Effective properties of acoustic metamaterial chains with low-frequency bandgaps controlled by the geometry of lightweight mass-link attachments

Abstract

The effective mass of an acoustical metamaterial chain, which consists of a modified monatomic chain with a lightweight attached mass–link system, is derived and used to analyse its low-frequency vibration-isolation properties. The effective mass is expressed in terms of the resonant and anti-resonant frequencies of a basic element of the chain, and it is shown that the geometry of the attached system can be used to lower the resonant and anti-resonant frequencies, in turn lowering the bandgap of the chain, and producing efficient low-frequency vibration isolation with lightweight attached masses. In certain parameter limits, the chain is shown to degenerate to two previously proposed chains with contrasting band structures, and this provides insights into controlling the underlying vibration-isolation mechanisms. Numerical simulations are presented that illustrate the efficiency of the proposed system in terms of minimising transmission of a low-frequency incident wave packet with only two units of the attached system.