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X构型张力非线性系统共振激励下的拍振现象

齐子涵 吴志强 焦云雷 贾文文

齐子涵,吴志强,焦云雷,贾文文. X构型张力非线性系统共振激励下的拍振现象 [J]. 应用数学和力学,2022,43(6):597-607 doi: 10.21656/1000-0887.420326
引用本文: 齐子涵,吴志强,焦云雷,贾文文. X构型张力非线性系统共振激励下的拍振现象 [J]. 应用数学和力学,2022,43(6):597-607 doi: 10.21656/1000-0887.420326
QI Zihan, WU Zhiqiang, JIAO Yunlei, JIA Wenwen. Beat Vibration of X-Configuration Tension Nonlinear Systems Under Resonance Excitation[J]. Applied Mathematics and Mechanics, 2022, 43(6): 597-607. doi: 10.21656/1000-0887.420326
Citation: QI Zihan, WU Zhiqiang, JIAO Yunlei, JIA Wenwen. Beat Vibration of X-Configuration Tension Nonlinear Systems Under Resonance Excitation[J]. Applied Mathematics and Mechanics, 2022, 43(6): 597-607. doi: 10.21656/1000-0887.420326

X构型张力非线性系统共振激励下的拍振现象

doi: 10.21656/1000-0887.420326
详细信息
    作者简介:

    齐子涵(1993―),男,硕士(E-mail:qizihan@tju.edu.cn

    吴志强(1968―),男,教授,博士,博士生导师(通讯作者. E-mail:zhiqwu@tju.edu.cn

    焦云雷(1982―),男,高级工程师

    贾文文(1991―),女,工程师

  • 中图分类号: O322

Beat Vibration of X-Configuration Tension Nonlinear Systems Under Resonance Excitation

  • 摘要:

    圆形太阳翼因收纳比高、供电能力强等特点受到人们的广泛重视。作为大尺寸薄膜结构,为了调节薄膜张力,通常会引入由绳和弹簧组成的张力调节装置,其力学特性具有强非线性特征,但目前还未有研究讨论其影响。该文提出了一种研究张力影响的机理模型,并利用Lagrange能量法建立了系统二自由度非线性动力学方程,以某工程样机为例,研究了张力机构出现肋板不对称时系统在共振激励下的响应。研究表明,激励幅值变化对系统拍振响应特点有重要影响,使其出现了混沌、概周期以及多倍周期等现象。这些结果对张力机构参数设计有重要参考作用。

  • 图  1  张力非线性结构模型示意图

    Figure  1.  Schematic diagram of the tension nonlinear symmetric model

    图  2  激励幅值为0.3线性系统的响应:(a) 肋板1时间历程图;(b) 肋板2时间历程图;(c) 肋板1频谱图;(d) 肋板2频谱图

    Figure  2.  With an excitation amplitude of 0.3, the linear system responses:(a) the time history diagram of rib 1; (b) the time history diagram of rib 2; (c) the spectrum diagram of rib 1; (d) the spectrum diagram of rib 2

    图  3  激励幅值为0.3非线性系统的响应:(a) 肋板1时间历程图;(b) 肋板2时间历程图;(c) 肋板1 Poincaré截面图;(d) 肋板2 Poincaré截面图;(e) 肋板1频谱图;(f) 肋板2频谱图;(g) 肋板1 Hilbert包络谱;(h) 肋板2 Hilbert包络谱

    Figure  3.  With an excitation amplitude of 0.3, the nonlinear system responses: (a) the time history diagram of rib 1; (b) the time history diagram of rib 2; (c) the Poincaré section diagram of rib 1; (d) the Poincaré section diagram of rib 2; (e) the spectrum diagram of rib 1; (f) the spectrum diagram of rib 2; (g) the Hilbert envelope spectrum diagram of rib 1; (h) the Hilbert envelope spectrum diagram of rib 2

    图  4  激励幅值改变下肋板分岔图:(a) 肋板1分岔图;(b) 肋板2分岔图

    Figure  4.  With a changing excitation amplitude, the bifurcation diagrams of the lower ribs: (a) the bifurcation diagram of rib 1; (b) the bifurcation diagram of rib 2

    图  5  激励幅值为0.67结构非对称系统的响应:(a) 肋板1时间历程图;(b) 肋板2时间历程图;(c) 肋板1 Poincaré截面图;(d) 肋板2 Poincaré截面图;(e) 肋板1频谱图;(f) 肋板2频谱图;(g) 肋板1 Hilbert包络谱;(h) 肋板2 Hilbert包络谱

    Figure  5.  With an excitation amplitude of 0.67, the asymmetric-structure system responses: (a) the time history diagram of rib 1; (b) the time history diagram of rib 2; (c) the Poincaré section diagram of rib 1; (d) the Poincaré section diagram of rib 2; (e) the spectrum diagram of rib 1; (f) the spectrum diagram of rib 2; (g) the Hilbert envelope spectrum diagram of rib 1; (h) the Hilbert envelope spectrum diagram of rib 2

    图  6  激励幅值为0.72结构非对称系统的响应:(a) 肋板1时间历程图;(b) 肋板2时间历程图;(c) 肋板1 Poincaré截面图;(d) 肋板2 Poincaré截面图;(e) 肋板1频谱图;(f) 肋板2频谱图;(g) 肋板1 Hilbert包络谱;(h) 肋板2 Hilbert包络谱

    Figure  6.  With an excitation amplitude of 0.72, the asymmetric-structure system responses: (a) the time history diagram of rib 1; (b) the time history diagram of rib 2; (c) the Poincaré section diagram of rib 1; (d) the Poincaré section diagram of rib 2; (e) the spectrum diagram of rib 1; (f) the spectrum diagram of rib 2; (g) the Hilbert envelope spectrum diagram of rib 1; (h) the Hilbert envelope spectrum diagram of rib 2

    图  7  激励幅值为2.66结构非对称系统的响应:(a) 肋板1时间历程图;(b) 肋板2时间历程图;(c) 肋板1 Poincaré截面图;(d) 肋板2 Poincaré截面图;(e) 肋板1频谱图;(f) 肋板2频谱图;(g) 肋板1 Hilbert包络谱;(h) 肋板2 Hilbert包络谱

    Figure  7.  With an excitation amplitude of 2.66, the asymmetric-structure system responses: (a) the time history diagram of rib 1; (b) the time history diagram of rib 2; (c) the Poincaré section diagram of rib 1; (d) the Poincaré section diagram of rib 2; (e) the spectrum diagram of rib 1; (f) the spectrum diagram of rib 2; (g) the Hilbert envelope spectrum diagram of rib 1; (h) the Hilbert envelope spectrum diagram of rib 2

    表  1  模型参数取值

    Table  1.   Values of model parameters

    parametervalue
    rib plate length l /m2.9
    elastic modulus E /Pa7.2 × 1010
    rib plate width e /m0.005
    rib plate 1 height h1 /m0.04
    rib plate 2 height h2 /m0.05
    material density ρ/(kg/m3)435
    tension spring stiffness k0/(N/m)5.59
    grounding spring stiffness k1/(N/m)2900
    structural damping C /(N·s·m-1)0.366
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出版历程
  • 收稿日期:  2021-10-28
  • 修回日期:  2021-11-16
  • 网络出版日期:  2022-05-23
  • 刊出日期:  2022-06-30

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