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平稳高斯激励下线性结构随机振动分析的辅助简谐激励广义法

范文亮 盛向前

范文亮, 盛向前. 平稳高斯激励下线性结构随机振动分析的辅助简谐激励广义法. 力学学报, 2022, 54(1): 197-209 doi: 10.6052/0459-1879-21-450
引用本文: 范文亮, 盛向前. 平稳高斯激励下线性结构随机振动分析的辅助简谐激励广义法. 力学学报, 2022, 54(1): 197-209 doi: 10.6052/0459-1879-21-450
Fan Wenliang, Sheng Xiangqian. Auxiliary harmonic excitation generalized method for random vibration analysis of linear structures under stationary Gaussian excitation. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 197-209 doi: 10.6052/0459-1879-21-450
Citation: Fan Wenliang, Sheng Xiangqian. Auxiliary harmonic excitation generalized method for random vibration analysis of linear structures under stationary Gaussian excitation. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 197-209 doi: 10.6052/0459-1879-21-450

平稳高斯激励下线性结构随机振动分析的辅助简谐激励广义法

doi: 10.6052/0459-1879-21-450
基金项目: 国家自然科学基金资助项目(51678092, 5217080983)
详细信息
    作者简介:

    范文亮, 教授, 主要研究方向: 随机振动力学、可靠度研究. E-mail: davidfwl@cqu.edu.cn

  • 中图分类号: TU311.3, O324

AUXILIARY HARMONIC EXCITATION GENERALIZED METHOD FOR RANDOM VIBRATION ANALYSIS OF LINEAR STRUCTURES UNDER STATIONARY GAUSSIAN EXCITATION

  • 摘要: 相比于时域法, 频域法是更为高效、易行的随机振动分析方法, 但对于平稳激励下的随机振动分析, 现有频域方法常需振型截断或功率谱矩阵分解, 将会影响计算精度和效率. 为此, 本文在频域法的框架下, 针对平稳高斯激励下线性结构的随机振动分析提出了一种精确且高效的辅助简谐激励广义法. 首先, 引入广义脉冲响应函数和广义频响函数的概念, 推导了与响应功率谱计算的完全二次项组合法等价的广义分析方法. 其次, 通过辅助简谐激励的响应乘积代替广义频响函数的乘积, 在广义分析方法的基础上进一步提出了更易于实现的辅助简谐激励广义法. 再次, 根据辅助简谐激励下结构响应求解方式的不同, 提出了具有不同适用性的两种辅助简谐激励广义法实现方案, 即基于振型叠加的辅助简谐激励广义法和基于时程分析的辅助简谐激励广义法; 同时, 给出了上述两种实现方案的计算性能及其与已有方法的对比分析. 最后, 通过两个算例验证本文所提方法的计算精度和效率. 由算例结果可知, 本文提出的辅助简谐激励广义法在计算响应功率谱时与完全二次项组合法和虚拟激励法的计算精度保持一致, 而计算效率相对完全二次项组合法和虚拟激励法具有显著的优势.

     

  • 图  1  NPEM-2/NPPM-2和自由度数目s的关系

    Figure  1.  The relationship between NPEM-2/NPPM-2 and the number of degrees of freedom s

    图  2  四层剪切框架

    Figure  2.  Four-story shear building

    图  3  第4层位移的自功率谱

    Figure  3.  The auto power spectrum of displacement at fourth floor

    图  4  位移的互功率谱

    Figure  4.  The cross-power spectrum of displacement

    图  5  频响函数相乘的幅值

    Figure  5.  The amplitude of frequency response function multiplication

    图  6  第4层位移的功率谱

    Figure  6.  The power spectrum of displacement at fourth floor

    图  7  位移的互功率谱SY2Y3 (ω)

    Figure  7.  The cross power spectrum SY2Y3 (ω) of displacement

    图  8  三维框架结构(单位: m)

    Figure  8.  Three-dimension frame (unit: m)

    图  9  激励功率谱

    Figure  9.  The power spectrum of excitation

    图  10  在工况1中第6层位移自功率谱SY6Y6 (ω)对数图

    Figure  10.  The auto-power spectrum SY6Y6 (ω) of displacement at 6th floor in case 1 with logarithmic scale

    图  11  第4层位移自功率谱SY4Y4(ω)对数图

    Figure  11.  The auto-power spectrum SY4Y4 (ω) of displacement at 4th floor with logarithmic scale

    图  12  楼层位移的互功率谱SY3Y5 (ω)对数图

    Figure  12.  The cross-power spectrum SY3Y5 (ω) of displacement with logarithmic scale

    图  13  点1的剪力功率谱对数图

    Figure  13.  The power spectrum of shear force at point 1 with logarithmic scale

    图  14  点2的弯矩功率谱对数图

    Figure  14.  The power spectrum of bending moment at point 2 with logarithmic scale

    表  1  不同方法的计算时间

    Table  1.   The computation time of different methods

    CaseMPEMCQCMAHEGMTPEMTAHEGM
    10.034 s1.17 s0.033 s80.49 s12.09 s
    20.95 s2.06 s0.057 s293.86 s55.71 s
    下载: 导出CSV

    表  2  不同楼层位移方差

    Table  2.   The variances of displacements at different floors

    CaseMethodFloor
    357
    Value/10−9ε/%Value/10−9ε/%Value/10−9ε/%
    1 SPEM 3.61 7.28 8.41
    CQC-1 2.17 39.89 5.01 31.18 6.72 20.01
    CQC-5 2.97 17.73 6.82 6.32 9.10 8.20
    CQC-30 3.61 0.00 7.29 0.14 8.49 0.95
    MAHEGM-30 3.61 0.00 7.29 0.14 8.49 0.95
    TAHEGM 3.61 0.00 7.28 0.00 8.41 0.00
    2 SPEM 6.10 11.90 13.50
    CQC-30 6.11 0.16 11.90 0.00 13.60 0.74
    MAHEGM -30 6.11 0.16 11.90 0.00 13.60 0.74
    TAHEGM 6.10 0.00 11.90 0.00 13.50 0.00
    3 SPEM 4.44 8.81 10.10
    CQC-30 4.44 0.00 8.82 0.11 10.20 0.99
    MAHEGM -30 4.44 0.00 8.82 0.11 10.20 0.99
    TAHEGM 4.44 0.00 8.81 0.00 10.10 0.00
    下载: 导出CSV

    表  3  不同方法的计算时间

    Table  3.   The computation time of different methods

    MethodTime/sTotal time/s
    Case 1Case 2Case 3
    SPEM34993.3934993.3934993.39104980.17
    CQC-12.312.31
    CQC-513.4713.47
    CQC-30335.22128.22128.22591.66
    MAHEGM -3017.170.220.2217.61
    TAHEGM7579.910.0170.0177579.944
    注: − 表示根据计算结果不需要计算.
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-09-06
  • 录用日期:  2021-11-02
  • 网络出版日期:  2021-11-04
  • 刊出日期:  2022-01-05

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