Theoretical Modeling and Numerical Simulation of Phononic Crystals

这个项目涉及声子晶体，它代表了一类新的功能复合材料，由两个或更多具有不同质量密度和弹性性质的介质的周期性阵列组成。本项目的主要目标是发展分析声子晶体中波传播的分析模型和有效的数值模拟技术，对有或没有缺陷和无序的声子晶体中的弹性波传播进行数值模拟，研究材料组合、周期、散射体的几何形状和大小以及缺陷和无序对波传播行为的影响。特别是，传输矩阵法、平面波展开法和小波方法将被发展并应用于一维声子晶体，而有限元方法和边界元方法将被用于分析二维和三维问题。通过系统而详细的分析和数值研究，研究弹性波在声子晶体中传播的基本特征，如带隙、波局域化、波聚焦、负折射、反常反射和波隧穿。该项目的主要目标是更好地理解和深入了解声子晶体的动态行为，这对声子晶体的设计和优化非常有用，以实现创新和具有挑战性的工程应用所需的动态特性。

This project deals with phononic crystals, which represent a new class of functional composite materials composed of periodic arrays of two or more media with different mass densities and elastic properties. The main objectives of the present project are the development of analytical models and efficient numerical simulation techniques for wave propagation analysis in phononic crystals, the numerical simulation of elastic wave propagation in phononic crystals with or without defects and disorders, and the investigation of the effects of the materials combination, periodicity, geometrical shape and size of the scatterers, as well as the defects and the disorders on the wave propagation behavior. In particular, the transfer matrix method, the plane wave expansion method and the wavelet method will be developed and applied to one-dimensional phononic crystals, while the finite element method and the boundary element method will be adopted for analyzing two-dimensional and three-dimensional problems. Through systematic and detailed analytical and numerical studies, the essential features of elastic wave propagation in phononic crystals such as band gaps, wave localization, wave focusing, negative refraction, anomalous reflection and wave tunneling should be investigated. The primary goal of the project is to gain a better understanding and a deeper insight into the dynamic behavior of phononic crystals, which are useful in the design and the optimization of phononic crystals to achieve desired dynamic properties for innovative and challenging engineering applications.