Subwavelength tunable topological interface modes in metamaterial beams on elastic foundation

Abstract

In this paper, by the aid of zone folding mechanism, the topological transition point (TTP) is produced in novel metamaterial beams on elastic foundation. Different from the existing topological system, the TTP is located between the locally resonant band gap (LRBG) and the transition zone, which are induced by the local resonance of resonators and Winkler foundation, respectively. The position of TTP can also be tuned effectively by the natural frequency of resonators and critical frequency of Winkler foundation. After opening the TTP by space modulation of resonators, two types of unit cells are produced, and a new topological band gap (TBG) is formed. Besides, topological properties of both types of unit cells are discussed by dispersion analysis. The band inversion and different Zak phase indicate that these two types of unit cells are topologically distinct. Therefore, the topologically protected interface mode (TPIM) will appear at the interface between two domains. The numerical simulation confirms the existence of TPIM. Meanwhile, the robustness of TPIM is investigated, including the influence of damping and defects. In detail, the transmission efficiency of TPIM is reduced with damping, while the frequency and width of TPIM are little affected. Interestingly, the introduction of mass defects is found to improve the transmission efficiency of TPIM. This novel topological system is expected to open new avenues for vibration mitigation and energy harvesting.