Multiple topological interface states in broadband locally resonant phononic crystals

Abstract

We design a one-dimensional locally resonant phononic crystal (LRPC) comprised of a substrate beam periodically attached with twin resonators. By alternating the position of the resonators, the bandgap forming mechanisms of the LRPC, namely, the band folding-induced bandgaps (BFBGs) and the locally resonant bandgap (LRBG), are analyzed. A broadband “pseudo-bandgap” formed by the LRBG and BFBG can be achieved. The topological properties of the LRPC are then studied, and it is found that the topological interface states can occur only in the BFBGs but not in the LRBG. By constructing a finite LRPC formed by two PCs with distinct topological properties connecting with each other, we numerically and experimentally demonstrate the existence of multiple topological interface states in the BFBGs. The interface state within the subwavelength regime can be achieved with strong energy localization and is little affected by material damping, while for the interface state at high frequencies, it is shown that damping could considerably weaken the energy localization. This work provides guidelines for the design of low-frequency elastic topological systems.