Nonlocal topological states in elastic wave metamaterials with active feedback control

•The effects of nonlocal connection on band structures and dynamic behaviors of rectilinear lattices are studied.•The honeycomb lattice with nonlocal interactions is investigated, which realizes interface transmission and hybrid order topological states.•The active feedback control systems can change the Young’s modulus of nonlocal metamaterials, which flexibly tune the topological characteristic of elastic waves. Topological elastic wave metamaterials provide a new mechanism to tune wave energy and provide engineering applications which are difficult to realize by traditional structures. This work reports topological characteristics of nonlocal elastic wave metamaterials with active feedback control. The effects of nonlocal connection on band structures and dynamic behaviors of rectilinear lattices are studied. Then, the honeycomb lattice with nonlocal interactions is investigated, which realizes interface transmission and hybrid order topological states. The introduction of active feedback control systems can change the Young’s modulus of nonlocal metamaterials, which flexibly tune the topological characteristic of elastic waves. According to finite element simulation and experiment, the interface transmission and hybrid order can be generated by active feedback control, which agrees with theoretical predictions.