如何在获得低频带隙的同时实现较高的负载能力是超材料设计中值得关注的问题。通过利用杆件的后屈曲变形,提出了一种新型张拉整体超材料。后屈曲的引入使结构刚度发生软化,在有较高的承载能力的同时,实现了低频隔振功能。利用椭圆积分法计算杆件后屈曲变形可以快速得到张拉整体单元的刚度。结合弹簧-质量双原子链模型,在周期性边界条件下利用Bloch定理对带隙进行计算。为了平衡带隙和负载能力,通过基于数据驱动的双目标优化方法获得了极限载荷和带隙下限的帕累托边界。经过优化设计后的超材料带隙频率可以低至3Hz,承载能力超过100N。与其它低频隔振超材料相比,在相同带隙频率下可以将极限承载能力提高3.6倍以上。

Balancing the attainment of low-frequency bandgap with achieving higher load capacity is a significant concern in metamaterial design. By harnessing the post-buckling characteristics of bars, a novel tensegrity metamaterial is proposed, where the introduction of post-buckling leads to a softening of the structure"s stiffness, thereby enabling a low-frequency vibration isolation functionality with enhanced load-bearing capability. Utilizing the elliptic integral method to compute the post-buckling deformations of bars allows for the rapid determination of the stiffness of the tensegrity unit. Combined with the spring-mass diatomic chain model, bandgaps are calculated using Bloch"s theorem under periodic boundary conditions. To strike a balance between band gaps and load capacity, a data-driven dual-objective optimization method is employed, yielding the Pareto frontier of the post-buckling tensegrity metamaterial"s ultimate load and lower bandgap limit. Optimization results demonstrate that the bandgap frequency of the optimized structure can be as low as 3Hz, with a load capacity exceeding 100N. Compared to other low-frequency vibration isolation metamaterials, the ultimate load capacity can be increased by over 3.6 times at the same bandgap frequency.

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国家自然科学基金项目（面上项目，重点项目，重大项目）