Bidirectional deep-subwavelength band gap induced by negative stiffness

Abstract

Owing to its tremendous potential application in wave manipulation, metamaterials have attracted significant interest since their appearance at the start of this century. The resonant mechanism breaks the dependency of the lattice constant on the operation frequency, successfully achieving wave manipulation in the subwavelength range. However, it fails to simultaneously control two types of wave propagations in the deep-subwavelength range due to the specific configuration of the resonator. In this study, we introduce a novel negative-stiffness mechanism into the resonator to open a bidirectional deep-subwavelength band gap. Both the translational and torsional stiffness of the resonator can be neutralised by the proposed negative-stiffness mechanism. More importantly, adjusting the parameters of the negative-stiffness mechanism provides a convenient way to tune the bidirectional stiffness characteristic of the resonator, which is beneficial for manipulating the elastic wave in a large frequency range. The fundamental principle of opening the bidirectional deep-subwavelength band gap is examined through mechanical analysis, dispersion relation, and wave propagation features. By cascading the presented resonator in a host structure, this study realises the suppression of the propagations of two types of elastic waves within the deep-subwavelength frequency range as well as the filtration of one of these two types of elastic waves in a particular frequency range.