二维和三维格子中波的传播和均匀化：半解析方法
Wave propagation and homogenization in 2D and 3D lattices: a semi-analytical approach
摘要：
本文研究了二维和三维周期性梁格中的波动问题。本文发展了一种求解布洛赫波谱的解析方法，其特征在于通过强制Floquet条件得到一个广义特征值方程。动态刚度矩阵被证明是显式埃尔米特和承认积极的特征值。分析了六角、矩形、四面体和立方晶胞的晶格。半解析方法可以渐近扩展到低频，得到描述准静态极限下波动的Christoffel矩阵的显式形式。
英文摘要：
Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized eigenvalue equation obtained by enforcing the Floquet condition. The dynamic stiffness matrix is shown to be explicitly Hermitian and to admit positive eigenvalues. Lattices with hexagonal, rectangular, tetrahedral and cubic unit cells are analyzed. The semi-analytical method can be asymptotically expanded for low frequency yielding explicit forms for the Christoffel matrix describing wave motion in the quasistatic limit.
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