Multiple-Pendulum Metamaterial: Ultralow-Frequency Vibration Suppression and Wave Splitting

Due to superior wave propagation manipulation and remarkable dynamic properties, mechanical metamaterials have attained pivotal importance across scientific and engineering domains in contemporary research. This study develops a multiple-pendulum metamaterial that exhibits a gravity-induced zero-frequency bandgap, demonstrating exceptional wave attenuation capabilities in ultralow-frequency ranges. The impact of multiple-pendulum structural parameters on the zero-frequency bandgap is investigated, and a simulation model is established to validate the attenuation characteristics within the zero-frequency bandgap. Furthermore, within the passband region, the dispersion relation exhibits a multi-wavevector characteristic, manifesting frequency ranges where multiple dispersion branches with distinct slopes coexist. This feature induces wave splitting phenomena in the multiple-pendulum metamaterial system. Numerical simulations validate wave-splitting phenomenon, where energy flux tracking through group velocity vector fields confirms the spatial separation of wave components. The discovery of the zero-frequency bandgap enables ultralow-frequency vibration isolation, whereas wave splitting within the multi-wavevector regime establishes a theoretical framework for designing multichannel wave control mechanisms.