Design of a broadband elastic metamaterial via topologically optimized inertial amplification mechanisms

Abstract

Elastic metamaterials enable to generate phononic band gaps below the Bragg limit. Most metamaterials in the literature are based on vibration absorption (local resonance) principle. In this study, a two dimensional elastic metamaterial is designed, which utilizes inertial amplification principle. This principle allows generating wide band gaps at low frequencies. Firstly, the theory of phononic gaps induced by inertial amplification in finite structures is discussed briefly utilizing a lumped parameter model. Afterwards, a compliant inertial amplification mechanism is introduced, which is the building block of the metamaterial designed in this paper. Topology optimization is performed on this mechanism to obtain a wide vibration stop band for a given mass constraint. Then, vibration transmissibilities of one dimensional finite periodic structures with various number of unit cells are presented. Subsequently, a two dimensional metamaterial is constructed by incorporating the topologically optimized compliant inertial amplification mechanisms. Finally, in-plane vibration isolation performance of this two dimensional system is demonstrated via vibration transmissibility plots. © 2020 European Association for Structural Dynamics. All rights reserved.