This paper derives and demonstrates a one-dimensional acoustic metamaterial homogenization method. The homogenization method uses a multiple-scales approximation with Hamilton's principle, a weak-form representation of the dynamic equation. While the multiple-scales approximation makes the predicted effective material properties of this method inexact, the method is shown to be highly versatile. Analytical and numerical examples are given showing the ability of the homogenization method to account for viscosity and finite-amplitude effects.

中文翻译：

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基于汉密尔顿原理的多尺度近似有效声超材料均质化。

本文推导并证明了一维声学超材料均质化方法。均质化方法使用汉密尔顿原理的多尺度近似，这是动力学方程的弱形式表示。尽管多尺度近似使该方法的预测有效材料性能不精确，但该方法显示出高度的通用性。给出了分析和数值示例，显示了均化方法解决粘度和有限振幅效应的能力。