Harnessing nonlocal effects for wave localization and multi-frequency rainbow trapping in periodic structures

This study introduces the concept of nonlocal effect into a monoatomic mass–spring periodic structure, leading to unique characteristics of dispersion curves. Through the incorporation of the second neighboring nonlocal effect, we have observed the emergence of negative group velocity and specific points with zero group velocity (ZGV) within the dispersion curves. By harnessing the distinctive property of ZGV, we successfully attained the localization of transmission at specific frequencies, leading to a rainbow trapping effect. Notably, with the appropriate tuning of the third neighboring nonlocal effect, we observe that multi-frequency can be localized at predetermined positions. Waves under these frequencies are trapped at the same location, demonstrating a multi-frequency rainbow trapping phenomenon. The results from this research provide a novel perspective on elastic wave manipulation in periodic structures, with potential implications for the design of advanced materials and devices.