Analysis of vibration characteristics of elastic metamaterial sandwich beam

Abstract

Elastic metamaterials (EMs) are a new kind of artificial composite medium composed of complex micro-structural elements, which have unique dynamic properties and elastic wave regulation ability that their constituent materials do not possess. The existing researches on EMs mainly focus on wave characteristics in two-dimensional and three-dimensional infinite domains. However, actual EM structures are always in the form of finite structures such as rods, beams and plates, so it is more important for engineering applications to understand and master their natural and forced vibration characteristics. Therefore, it is necessary to establish an effective simplified solution method and framework with certain accuracy for the vibration analysis of such structures. In the early stage, we have studied the natural and forced vibration characteristics of EM beams from this point of view, and presented a simplified solution process. In this paper, a kind of sandwich beam structure with EMs as the core is further constructed, the simplified solution process is extended to such more practical model analysis, and the free and steady forced vibration analysis processes of the finite-size sandwich beam are given. The vibration characteristics different from the traditional sandwich beam are investigated, and some interesting and useful phenomena are revealed, including the absence of natural frequencies within bandgap (BG), the gathering of natural frequencies in the vicinity of band edges, and the particular modal correspondence before and after BG. Then, the corresponding formation mechanisms are explained from the perspective of wave propagation.