Design principle for effective mechanical boundary using a resonance band gap under elastic waves

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.