A Progressive Circular-Unit Hexagonal Metamaterial for Tunable Vibration Isolation and Energy Absorption

Engineering structures are increasingly required to combine vibration isolation, load-bearing capacity, and energy absorption in practical applications. In this study, three progressive circular-unit metamaterial structures are developed from a regular hexagonal unit cell to achieve the synergistic integration of bandgap-based vibration isolation and quasi-static compressive energy absorption. The proposed structures are constructed by incorporating concentric circular units and tangential ligaments with alternating chirality, producing a progressive geometric transition from Structure I to Structure III. Dispersion analyses show that the internal circular units and tangential ligaments can effectively induce out-of-plane bandgaps within the 0-5000 Hz range. As the number of circular units increases, the total bandgap width expands progressively. Structure III achieves the largest total bandgap width of 1258.33 Hz, corresponding to 25.17% of the target frequency range. Finite-structure vibration transmissibility analysis and experimental tests further confirm its vibration attenuation capability. Moreover, embedding stainless-steel mass blocks in the innermost circular rings shifts the attenuation range toward lower frequencies, demonstrating tunable low-frequency vibration isolation. Quasi-static compression simulations show that the designed structures develop progressive deformation modes and effectively absorb mechanical energy before densification. Structure III achieves a specific energy absorption of 11.28 J/g under y-direction compression, whereas Structure I achieves 6.69 J/g under x-direction compression, revealing direction-dependent energy absorption characteristics. Vibration transmissibility and x-direction compression experiments conducted on Structure III provide experimental support for the numerical predictions of low-frequency vibration attenuation and quasi-static compressive response, respectively. This study provides a manufacturable route to multifunctional metamaterials that combine tunable vibration isolation with load-bearing capacity and energy absorption.