Theoretical Modeling and Numerical Simulation of Phononic Crystals

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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.