Bandgap and vibration transfer characteristics of scissor-like periodic metamaterials

Abstract

A periodic mass-spring-truss chain based on a scissor-like structure and inertial amplification is proposed to seek for low-frequency vibration attenuation. The resonant and anti-resonant frequencies of a basic element are obtained analytically to explain the resonance and anti-resonance of the periodic chain. The formation of bandgaps is explored, revealing that the vertical movements of the vertices take the input kinetic energy away from the horizontal movement energy. The cut-off frequencies of three models are derived analytically to compare the effect of the inertia amplification, which can reach more than three times the classical mass-spring chain with a small angle. Also, the effect of stiffness amplification is presented when the spring mounted vertically, unlike the classical inertial amplification systems. Thus, the optimal configuration for low-frequency attenuation is obtained, that is, the spring mounted horizontally and the masses mounted at the upper and lower vertices. The chain with mass on the upper and lower vertices has the lowest cut-off frequency, which is 17.7% lower than that of the classical mass-spring chain. A diatomic chain is studied to find lower and wider bandgaps, where the central frequency is 25% lower than the classical mass-spring diatomic chain. The central frequency and width of the new bandgap can be tunable accordingly. The result shows that small angles or low stiffness ratios result in lower bandgaps. Meanwhile, the large angles, big differences of masses, or high stiffness ratios lead to wider bandgaps.