Higher order asymptotic homogenization and wave propagation in periodic composite materials
Higher order asymptotic homogenization and wave propagation in periodic composite materials
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DOI：
10.1098/rspa.2007.0267
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发表时间：
2008-05-08
影响因子：
3.5
通讯作者：
Weichert, Dieter
中科院分区：
文献类型：
--
作者：
Andrianov, Igor V.;Bolshakov, Vladimir I.;Weichert, Dieter
本文将高阶渐近均匀化方法（AHM）应用于周期性复合材料中的波频散问题。当行进信号的波长变得与不均匀性的大小相当时，波在组件界面处的连续反射和折射导致形成通过和停止频带的复杂序列。AHM的应用提供了在低频范围内有效的长波近似。高频率的解决方案的Floquet布洛赫方法的基础上，通过扩展空间变化的特性的复合介质中的傅立叶级数和表示未知的位移场的无限平面波展开。稳态弹性纵波在复合材料杆（一维问题，允许精确的解析解）和横向反平面剪切波在纤维增强复合材料与方形格子的圆柱形夹杂物（二维问题）被认为是。得到了色散曲线，确定了通带和阻带。
We present an application of the higher order asymptotic homogenization method (AHM) to the study of wave dispersion in periodic composite materials. When the wavelength of a travelling signal becomes comparable with the size of heterogeneities, successive reflections and refractions of the waves at the component interfaces lead to the formation of a complicated sequence of the pass and stop frequency bands. Application of the AHM provides a long-wave approximation valid in the low-frequency range. Solution for the high frequencies is obtained on the basis of the Floquet Bloch approach by expanding spatially varying properties of a composite medium in a Fourier series and representing unknown displacement fields by infinite plane-wave expansions. Steady-state elastic longitudinal waves in a composite rod (one-dimensional problem allowing the exact analytical solution) and transverse anti-plane shear waves in a fibre-reinforced composite with a square lattice of cylindrical inclusions (two-dimensional problem) are considered. The dispersion curves are obtained, the pass and stop frequency bands are identified.