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.

中文翻译：

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使用磁负刚度的高静态低动态刚度谐振器的质量梯度超结构的加宽低频带隙

具有周期性排列的高静态低动态刚度 （HSLDs） 谐振器的超结构可以产生低频带隙，因此在低频振动抑制中得到了广泛的应用。然而，随着带隙向低频移动，带隙的宽度减小，严重降低了频率失谐中超结构的鲁棒性。在本研究中，由一个框架、两个螺旋弹簧和一个内部质量线性梯度的 HSLDs 谐振器组成的晶胞周期性地逐个连接，形成一个一维质量梯度的元结构，用于在低频范围内扩展元结构的局部共振带隙。在每个 HSLD 谐振器中，使用一对磁瓦组的负刚度磁弹簧 （NSMS） 与两个表现出正刚度的螺旋弯曲弹簧 （SFS） 并联，以实现 HSLD 特性。同时，谐振器的内部质量可以分为一个可调谐分量，即几个薄质量块和一个常数分量。调整 resonator 中 thin mass 块的数量使 resonator 质量可调。首先介绍了谐振器中 NSMS 和 SFS 的设计。然后，建立质量梯度超结构的解析模型，并进行参数分析，研究展宽对质量间距、阻尼和晶胞数量的带隙的影响。与均匀超结构相比，实验中提出的质量梯度超结构可以实现低频带隙宽度增加 142%。