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中文摘要：
基于应用力学的辛数学理论．阐述了界带分析的基本理论与计算方法，主要包括：彝带分析的基本概念、界带分析的变分原理、单个与不同原子周期链的波的色散关系、子结构界带分析计算方法以及数值算例等多方面内容。研究工作在表明辛数学理论优势和潜力的同时，也为相关问题的深入研究奠定了理论与算法基础。
英文摘要：
Based on the symplectic theories founded in applied Mechanics, the fundamental theory and computational algorithm for Inter-Belt analysis are developed. The theoretical frame of Inter-Belt analysis consists of the following aspects： the basic concept and variational principle of Inter-Belt analysis, wave propagation and dispersion of single atom and periodic atomic-string, substructure method and bas- ic a}gorithm of Inter-Belt analysis. The present study demonstrates again the advantages and potential of the symplectic-mathematics and establishes firm basis for further research.
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