检测粘接弹性杆中的分层通过非线性波散射
Detecting Delamination via Nonlinear Wave Scattering in a Bonded Elastic Bar
AI总结：
本文通过非线性波散射检测粘接弹性杆中的分层，利用耦合Boussinesq方程和逆散射变换预测分层长度，发现波结构变化与入射孤子半高全宽相关，为层状结构完整性测试提供框架。
摘要：
本文研究了分层对波散射的影响，旨在为各种粘接类型的层状波导创建一种控制措施。以往的研究在模拟中考虑了特定宽度的孤立波，而未分析改变孤子参数的影响。我们考虑两种多层结构：一种包含由完美粘接“夹持”的分层，另一种包含由软粘接“夹持”的分层。这些结构由耦合的Boussinesq型方程建模。匹配渐近多尺度展开在软粘接区域导出耦合的Ostrovsky方程，在完美粘接和分层区域导出Korteweg-De Vries方程。我们使用逆散射变换来预测分层区域的行为。在两种情况下，数值分析表明，我们可以通过波结构的变化来预测分层长度，并且这些变化取决于入射孤子的半高全宽（FWHM）。在完美粘接的情况下，我们推导了变化的理论预测并数值确认了该预测。对于软粘接情况，我们数值上识别出使用振幅变化的类似关系。因此，我们只需计算一条曲线即可确定任何入射孤立波的行为，从而为设计测量活动以严格测试层状结构的完整性创建了一个框架。
英文摘要：
In this paper we examine the effect of delamination on wave scattering, with the aim of creating a control measure for layered waveguides of various bonding types. Previous works have considered specific widths of solitary waves for the simulations, without analysing the effect of changing the soliton parameters. We consider two multi-layered structures: one containing delamination "sandwiched" by perfect bonding and one containing delamination but "sandwiched" by soft bonding. These structures are modelled by coupled Boussinesq-type equations. Matched asymptotic multiple-scale expansions lead to coupled Ostrovsky equations in soft bonded regions and Korteweg-De Vries equations in the perfectly bonded and delaminated region. We use the Inverse Scattering Transform to predict the behaviour in the delaminated regions. In both cases, numerical analysis shows that we can predict the delamination length by changes in the wave structure, and that these changes depend upon the Full Width at Half Magnitude (FWHM) of the incident soliton. In the case of perfect bonding, we derive a theoretical prediction for the change and confirm this numerically. For the soft bonding case, we numerically identify a similar relationship using the change in amplitude. Therefore we only need to compute one curve to determine the behaviour for any incident solitary wave, creating a framework for designing measurement campaigns for rigorously testing the integrity of layered structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
