Bandgap and wave propagation of spring–mass–truss elastic metamaterial with a scissor-like structure

Abstract

Inspired by the inertial amplification mechanism and bandgap characteristic of periodic structures, a type of scissor-like elastic metamaterial is studied for low-frequency vibration attenuation in this paper. Firstly, the 1DOF (degree of freedom) scissor-like chain consisting of masses, trusses, and springs is investigated. The formation of inertial amplification is illustrated, that is, input horizontal movements are converted into larger vertical movements of vertex masses by a scissor-like structure. The resonance and anti-resonance phenomena in transmission curves are explained. Especially, the optimal configuration for low-frequency attenuation is obtained by analytical expressions of the dispersion relation. Then, a 2DOF spring–mass–truss chain is considered to open a bandgap below the vibration attenuation range of the 1DOF chain. The relative movement of masses at different frequencies is explored to understand the bandgap generation. The influence of parameters including the mass ratio, tensile stiffness ratio, shear stiffness ratio, and angle on bandgap boundaries is discussed. Finally, the spatial propagation of a wavelet packet is presented to illustrate the efficiency of the proposed structure in terms of minimizing a broadband excitation transmission. The transmitted component of a wavelet packet through three units of the proposed structure is only 3.8%, which is 22.8% of that through the classic 1D local resonance metamaterial.