Abstract One representative feature of a locally resonant elastic metamaterial (LREM) is that they can prohibit elastic wave propagation at the frequencies inside a band gap, which means that no energy is transmitted. When an incident wave propagates in a host medium at the frequencies inside band gaps, the incident wave is totally reflected at the interface between the host medium and an LREM. However, it remains unexplored what kind of mechanical boundary (e.g. fixed or free) is formed at the interface between the host medium and the LREM. This study thus aims at finding design principles for effective mechanical boundary (EMB) formation and validating the principles by numerical simulation. Conditions for certain EMBs were derived from the magnitude and phase of the reflection coefficient of the LREM. According to the conditions, an LREM is designed and attached to a host medium. It was confirmed from time-harmonic simulation that the velocity at the interface between the host medium and the LREM approached zero when the effective fixed boundary is formed, while the stress at the interface approached zero when the effective free boundary is formed.

中文翻译：

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弹性波下利用共振带隙的有效机械边界设计原理

摘要 局部共振弹性超材料（LREM）的一个代表性特征是它们可以阻止弹性波在带隙内的频率传播，这意味着没有能量传输。当入射波以带隙内的频率在主介质中传播时，入射波在主介质和 LREM 之间的界面处被全反射。然而，在主介质和 LREM 之间的界面处形成什么样的机械边界（例如固定的或自由的）仍未探索。因此，本研究旨在寻找有效机械边界 (EMB) 形成的设计原则，并通过数值模拟验证这些原则。某些 EMB 的条件来自 LREM 反射系数的幅度和相位。根据条件，LREM 被设计并附加到宿主介质上。时谐模拟证实，当有效固定边界形成时，主介质与LREM界面处的速度接近于零，而当形成有效自由边界时，界面处的应力接近于零。