Effective elastic moduli for 3D solid-solid phononic crystals of arbitrary anisotropy and oblique lattice structure are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in two dimensions with direct numerical integration along the third direction. As a result, the MM method converges much quicker to the exact moduli in comparison with the PWE as the number of Fourier coefficients increases. The MM method yields a more explicit formula than previous results, enabling a closed-form upper bound on the effective Christoffel tensor. The MM approach significantly improves the efficiency and accuracy of evaluating effective wave speeds for high-contrast composites and for configurations of closely spaced inclusions, as demonstrated by three-dimensional examples.
报告人简介： Norris教授于1977年和1978年分别获都柏林大学数学物理系学士和硕士学位，1981年获美国西北大学工程科学和应用数学博士学位。1981-1983年在西北大学工程科学和应用数学系工作，1983-1984年在埃克森公司研究科学实验室从事科学研究，1985年至今任教于罗格斯大学机械和航空工程系，其中2000-2005年任系主任。主要研究领域为结构裂纹的超声无损检测，地球物理勘探的地下声模型以及面向海军应用的结构声学，在国际重要期刊发表论文150余篇，目前是美国声学学会、数学与应用研究所会士，担任Wave Motion主编，及J. Acoustical Society of America, SIAM J. Applied Mathematics, and J. Elasticity等期刊编委。
