Wave Propagation in Periodic Composites: Higher-Order Asymptotic Analysis Versus Plane-Wave Expansions Method
Wave Propagation in Periodic Composites: Higher-Order Asymptotic Analysis Versus Plane-Wave Expansions Method
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DOI：
10.1115/1.4002389
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发表时间：
2011-01-01
影响因子：
2
通讯作者：
Weichert, D.
中科院分区：
文献类型：
--
作者：
Andrianov, I. V.;Awrejcewicz, J.;Weichert, D.
本文对一维和二维周期性非均匀介质中不同的阻带确定方法进行了比较。对于一维情形，通过渐近方法研究了著名的色散方程。特别是，我们展示了如何均匀化的解决方案，可以通过使用任何高阶的基本系列。我们说明并讨论了一个可能的应用渐近级数关于参数以外的波长和频率。此外，我们研究了反平面弹性剪切波在平面内传播通过一个空间无限的周期性复合材料组成的一个无限矩阵和一个正方形格子的圆形夹杂物。为了解决这一问题，提出了一种与大体积裂缝包含体单元渐进解相匹配的均匀化方法，并成功应用。平均方法的第一和第二近似项提供第一阻带的估计。为了有效性和与其他方法的比较，我们也采用了傅立叶方法。傅立叶方法被示出为对于相对小的夹杂物，即，当夹杂物相关的参数和矩阵彼此稍微不同时。然而，对于明显对比的结构和大的夹杂物，高阶均匀化方法是有利的。因此，高阶均匀化方法和傅立叶分析可以被视为相互补充。[DOI：10.1115/1.4002389]
This work is devoted to a comparison of different methods determining stop-bands in 1D and 2D periodic heterogeneous media. For a 1D case, the well-known dispersion equation is studied via asymptotic approach. In particular, we show how homogenized solutions can be obtained by elementary series used up to any higher-order. We illustrate and discuss a possible application of asymptotic series regarding parameters other than wavelength and frequency. In addition, we study antiplane elastic shear waves propagating in the plane through a spatially infinite periodic composite material consisting of an infinite matrix and a square lattice of circular inclusions. In order to solve the problem, a homogenization method matched with asymptotic solution on the cell with inclusion of the large volume fracture is proposed and successfully applied. First and second approximation terms of the averaging method provide the estimation of the first stop-band. For validity and comparison with other approaches, we have also applied the Fourier method. The Fourier method is shown to work well for relatively small inclusions, i.e., when the inclusion-associated parameters and matrices slightly differ from each other. However, for evidently contrasting structures and for large inclusions, a higher-order homogenization method is advantageous. Therefore, a higher-order homogenization method and the Fourier analysis can be treated as mutually complementary. [DOI: 10.1115/1.4002389]