Bandgap characteristics and wave attenuation of metamaterials based on negative-stiffness dynamic vibration absorbers

Abstract

Metamaterials with ultra-low frequency and broad bandgaps have seldom been reported. In this paper, we propose a metamaterial whose unit cell consists of a dynamic vibration absorber with negative stiffness (NSDVA). Firstly, the band structure, effective indices and stability of the metamaterial were investigated considering an infinite lattice. Unlike traditional metamaterials, the proposed metamaterial exhibits a quasi-static bandgap and negative effective stiffness due to the presence of a negative-stiffness element. The stable condition was defined by the critical value of the negative stiffness, which was derived analytically through the closed solution of the bandgap’s start frequency. Parametric studies on the quasi-static bandgap were conducted. It was found that, in the stable condition, the stopband becomes wider when the stiffness ratio increases and the mass ratio decreases. Furthermore, transmission and transient analyses were conducted considering a finite chain. The results of the parametric studies on the transmission were consistent with the relevant predictions on the bandgap. A harmonic transient analysis validated the capability of wave attenuation, and the wavenumber-frequency spectrum of the output signal excited by white noise further verified the band structure. Finally, the proposed metamaterial was used as a seismic metabarrier consisting of built-up steel barriers, resonators, RC retaining walls, and wire ropes. The investigation on the seismic performance of the metabarrier revealed its applicability in urban regional earthquake resistance.