后屈曲张拉整体超材料的建模和优化设计
作者:
作者单位:

重庆大学 航空航天学院,重庆 400044

作者简介:

张泽轩(1997—),男,硕士研究生,主要从事张拉整体超材料方向研究,(E-mail)zhangzx@cqu.edu.cn。

通讯作者:

葛艺芃,男,助理教授,(E-mail)y.ge@cqu.edu.cn。

中图分类号:

O328

基金项目:

国家自然科学基金资助项目(12272068)。


Modeling and optimization design of post-buckling tensegrity metamaterial
Author:
Affiliation:

College of Aerospace Engineering, Chongqing University, Chongqing 400044, P. R. China

Fund Project:

Supported by National Natural Science Foundation of China (12272068).

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    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。

    Abstract:

    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.

    参考文献
    [1] Berglund B, Hassmén P, Job R F. Sources and effects of low-frequency noise[J]. The Journal of the Acoustical Society of America, 1996, 99(5): 2985-3002.
    [2] Griffin M J, Erdreich J. Handbook of human vibration[J]. The Journal of the Acoustical Society of America, 1991, 90(4): 2213.
    [3] Lai Y, Zhang X D, Zhang Z Q. Engineering acoustic band gaps[J]. Applied Physics Letters, 2001, 79(20): 3224-3226.
    [4] Romeo F, Luongo A. Vibration reduction in piecewise bi-coupled periodic structures[J]. Journal of Sound Vibration, 2003, 268(3): 601-615.
    [5] Yu D L, Wen J H, Zhao H G, et al. Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid[J]. Journal of Sound Vibration, 2008, 318(1/2): 193-205.
    [6] Oh J H, Assouar B. Quasi-static stop band with flexural metamaterial having zero rotational stiffness[J]. Scientific Reports, 2016, 6: 33410.
    [7] Zhou J X, Wang K, Xu D L, et al. Local resonator with high-static-low-dynamic stiffness for lowering band gaps of flexural wave in beams[J]. Journal of Applied Physics, 2017, 121(4): 044902.
    [8] Cai C Q, Zhou J X, Wu L C, et al. Design and numerical validation of quasi-zero-stiffness metamaterials for very low-frequency band gaps[J]. Composite Structures, 2020, 236: 111862.
    [9] 王凯, 周加喜, 蔡昌琦, 等. 低频弹性波超材料的若干进展[J]. 力学学报, 2022, 54(10): 2678-2694.Wang K, Zhou J X, Cai C Q, et al. Review of low-frequency elastic wave metamaterials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2678-2694. (in Chinese)
    [10] Kan Z Y, Peng H J, Chen B, et al. Nonlinear dynamic and deployment analysis of clustered tensegrity structures using a positional formulation FEM[J]. Composite Structures, 2018, 187: 241-258.
    [11] Amendola A, Krushynska A, Daraio C, et al. Tuning frequency band gaps of tensegrity mass-spring chains with local and global prestress[J]. International Journal of Solids and Structures, 2018, 155: 47-56.
    [12] Wang Y T, Liu X N, Zhu R, et al. Wave propagation in tunable lightweight tensegrity metastructure[J]. Scientific Reports, 2018, 8: 11482.
    [13] Yin X, Zhang S, Xu G K, et al. Bandgap characteristics of a tensegrity metamaterial chain with defects[J]. Extreme Mechanics Letters, 2020, 36: 100668.
    [14] Zhang L Y, Yin X, Yang J, et al. Multilevel structural defects-induced elastic wave tunability and localization of a tensegrity metamaterial[J]. Composites Science and Technology, 2021, 207: 108740.
    [15] Wang Y T, Zhao W J, Rimoli J J, et al. Prestress-controlled asymmetric wave propagation and reciprocity-breaking in tensegrity metastructure[J]. Extreme Mechanics Letters, 2020, 37: 100724.
    [16] Zhang Q, Jiang B, Xiao Z M, et al. Post-buckling analysis of compressed rods in cylinders by using dynamic relaxation method[J]. International Journal of Mechanical Sciences, 2019, 159: 103-115.
    [17] Rimoli J J. A reduced-order model for the dynamic and post-buckling behavior of tensegrity structures[J]. Mechanics of Materials, 2018, 116: 146-157.
    [18] Nan G, Qu S C, Li J, et al. Harnessing post-buckling deformation to tune sound absorption in soft Helmholtz absorbers[J]. International Journal of Mechanical Sciences, 2021, 208: 106695.
    [19] Bessa M A, Bostanabad R, Liu Z, et al. A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality[J]. Computer Methods in Applied Mechanics and Engineering, 2017, 320: 633-667.
    [20] Ge Y P, He Z G, Li S F, et al. A machine learning-based probabilistic computational framework for uncertainty quantification of actuation of clustered tensegrity structures[J]. Computational Mechanics, 2023, 72(3): 431-450.
    [21] Zhao J Y, Dong Y L, Ye C. Optimization of residual stresses generated by ultrasonic nanocrystalline surface modification through analytical modeling and data-driven prediction[J]. International Journal of Mechanical Sciences, 2021, 197: 106307.
    [22] Fraternali F, Carpentieri G, Amendola A. On the mechanical modeling of the extreme softening/stiffening response of axially loaded tensegrity prisms[J]. Journal of Mechanics Physics of Solids, 2015, 74: 136-157.
    [23] 铁摩辛柯 S P, 盖莱 J M. 弹性稳定理论[M]. 张福范, 译. 北京: 科学出版社, 1965.Timoshenko S P, Gere J M. Theory of elastic stability[M]. Zhang F F, trans. Beijing: Science Press, 1965. (in Chinese)
    [24] Meaud J, Che K K. Tuning elastic wave propagation in multistable architected materials[J]. International Journal of Solids and Structures, 2017, 122/123: 69-80.
    [25] Jensen J S. Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures[J]. Journal of Sound Vibration, 2003, 266(5): 1053-1078.
    [26] Herbold E B, Kim J, Nesterenko V F, et al. Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap[J]. Acta Mechanica, 2009, 205(1): 85-103.
    [27] Bessa M A, Pellegrino S. Design of ultra-thin shell structures in the stochastic post-buckling range using Bayesian machine learning and optimization[J]. International Journal of Solids and Structures, 2018, 139/140: 174-188.
    [28] Deb K, Pratap A, Agarwal S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.
    [29] Lee S, Lim Y, Galdos L, et al. Gaussian process regression-driven deep drawing blank design method[J]. International Journal of Mechanical Sciences, 2024, 265: 108898.
    [30] Zhou J X, Pan H B, Cai C Q, et al. Tunable ultralow frequency wave attenuations in one-dimensional quasi-zero-stiffness metamaterial[J]. International Journal of Mechanics and Materials in Design, 2021, 17(2): 285-300.
    [31] Hu H Y, Hu G K, Wang Y T, et al. Isolating low-frequency vibration via lightweight embedded metastructures[J]. Scientia Sinica Physica, Mechanica & Astronomica, 2020, 50(9): 090010.
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张泽轩,张亮,葛艺芃,章俊.后屈曲张拉整体超材料的建模和优化设计[J].重庆大学学报,2025,48(4):1-11.

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  • 收稿日期:2024-03-12
  • 在线发布日期: 2025-04-25
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