On band gap and damping of metamaterials involving negative-stiffness elements

This study proposes a viscoelastic metamaterial containing negative-stiffness elements, which exhibits both a damping enhancement effect and a tunable ultra-low frequency band gap. A dynamic model involving static large predeformation of the viscoelastic metamaterial is established based on the updated Lagrangian scheme and solved by finite element method. Numerical results show that the presence of negative-stiffness elements can reduce the frequency of the band gap and increase its damping performance by two orders of magnitude. The mechanism roots in the fact that the negative stiffness elements enable the viscoelastic metamaterials with extremely low local incremental stiffness, resulting in low-frequency local resonance and damping enhancement. This study facilitates the design of damping composites with both high stiffness and damping capacity, which are widely required in vibration and noise control. • The present study proposes a novel viscoelastic metamaterial with a damping enhancement effect and a tunable low-frequency band gap due to the introduction of negative-stiffness elements. • The nonlinear dynamic model of the viscoelastic metamaterials with negative-stiffness elements for elastic wave propagation is established base on the updated Lagrangian scheme. • The damping capacity of the viscoelastic metamaterial is improved by up to two orders of magnitude as a result of low-frequency local resonance, and simultaneously high stiffness is maintained. • The presence of negative-stiffness elements is able to lower the frequency of locally resonant band gap by an order of magnitude, and the frequency of the band gap can be adjusted by an external static load based on the sensitivity of the precompressed and buckling beam to prestress.