后屈曲张拉整体超材料的建模和优化设计  

Modeling and optimization design of post-buckling tensegrity metamaterial

作　　者：张泽轩 张亮[1] 葛艺芃 章俊[1] ZHANG Zexuan;ZHANG Liang;GE Yipeng;ZHANG Jun(College of Aerospace Engineering,Chongqing University,Chongqing 400044,P.R.China)

机构地区：[1]重庆大学航空航天学院,重庆400044

出　　处：《重庆大学学报》2025年第4期1-11,共11页Journal of Chongqing University

基　　金：国家自然科学基金资助项目(12272068)。

摘　　要：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3 Hz,承载能力超过100 N。与其他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。Achieving a balance between low-frequency bandgaps and high load capacity is a critical challenge in metamaterial design.Leveraging the post-buckling behavior of bars,this study proposes a novel tensegrity metamaterial where post-buckling induces a reduction in structural stiffness,thereby enabling low-frequency vibration isolation while enhancing load-bearing capacity.The elliptic integral method is employed to rapidly compute post-buckling deformations and determine the stiffness of the tensegrity unit.Bandgap frequencies are calculated using Bloch’s theorem under periodic boundary conditions,combined with a spring-mass diatomic chain model.To optimize both band gap and load capacity,a data-driven,dual-objective optimization method is employed,yielding the Pareto frontier for the metamaterial’s ultimate load and lower bandgap limit.The results demonstrate that the optimized structure can achieve bandgap frequency as low as 3 Hz,with a load capacity exceeding 100 N.Compared to existing low-frequency vibration isolation metamaterials,the ultimate load capacity is increased by over 3.6 times at the same bandgap frequency.

关 键 词：后屈曲变形 张拉整体超材料 带隙下限 极限载荷 多目标优化 

分 类 号：O328[理学—一般力学与力学基础]