EI、Scopus 收录
中文核心期刊

多稳态串联折纸结构的非线性动力学特性

邱海, 方虹斌, 徐鉴

邱海, 方虹斌, 徐鉴. 多稳态串联折纸结构的非线性动力学特性[J]. 力学学报, 2019, 51(4): 1110-1121. DOI: 10.6052/0459-1879-19-115
引用本文: 邱海, 方虹斌, 徐鉴. 多稳态串联折纸结构的非线性动力学特性[J]. 力学学报, 2019, 51(4): 1110-1121. DOI: 10.6052/0459-1879-19-115
Qiu Hai, Fang Hongbin, Xu Jian. NONLINEAR DYNAMICAL CHARACTERISTICS OF A MULTI-STABLE SERIES ORIGAMI STRUCTURE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1110-1121. DOI: 10.6052/0459-1879-19-115
Citation: Qiu Hai, Fang Hongbin, Xu Jian. NONLINEAR DYNAMICAL CHARACTERISTICS OF A MULTI-STABLE SERIES ORIGAMI STRUCTURE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1110-1121. DOI: 10.6052/0459-1879-19-115
邱海, 方虹斌, 徐鉴. 多稳态串联折纸结构的非线性动力学特性[J]. 力学学报, 2019, 51(4): 1110-1121. CSTR: 32045.14.0459-1879-19-115
引用本文: 邱海, 方虹斌, 徐鉴. 多稳态串联折纸结构的非线性动力学特性[J]. 力学学报, 2019, 51(4): 1110-1121. CSTR: 32045.14.0459-1879-19-115
Qiu Hai, Fang Hongbin, Xu Jian. NONLINEAR DYNAMICAL CHARACTERISTICS OF A MULTI-STABLE SERIES ORIGAMI STRUCTURE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1110-1121. CSTR: 32045.14.0459-1879-19-115
Citation: Qiu Hai, Fang Hongbin, Xu Jian. NONLINEAR DYNAMICAL CHARACTERISTICS OF A MULTI-STABLE SERIES ORIGAMI STRUCTURE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1110-1121. CSTR: 32045.14.0459-1879-19-115

多稳态串联折纸结构的非线性动力学特性

基金项目: 1) 国家自然科学基金资助项目(11772229);国家自然科学基金资助项目(11572224);国家自然科学基金资助项目(91748203)
详细信息
    通讯作者:

    方虹斌

  • 中图分类号: O322

NONLINEAR DYNAMICAL CHARACTERISTICS OF A MULTI-STABLE SERIES ORIGAMI STRUCTURE

  • 摘要: 折纸结构和折纸力学超材料由于其无穷的设计空间、出色的变形能力、超常规力学特性和广泛的应用前景,最近受到了学术界和工程界的 广泛关注.特别地,某些折纸结构单胞由于具有独特的双稳态特性而获得深入研究.注意到折纸结构和折纸超材料通常由多胞构成,但多胞 结构的多稳态特性及其诱发的动力学行为尚不清晰,相关的研究还较少.本文在双稳态Miura-ori堆叠结构单胞的基础上,研究由两个异构 双稳态单胞基于力平衡串联而成的结构.静力学分析指出,双胞串联结构具有4个定性不同的稳定构型,呈现出多稳态特征.动力学分析指 出,双胞串联结构在4个稳定构型处具有显著不同的固有频率特征. 逐渐增大激励幅值,双胞串联结构的多稳态特性诱发出类型丰富的复杂 非线性动力学响应,包括亚谐、超谐甚至混沌的阱内和阱间振动. 根据幅值特征,我们将稳态动力学响应分为九类,并开展了动力学响应的 吸引盆和吸引盆稳定性分析.结果表明,不同类型动力学响应的吸引盆稳定性(即出现概率)显著不同,且与激励幅值密切相关.本文得到的 多稳态双胞串联结构的静力学特性、动力学响应的分类,以及吸引盆稳定性相对于激励幅值的演化规律,对深入认识多稳态折纸结构的非 线性动力学特性,调控非线性动力学响应具有参考价值和指导意义.
    Abstract: Recently, origami structures and origami mechanical metamaterials receive extensive attention from the science and engineering communities due to the infinite design space, excellent deformability, extraordinary mechanical properties, and wide application potentials. In particular, some origami structures have been well studied due to their unique bistability. Note that origami structures and origami metamaterials are always composed of multiple cells; however, for multi-cell origami structures, their multistability characteristics and the induced dynamical behaviors have not been well understood. On the basis of the bistable stacked Miura-ori structure, this paper studies an origami structure connected by two heterogeneous cells in series based on force balance. Static analysis suggests that the two-cell series structure have four different stable configurations, exhibiting a multi-stable profile. Dynamical analysis reveals that the two-cell series origami structure presents significantly different natural frequencies at the four stable configurations. With the increase of the excitation amplitude, the multistability of the two-cell series structure could induce complex nonlinear dynamical responses, including intrawell and interwell oscillations that are sub-harmonic, super-harmonic, or even chaotic. They can be classified into nine types based on the response amplitude characteristics. Moreover, the basin of attraction and the basin stability of these dynamical responses are examined. The results indicate that the basin stabilities (i.e., the appearing probabilities) of these types of dynamical response are significantly different and closely relate to the excitation amplitude. In summary, the outcomes of this paper, i.e., the static characteristics of the two-cell series structure, the classification on dynamical responses, and the evolution rule of the basin stabilities with respect to the excitation amplitude, would contribute to the understanding on the nonlinear dynamics of multi-stable origami structures, and provide the basis for controlling the nonlinear dynamical responses.
  • [1] Perazahernandez EA, Hartl DJ, Malak RJJ , et al. Origami-inspired active structures: a synthesis and review. Smart Materials & Structures, 2014,23(9):094001
    [2] Lebée A . From folds to structures, a review. International Journal of Space Structures, 2015,30(2):55-74
    [3] Ning X, Wang X, Zhang Y , et al. Assembly of advanced materials into 3D functional structures by methods inspired by origami and Kirigami: A review. Advanced Materials Interfaces, 2018,1800284
    [4] Turner N, Goodwine B, Sen M . A review of origami applications in mechanical engineering. Journal of Mechanical Engineering Science, 2016,230(14):2345-2362
    [5] Park JJ, Won P, Ko SW . A review on hierarchical origami and kirigami structure for engineering applications. International Journal of Precision Engineering and Manufacturing-Green Technology, 2019,6(1):147-161
    [6] Rus D, Tolley MT . Design, fabrication and control of origami robots. Nature Reviews Materials, 2018,3:101-112
    [7] 陈仕魁, 顾险峰 . 心脏支架、折纸艺术与超材料设计. 科技导报, 2017(10):107
    [7] ( Chen Shikui, Gu Xianfeng . Heart stent, origami and metamaterial design. Science & Technology Review, 2017(10):107 (in Chinese))
    [8] 李笑, 李明 . 折纸及其折痕设计研究综述. 力学学报, 2018,50(3):23-32
    [8] ( Li Xiao, Li Ming . A review of origami and its crease design. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(3):23-32 (in Chinese))
    [9] 常若菲, 张一慧, 宋吉舟 . 可延展结构的设计及力学研究新进展. 固体力学学报, 2016,37(2):95-106
    [9] ( Chang Roufei, Zhang Yihui, Song Jizhou . Recent advances in mechanics of stretchable designs. Chinese Journal of Solid Mechanics, 2016,37(2):95-106 (in Chinese))
    [10] 冯慧娟, 杨名远, 姚国强 等. 折纸机器人. 中国科学: 技术科学, 2018,48(12):5-20
    [10] ( Feng Huijuan, Yang Mingyuan, Yao Guoqiang , et al. Origami robots. Scientia Sinica Technologica, 2018,48(12):5-20 (in Chinese))
    [11] Miura K . Method of packaging and deployment of large membranes in space. Title The Institute of Space and Astronautical Science Report, 1985,618:1
    [12] Sareh P, Chermprayong P, Emmanuelli M , et al. Rotorigami: A rotary origami protective system for robotic rotorcraft. Science Robotics, 2018,3:5228
    [13] Gattas JM, You Z . Geometric assembly of rigid-foldable morphing sandwich structures. Engineering Structures, 2015,94:149-159
    [14] Karagiozova D, Zhang J, Lu G , et al. Dynamic in-plane compression of Miura-ori patterned metamaterials. International Journal of Impact Engineering, 2019,129:80-100
    [15] Harne RL, Lynd DT . Origami acoustics: Using principles of folding structural acoustics for simple and large focusing of sound energy. Smart Materials and Structures, 2016,25(8):085031
    [16] Thota M, Wang KW . Reconfigurable origami sonic barriers with tunable bandgaps for traffic noise mitigation. Journal of Applied Physics, 2017,122(15):154901
    [17] Thota M, Wang KW . Tunable waveguiding in origami phononic structures. Journal of Sound and Vibration, 2018,430:93-100
    [18] Thota M, Li S, Wang KW . Lattice reconfiguration and phononic band-gap adaptation via origami folding. Physical Review B, 2017,95:064307
    [19] Dudte LH, Vouga E, Tachi T , et al. Programming curvature using origami tessellations. Nature Materials, 2016,15:583-588
    [20] Boatti E, Vasios N, Bertoldi K . Origami metamaterials for tunable thermal expansion. Advanced Materials, 2017,29:1700360
    [21] Na J, Evans A, Bae J , et al. Programming reversibly self-folding origami with micropatterned photo-crosslinkable polymer trilayers. Advanced Materials, 2015,27(1):79-85
    [22] Silverberg JL, Evans AA, McLeod L , et al. Using origami design principles to fold reprogrammable mechanical metamaterials. Science, 2014,345(6197):647-650
    [23] Schenk M, Guest SD . Geometry of Miura-folded metamaterials. Proceedings of the National Academy of Sciences, 2013,110(9):3276-3281
    [24] Li S, Fang H, Sadeghi S , et al. Architected origami materials: How folding creates sophisticated mechanical properties. Advanced Materials, 2018,31(5):1805282
    [25] Fang H, Chu SC, Xia Y , et al. Programmable self-locking origami mechanical metamaterials. Advanced Materials, 2018,30(15):1706311
    [26] Filipov ET, Tachi T, Paulino GH . Origami tubes assembled into stiff, yet reconfigurable structures and metamaterials// Proceedings of the National Academy of Sciences of the United States of America, 2015
    [27] Filipov ET, Paulino GH, Tachi T . Origami tubes with reconfigurable polygonal cross-sections. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2016,472(2185):20150607
    [28] Li S, Wang KW . Fluidic origami with embedded pressure dependent multi-stability: A plant inspired innovation. Journal of The Royal Society Interface, 2015,12(111):20150639
    [29] 陆泽琦, 陈立群 . 非线性被动隔振的若干进展. 力学学报, 2017,49(3):550-564
    [29] ( Lu Zeqi, Chen Liqun . Some recent progresses in nonlinear passive isolations of vibrations. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(3):550-564 (in Chinese))
    [30] 曹登庆, 白坤朝, 丁虎 等. 大型柔性航天器动力学与振动控制研究进展. 力学学报, 2019,51(1):1-13
    [30] ( Cao Dengqing, Bai Kunchao, Ding Hu , et al. Advances in dynamics and vibration control of large-scale flexible spacecraft. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):1-13 (in Chinese))
    [31] 刘坚, 雷济荣, 夏百战 . 基于Chebyshev展开的区间穿孔板超材料分析. 力学学报, 2017,49(1):137-148
    [31] ( Liu Jian, Lei Jirong, Xia Baizhan . The interval analysis of multilayer-meramaterials with perforated apertures based on Chebyshev expansion. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(1):137-148 (in Chinese))
    [32] 修晨曦, 楚锡华 . 基于微形态模型的颗粒材料中波的频散现象研究. 力学学报, 2018,50(2):315-328
    [32] ( Xiu Chenxi, Chu Xihua . Study on dispersion behavior and band gap in granular materials based on a micromorhpic model. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(2):315-328 (in Chinese))
    [33] Rodrigues GV, Fonseca LM, Savi MA , et al. Nonlinear dynamics of an adaptive origami-stent system. International Journal of Mechanical Sciences, 2017,133:303-318
    [34] Yasuda H, Chong C, Charalampidis EG , et al. Formation of rarefaction waves in origami-based metamaterials. Physical Review E, 2016,93(4):043004
    [35] Fang H, Li S, Ji H , et al. Dynamics of a bistable Miura-origami structure. Physical Review E, 2017,95(5):052211
    [36] Liu Z, Fang H, Wang KW , et al. A parameter identification method for continuous-time nonlinear systems and its realization on a Miura-origami structure. Mechanical Systems and Signal Processing, 2018,108:369-386
    [37] Fang H, Wang KW, Li S . Asymmetric energy barrier and mechanical diode effect from folding multi-stable stacked-origami. Extreme Mechanics Letters, 2017,17:7-15
    [38] Kuribayashi K, Tsuchiya K, You Z , et al. Self-deployable origami stent grafts as a biomedical application of Ni-rich TiNi shape memory alloy foil. Materials Science & Engineering A, 2006,419(1):131-137
    [39] Fonseca LM, Rodrigues GV, Savi MA , et al. Nonlinear dynamics of an origami wheel with shape memory alloy actuators. Chaos, Solitons & Fractals, 2019,122:245-261
    [40] Lenci S, Rega G . Forced harmonic vibration in a duffing oscillator with negative linear stiffness and linear viscous damping// The Duffing Equation: Nonlinear Oscillators and their Behaviour, John Wiley & Sons Ltd, 2015
    [41] Menck PJ, Heitzig J, Marwan N , et al. How basin stability complements the linear-stability paradigm. Nature Physics, 2013,9(2):89-92
  • 期刊类型引用(14)

    1. 何远鹏,王凌峰,杨秋松,李哲健,郝洪,陈文苏. 多折角梯形台面折纸夹层结构的冲击防护性能. 爆炸与冲击. 2024(04): 36-48 . 百度学术
    2. 靳明珠,侯秀慧,赵文皓,邓子辰. 多层级曲梁多稳态超材料的可重用性研究. 力学学报. 2024(11): 3227-3242 . 本站查看
    3. 万世雯,张琦炜,方虹斌,徐鉴. 三单元同构/异构MSC串联折纸结构的实验分析. 华中科技大学学报(自然科学版). 2023(01): 26-33 . 百度学术
    4. 方虹斌,吴海平,刘作林,张琦炜,徐鉴. 折纸结构和折纸超材料动力学研究进展. 力学学报. 2022(01): 1-38 . 本站查看
    5. 刘鹏飞,朱凌云,苟向锋,石建飞,金国光. 计及短周期误差的直齿轮副近周期运动及其辨识. 力学学报. 2022(03): 786-799 . 本站查看
    6. 严嘉怡,李佳强,陈耀,冯健. 基于图论方法与优化算法的六折痕折纸结构构型研究. 建筑结构学报. 2022(09): 277-285 . 百度学术
    7. 陈耀,叶王杰,史佳遥,冯健. 三浦折纸超材料结构数字化设计与模型验证. 力学学报. 2022(07): 2019-2029 . 本站查看
    8. 袁婷婷,任昆明,方雨桥,刘锦阳. 考虑非线性本构的非刚性折纸结构动力学建模与分析. 力学学报. 2022(09): 2552-2566 . 本站查看
    9. 王海瑞,申薛靖,王宙恒,贾璐,李传檑,朱龙基,赵丹阳. 折纸超材料折展稳态特性研究. 力学学报. 2022(10): 2726-2732 . 本站查看
    10. 肖伯雅,杨洮,冯亚菲,刘宇,徐文帅,陈猛,姜恒,王育人. 可重构力学超材料的设计与波动特性研究. 力学学报. 2022(10): 2708-2716 . 本站查看
    11. 王凯,周加喜,蔡昌琦,徐道临,文桂林. 低频弹性波超材料的若干进展. 力学学报. 2022(10): 2678-2694 . 本站查看
    12. 侯秀慧,吕游,周世奇,朱志韦,张凯,邓子辰. 新型负刚度吸能结构力学特性分析. 力学学报. 2021(07): 1940-1950 . 本站查看
    13. 万世雯,张琦炜,徐鉴. MSC折纸结构设计及其双稳态解析与实验. 力学季刊. 2021(03): 429-437 . 百度学术
    14. 吕阳,方虹斌,徐鉴,马建敏,王启宁,张晓旭. 四连杆膝关节假肢的动力学建模与分析. 力学学报. 2020(04): 1157-1173 . 本站查看

    其他类型引用(16)

计量
  • 文章访问数:  2503
  • HTML全文浏览量:  287
  • PDF下载量:  724
  • 被引次数: 30
出版历程
  • 收稿日期:  2019-05-04
  • 刊出日期:  2019-07-17

目录

    /

    返回文章
    返回