter M R
Department of Mathematical Sciences , Loughborough University , Loughborough LE11 3TU, UK.
Proc Math Phys Eng Sci. 2015 Nov 8;471(2183):20150584. doi: 10.1098/rspa.2015.0584.
Integrity of layered structures, extensively used in modern industry, strongly depends on the quality of their interfaces; poor adhesion or delamination can lead to a failure of the structure. Can nonlinear waves help us to control the quality of layered structures? In this paper, we numerically model the dynamics of a long longitudinal strain solitary wave in a split, symmetric layered bar. The recently developed analytical approach, based on matching two asymptotic multiple-scales expansions and the integrability theory of the Korteweg-de Vries equation by the inverse scattering transform, is used to develop an effective semi-analytical numerical approach for these types of problems. We also employ a direct finite-difference method and compare the numerical results with each other, and with the analytical predictions. The numerical modelling confirms that delamination causes fission of an incident solitary wave and, thus, can be used to detect the defect.
广泛应用于现代工业的层状结构的完整性，在很大程度上取决于其界面的质量；附着力差或分层会导致结构失效。非线性波能帮助我们控制层状结构的质量吗？在本文中，我们对一个分裂的对称层状杆中的长纵向应变孤立波的动力学进行了数值模拟。基于匹配两个渐近多尺度展开以及通过逆散射变换的Korteweg-de Vries方程的可积性理论，最近开发的分析方法被用于为这类问题开发一种有效的半解析数值方法。我们还采用了直接有限差分法，并将数值结果相互比较，以及与解析预测结果进行比较。数值模拟证实分层会导致入射孤立波的裂变，因此可用于检测缺陷。
