Mechanical metamaterials have attracted extensive attention. This paper reports a metamaterial with tunable elastic wave bandgaps based on bistable buckling structure. First, we find that deformation of two symmetric buckling shells is intrinsically asymmetric, which blocks the realisation of robust tunability. Based on an analytical model, we clarify that the mechanisms for this intrinsic asymmetricity are the bifurcations on force–deformation curves. Then we propose a superposition method of buckling shells, which can realise the symmetric deformation for robust tunable stiffness. Using this variable-stiffness oscillator, we design a metamaterial sandwich beam, and numerically and experimentally demonstrate its tunable bandgap for vibration suppression. This paper presents the unusual deformation process of buckling elements widely used for constructing metamaterials, and provides a robust way to realise metamaterials with tunable vibration bandgaps.
