Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers
Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers
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具有对比刚度和层密度的叠层梁中的多连续谱波传播
DOI：
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发表时间：
2018
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通讯作者：
G. Panasenko
中科院分区：
文献类型：
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作者：
G. Panasenko
考虑了具有不同刚度和密度层合梁的波动方程。该问题包含两个参数：ε是一个几何小参数（直径与其特征纵向尺寸之比），ω是一个物理大参数（交替层的刚度与密度之比）。解的渐近性态依赖于参数ε 2 ω的组合。如果这个值很小，那么极限模型就是标准的均匀化一维波动方程。相反，如果ε 2 ω不小，则极限模型由所谓的多连续模型表示，即，多个一维波动方程，耦合或非耦合，并在每一点“共存”。这些结果的证明使用多组分均匀化方法。
The wave equation in a thin laminated beam with contrasting stiffness and density of layers is considered. The problem contains two parameters: ε is a geometric small parameter (the ratio of the diameter and its characteristic longitudinal size) and ω is a physical large parameter (the ratio of stiffness and densities of alternating layers). The asymptotic behavior of the solution depends on the combination of parameters ε2ω. If this value is small, then the limit model is the standard homogenized one-dimensional wave equation. On the contrary, if ε2ω is not small, then the limit model is presented by the so-called multicontinuum model, i.e., multiple one-dimensional wave equations, coupled or noncoupled and “co-existing” at every point. The proof of these results uses the milticomponent homogenization method.