High-frequency asymptotics for microstructured thin elastic plates and platonics
High-frequency asymptotics for microstructured thin elastic plates and platonics
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DOI：
10.1098/rspa.2011.0652
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发表时间：
2012-05-08
影响因子：
3.5
通讯作者：
Craster, R. V.
中科院分区：
文献类型：
--
作者：
Antonakakis, T.;Craster, R. V.
我们认为微结构薄弹性板，具有潜在的周期性结构，并开发一个渐近连续模型，捕捉基本的微观结构行为完全在宏观尺度设置。渐近性是基于一个两尺度的方法，即使在高频率时，波长和微尺度长度是相同的顺序是有效的。一般的理论说明通过一个和两个维度的模型问题，有零频率阻带，排除传统的平均和均匀化理论。局部缺陷模式所产生的材料变化也建模使用的理论和数值模拟进行比较。
We consider microstructured thin elastic plates that have an underlying periodic structure, and develop an asymptotic continuum model that captures the essential microstructural behaviour entirely in a macroscale setting. The asymptotics are based upon a two-scale approach and are valid even at high frequencies when the wavelength and microscale length are of the same order. The general theory is illustrated via one-and two-dimensional model problems that have zero-frequency stop bands that preclude conventional averaging and homogenization theories. Localized defect modes created by material variations are also modelled using the theory and compared with numerical simulations.