In this paper, elastic wave propagation in a one-dimensional micromorphic medium characterized by two internal variables is investigated. The evolution equations are deduced following two different approaches, namely using: (i) the balance of linear momentum and the Clausius–Duhem inequality, and (ii) an assumed Lagrangian functional (including a gyroscopic coupling) together with a variational principle. The dispersion relation is obtained and the possibility of the emerging band gaps is shown in such microstructured materials. Some numerical simulations are also performed in order to highlight the dispersive nature of the material under study.

中文翻译：

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关于微结构固体中的波色散

本文研究了弹性波在以两个内部变量为特征的一维微形态介质中的传播。演化方程是通过两种不同的方法推导的，即使用：（i）线性动量的平衡和克劳修斯-杜姆不等式，以及（ii）假定的拉格朗日泛函（包括陀螺仪耦合）和变分原理。在这种微结构材料中，获得了色散关系，并显示了出现带隙的可能性。为了突出研究材料的分散性，还进行了一些数值模拟。