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.
報告人簡介： Norris教授于1977年和1978年分别獲都柏林大學數學物理系學士和碩士學位，1981年獲美國西北大學工程科學和應用數學博士學位。1981-1983年在西北大學工程科學和應用數學系工作，1983-1984年在埃克森公司研究科學實驗室從事科學研究，1985年至今任教于羅格斯大學機械和航空工程系，其中2000-2005年任系主任。主要研究領域為結構裂紋的超聲無損檢測，地球物理勘探的地下聲模型以及面向海軍應用的結構聲學，在國際重要期刊發表論文150餘篇，目前是美國聲學學會、數學與應用研究所會士，擔任Wave Motion主編，及J. Acoustical Society of America, SIAM J. Applied Mathematics, and J. Elasticity等期刊編委。
