Enhanced band gap modulation via rigid–flexible coupling in two-link metamaterial resonators

This study proposes a rigid–flexible two-link resonator for tunable vibration attenuation in metamaterial beams. Eccentric rigid bodies are introduced into the resonator to couple translational and rotational motions, providing additional parameters for band gap modulation. An exact dynamic stiffness model is developed to calculate the vibration transmission and dispersion characteristics. The results show that rigid-body rotary inertia and eccentric offsets significantly affect the band gap behavior, especially in the mid- and high-frequency ranges. Sensitivity analysis identifies the dominant coupling parameters in different frequency ranges, and optimization results demonstrate that these parameters can be tuned to obtain broadband attenuation over prescribed target bands. Experiments using 3D-printed resonators confirm that changing rigid-body orientations and unit-cell combinations can produce measurable shifts and broadening of band gaps. The proposed design provides a simple and flexible route for tunable vibration attenuation in beam-like metamaterial structures.