双层脱层中辐射孤立波与耦合Ostrovsky方程
On radiating solitary waves in bi-layers with delamination and coupled Ostrovsky equations
摘要：
我们研究了一个长的纵向辐射体应变孤立波的散射在分层区域的两层弹性结构与软（“软”）之间的层耦合Boussinesq方程的范围内的结合。直接数值模拟这个和类似的问题是具有挑战性的，有自然的局限性。我们开发了一种半解析方法，基于使用几个匹配的渐近多尺度展开和平均相对于快速的空间变量，导致耦合Ostrovsky方程在保税区和非耦合Korteweg-de Vries方程在脱层区域。我们表明，半解析方法与直接数值模拟吻合良好，并使用它来研究辐射孤立波的非线性动力学和散射在广泛的双层脱层。结果表明，辐射孤立波可以帮助我们控制具有不完美界面的层状结构的完整性。
英文摘要：
We study the scattering of a long longitudinal radiating bulk strain solitary wave in the delaminated area of a two-layered elastic structure with soft (`imperfect') bonding between the layers within the scope of the coupled Boussinesq equations. The direct numerical modelling of this and similar problems is challenging and has natural limitations. We develop a semi-analytical approach, based on the use of several matched asymptotic multiple-scale expansions and averaging with respect to the fast space variable, leading to the coupled Ostrovsky equations in bonded regions and uncoupled Korteweg-de Vries equations in the delaminated region. We show that the semi-analytical approach agrees well with direct numerical simulations and use it to study the nonlinear dynamics and scattering of the radiating solitary wave in a wide range of bi-layers with delamination. The results indicate that radiating solitary waves could help us to control the integrity of layered structures with imperfect interfaces.
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