Wave propagation and manipulation in periodic piezoelectric laminates with electrodes and cracks

本项目致力于分析智能周期压电层合板中弹性波的传播和操纵。为此，将发展理论模型以及精确和高效的数值方法。特别是，将发展半解析和数学基础良好的积分方法(IA)和高效的数值方法。特别是，将实施半解析积分法(IA)和谱元素法(SEM)及其耦合形式(IA-SEM)。IA的半解析性使我们能够更深入地了解物理和机理，而扫描电子显微镜对于复杂波传播现象的数值模拟则更加灵活。结合这两种方法的优点，将建立一种高精度、高效率的数值模拟工具。将考虑带有电极和裂纹的周期压电层合板。埋入电极使我们能够控制和操纵弹性波的传播，而裂纹类缺陷的考虑使我们能够评估智能周期压电层合板的可靠性。该项目将研究三种不同类型的电极和裂纹，即有限数量的多个电极和裂纹、周期性的电极和裂纹阵列以及多个周期性的电极和裂纹阵列。利用所建立的理论模型和数值方法，将详细研究复杂的波传播现象，如全波反射、宽带隙、负折射、波共振、波的局部化和聚焦、波的遮盖和电极和裂纹尖端附近的局部场集中。这种独特的波传播特性在断裂和损伤力学、无损材料检测、在线结构健康监测以及新型声学装置、噪声和减振结构和部件的设计和优化中具有新颖和创新的应用。通过调整这些关键的影响参数，可以得到具有宽带隙和遮波能力等特殊波传播特性的有利的和优选的周期性压电层合板。本项目中需要解决的问题是高度新兴的，尚未在文献中得到解决，需要开发的解决方法也是原创性的。该项目具有多学科性质，涉及固体力学、断裂力学、应用数学、物理、计算方法和编程等不同科学学科。这是德国和俄罗斯申请者的合作项目，将结合各自的研究优势，促进参与的德国和俄罗斯年轻科学家。

This project is devoted to the analysis of the elastic wave propagation and manipulation in smart periodic piezoelectric laminates. For this purpose, theoretical models as well as accurate and efficient numerical methods will be developed. In particular, the semi-analytical and mathematically well-founded integral approach (IA) and efficient numerical methods will be developed. In particular, the semi-analytical integral approach (IA) and spectral element method (SEM) as well as their coupled form (IA-SEM) will be implemented. The semi-analytical nature of the IA allows us to gain a deeper insight into the physics and mechanisms, while the SEM is more flexible for the numerical simulation of the complex wave propagation phenomena. By combining the advantages of both methods, a highly accurate and efficient numerical simulation tool will be established. Periodic piezoelectric laminates with electrodes and cracks will be considered. Embedded electrodes allow us to control and manipulate elastic wave propagation, while the consideration of crack-like defects enables us to assess the reliability of the smart periodic piezoelectric laminates. Three different types of electrodes and cracks will be investigated in the project, namely, a finite number of multiple electrodes and cracks, a periodic array of electrodes and cracks, and multiple periodic arrays of electrodes and cracks.By using the developed theoretical models and numerical methods, complex wave propagation phenomena such as total wave reflection, wide band-gaps, negative refraction, wave resonances, wave localization and focusing, wave cloaking and local field concentrations near the electrodes and crack-tips will be investigated in details. Such distinct wave propagation characteristics have novel and innovative applications in fracture and damage mechanics, non-destructive material testing, on-line structural health monitoring, as well as design and optimization of novel acoustic devices, noise and vibration attenuating structures and components The following key influencing factors should be analyzed in details: material parameters, geometrical parameters, sizes and locations of the electrodes/cracks, and the applied electric field. By adjusting these key influencing parameters, beneficial and preferred periodic piezoelectric laminates with special wave propagation characteristics such as wide band-gaps and wave cloaking capability can be achieved. The problems to be solved in this project are highly emerging and not yet tackled in literature, and the solution methods to be developed are original. The project has a multi-disciplinary character and it involves different scientific disciplines, such as solid mechanics, fracture mechanics, applied mathematics, physics, computational methods and programming.This is a cooperation project by the German and Russian applicants, which will combine their individual research strengths and promote participating young German and Russian scientists.