Metastructure for broadband vibration suppression and ultra-low frequency energy harvesting by integrating intercell negative stiffness mechanism with 2-DOF oscillators

Metastructures consisting of periodic unit cells arranged in one, two, or three dimensions have shown great potential in vibration suppression, but they exhibit low efficiency in ultra-low frequencies (<10 Hz). In this study, we introduce a novel metastructure design that integrates two degree-of-freedom (2-DOF) local resonators with an intercell negative stiffness mechanism (NSM) to improve vibration suppression and energy harvesting across a broad frequency range. The proposed design increases the width of quasi-static bandgap by 80 % compared to existing designs employing single-degree-of-freedom resonators, while also introducing an additional bandgap with substantial broad width. Moreover, it overcomes the large size constraints associated with existing designs employing similar NSM principles. Dispersion analyses and transmission analyses reveal that multiple, tunable, and mergeable bandgaps can be generated, enabling efficient ultra-low-frequency energy harvesting and broadband vibration attenuation. Analytical solutions for the mechanical and electrical responses of the proposed nonlinear system are derived through the harmonic balance method and are validated through numerical simulations and published experimental data. Increasing the negative stiffness ratio amplitude shifts bandgaps to ultra-low frequencies, achieving a quasi-static bandgap while broadening the bandgap width. Moreover, the proposed mechanism significantly boosts the power output and expands the power bandwidth by 800 % at a power level of 5 mW compared to conventional linear designs. A guideline for configuring electromechanical coupling is also provided to optimize vibration suppression and energy harvesting performance.