Defect states and polarization characteristics of programmable gyroscopic metamaterials

Abstract This paper investigates the bandgap characteristics, localized defect states and multidimensional polarization features of a one-dimensional diatomic gyroscopic periodic structure. A unified mathematical framework is established by introducing binary structural operators, enabling a systematic analysis of the Hamiltonian perturbation mechanisms and wave manipulation capabilities of perfect, defect-spring and defect-gyroscope configurations. The results indicate that the intrinsic Coriolis coupling breaks the time-reversal symmetry of the system, lifting band degeneracy and modulating the Bragg bandgap. Compared with the purely elastic potential perturbations governing the defect-spring configuration, the defect-gyroscope structure driven by dynamic kinetic-Coriolis perturbations exhibits enhanced tuning sensitivity and facilitates a novel dynamic decoupling mechanism. Wave propagation analysis reveals that the system not only supports high-fidelity linear polarization preservation within overlapping passbands but also achieves strictly non-reciprocal chiral filtering of circularly polarized waves within isolated passbands. Furthermore, the localized states within the defect-gyroscope structure trigger isolated, highly confined orientation angle reversals, providing a highly sensitive spatial phase transition mechanism for angular polarization. These findings enrich the fundamental understanding of multidimensional elastic wave manipulation in gyroscopic mechanical systems. Consequently, they offer profound insights and establish a solid foundation for the development of advanced programmable vector vibration controllers, non-reciprocal waveguides, and ultra-sensitive phononic defect sensors.