圆管结构中周向超声导波非线性效应的理论与实验研究

The circumferential ultrasonic guided wave (abbr. CUGW) propagation in hollow cylindrical structures will exhibit a variety of phenomena of nonlinear wave motion due to its complicated dispersion and wave field pattern, as well as its closed nature of propagation path. In this project, the modal expansion equation governing the second-harmonic field of the CUGW propagation in hollow cylindrical structures will be established, and its analytical solution will be presented, based on the combination of second-order perturbation and modal expansion approach for waveguide excitation. Theoretically, the intrinsic relationship of the CUGW's wave field, dispersion and the closed detouring feature of the CUGW's circumferential propagation on the effect of second-harmonic generation will be investigated in depth. The influence of change either in the interfacial properties between layers of a multi-layered hollow cylindrical structure or in high-order elastic constants of solids on the effect of second-harmonic generation by the CUGW propagation will be clarified, respectively. Moreover, the method or approach for enhancing the efficiency of second-harmonic generation by the CUGW propagation will be studied and provided. Based on the above theoretical results, the experimental measurement technique of the CUGW's second-harmonic signals will be proposed. Whereafter, the cumulative effect (along the circumferential direction of propagation) of the second harmonic of the CUGW propagation will be experimentally examined, as well as the enhanced role of the closed detouring feature of the CUGW's circumferential propagation in the measurement of the CUGW's second-harmonic signal. Furthermore, the feasibility and effectiveness will be experimentally verified of using the effect of second-harmonic generation by the CUGW propagation to evaluate the early damage in metallic cylindrical tubes. For the purpose of promoting and facilitating the further development of theory of nonlinear ultrasonic guided waves, as well as laying the theoretical and experimental foundation for relevant applied researches, there is no doubt that the results obtained in this project will have important theoretical and practical significance.

周向超声导波复杂的声场和频散特性以及其传播路径的闭合性，将使其呈现出更为丰富的非线性波动现象。项目将二阶微扰与模式展开方法相结合，建立圆管结构中周向超声导波二次谐波的模式展开方程并给出其解析解。理论上深入研究周向超声导波的声场、频散以及其沿周向的闭合绕行特性等，与其二次谐波发生效应之间的内在关系；厘清管间界面特性及材料高阶弹性常数的改变对其二次谐波发生效应所产生的影响；研究周向超声导波的二次谐波发生效率得以增强的方法或途径。在此基础上，提出周向超声导波二次谐波的实验测量方法。实验研究周向超声导波的二次谐波沿周向传播的积累效应，以及其沿周向的闭合绕行特性对二次谐波信号测量所起的增强作用；实验研究以周向超声导波的二次谐波发生效应评价金属圆管早期损伤的可行性及有效性。项目成果对于推动和促进非线性超声导波理论的进一步丰富和发展，以及奠定相关应用研究的理论与实验基础，具有重要的理论和实际意义。

周向超声导波作为在圆管结构中传播的一类重要导波模式，对其非线性效应开展系统的理论与实验研究，是对已有非线性超声导波研究工作的进一步深化与拓展。开展周向超声导波非线性效应的理论与实验研究工作，在诸如圆管结构早期损伤及管间界面特性退化的准确定征等方面，具有重要的实际应用价值。在国家自然科学基金的大力支持下，项目对圆管结构中的非线性超声导波开展了系统的理论、实验及应用研究。构建了圆管结构中周向超声导波二次谐波发生效应的理论分析模型，给出了周向超声导波二次谐波声场之解析解；揭示了周向超声导波的声场、频散以及其沿周向传播的空间周期性等，与其二次谐波发生效应之间的内在关系；厘清了管间界面特性及材料高阶弹性常数的改变对周向超声导波二次谐波发生效应所产生的影响。理论分析与数值仿真结果表明，基于周向超声导波的二次谐波发生效应，可对圆管的早期损伤及管间界面特性退化予以准确定征。建立了周向超声导波二次谐波信号的实验测量系统，实验观察了周向超声导波二次谐波所具有的空间积累增长效应，实验验证了周向超声导波的沿周向传播的空间周期性对其二次谐波信号测量所起的增强作用，实验证明了采用非线性周向超声导波评价圆管早期损伤的可行性。在理论与实验研究基础上，提出了一种用于评价圆管结构早期损伤的非线性周向超声导波方法。受项目资助，现已发表期刊论文39篇，其中有32篇被SCIE收录。通过理论分析、数值仿真和实验相结合的方式，项目深刻揭示了圆管结构中周向超声导波二次谐波发生效应的物理过程及传播规律。项目成果对于促进非线性超声导波理论的进一步丰富和发展，以及奠定相关应用研究的理论与实验基础，具有重要的理论和实际意义。