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

本计画主要研究弹性波在周期性压电层合板中的传播与操控。为此，将开发理论模型以及准确有效的数值方法。特别是，半解析和数学上有充分依据的积分方法（IA）和有效的数值方法将被开发。特别是，半解析积分法（IA）和谱元法（SEM）以及它们的耦合形式（IA-SEM）将被实施。IA的半分析性质使我们能够更深入地了解物理和机制，而SEM对于复杂波传播现象的数值模拟更灵活。结合两种方法的优点，将建立一个高精度和高效率的数值模拟工具。将考虑具有电极和裂纹的周期压电层合板。嵌入式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的智能周期压电层合板的可靠性。本计画将研究有限个多重电极与裂缝、周期性电极与裂缝、多重周期性电极与裂缝等三种不同类型的电极与裂缝，并利用已发展的理论模型与数值方法，探讨复杂的波传播现象，如全波反射、宽带隙、负折射、波共振、将详细研究波的局部化和聚焦、波的遮蔽以及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、噪声和振动衰减结构和部件的设计和优化中具有新颖和创新的应用。材料参数、几何参数、电极/裂纹的尺寸和位置以及所施加的电场。通过调整这些关键的影响参数，有益的和优选的周期性压电层压板具有特殊的波传播特性，如宽带隙和波隐身能力，可以实现。在这个项目中要解决的问题是高度新兴的，尚未在文献中解决，要开发的解决方法是原创的。该项目具有多学科性质，涉及固体力学、断裂力学、应用数学、物理学、计算方法和程序设计等不同学科，是德国和俄罗斯申请人的合作项目，将联合收割机结合各自的研究优势，促进德国和俄罗斯青年科学家的参与。

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.