Broadened low-frequency bandgap of a mass-graded metastructure with high-static-low-dynamic stiffness resonators using magnetic negative stiffness

Metastructures with periodically arranged high-static-low-dynamic stiffness (HSLDs) resonators can generate low frequency bandgap, thereby they are widely applied in low-frequency vibration suppression. However, the width of the bandgap decreases as the bandgap shifts to low frequency, severely reducing the robustness of the metastructure in frequency detuning. In this study, unit cells that consist of a frame, two helical springs and a HSLDs resonator with linearly graded internal mass are periodically connected one by one to form a one-dimensional mass-graded metastructure for expanding the local resonance bandgap of metastructure in low frequency range. In each HSLDs resonator, a negative stiffness magnetic spring (NSMS) using a pair of magnetic tile groups is connected in parallel with two spiral flexure springs (SFS) that exhibit positive stiffness to achieve the HSLDs property. Meanwhile, the internal mass of the resonator can be divided into a tunable component, namely, several thin mass blocks, and a constant component. Adjusting the number of thin mass blocks in resonator makes the resonator mass-tunable. The design of NSMS and SFS in the resonators is presented firstly. Afterwards, the analytical model of the mass-graded metastructure is established, and parametric analyses are conducted to investigate the broadening effect on the bandgap of mass-spacing, damping, and the number of unit cells. Compared with the uniform metastructure, a 142% increase in the width of the low-frequency bandgap can be realized by the proposed mass-graded metastructure in the experiment.