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平稳/非平稳激励下中厚圆柱壳随机振动响应的基准解

霍慧 陈国海 王文培 杨迪雄

霍慧, 陈国海, 王文培, 杨迪雄. 平稳/非平稳激励下中厚圆柱壳随机振动响应的基准解. 力学学报, 2022, 54(3): 762-776 doi: 10.6052/0459-1879-21-538
引用本文: 霍慧, 陈国海, 王文培, 杨迪雄. 平稳/非平稳激励下中厚圆柱壳随机振动响应的基准解. 力学学报, 2022, 54(3): 762-776 doi: 10.6052/0459-1879-21-538
Huo Hui, Chen Guohai, Wang Wenpei, Yang Dixiong. Benchmark solutions of random vibration responses for moderately thick cylindrical shells under stationary/nonstationary excitations. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 762-776 doi: 10.6052/0459-1879-21-538
Citation: Huo Hui, Chen Guohai, Wang Wenpei, Yang Dixiong. Benchmark solutions of random vibration responses for moderately thick cylindrical shells under stationary/nonstationary excitations. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 762-776 doi: 10.6052/0459-1879-21-538

平稳/非平稳激励下中厚圆柱壳随机振动响应的基准解

doi: 10.6052/0459-1879-21-538
基金项目: 国家自然科学基金资助项目(12032008, 12102080)
详细信息
    作者简介:

    杨迪雄, 教授, 主要研究方向: 随机振动与结构可靠度、结构抗震减灾和优化设计. E-mail: yangdx@dlut.edu.cn

  • 中图分类号: O324

BENCHMARK SOLUTIONS OF RANDOM VIBRATION RESPONSES FOR MODERATELY THICK CYLINDRICAL SHELLS UNDER STATIONARY/NONSTATIONARY EXCITATIONS

  • 摘要: 圆柱壳结构被广泛应用于航空航天、船舶、汽车工程等领域. 由于服役环境复杂, 圆柱壳会受到随机激励作用, 从而产生随机振动响应. 本文针对考虑横向剪切变形和转动惯量的中厚圆柱壳, 将虚拟激励法拓展到连续体结构, 高效获得了各类随机激励下响应均方根的基准解. 首先, 开展了简支条件下中厚圆柱壳的自由振动分析, 精确求得各阶自振频率和解析振型函数. 其次, 根据随机激励形式, 利用虚拟激励法和振型叠加技术, 构造虚拟激励, 将解析精确频率和振型函数引入随机振动分析, 导出平稳、非平稳激励作用下中厚圆柱壳的随机振动响应功率谱密度函数解析解, 并积分得到响应均方根. 解析求解涉及空间域、频域和时间域的积分运算, 利用解析积分可获得精确封闭解, 但其难度和效率随参振频率的增加而显著增加. 为充分发挥虚拟激励法在矩阵运算中的显著优势, 将空间域积分解析求解, 频域和时域数值求解, 进而提出了离散解析法高效获得封闭和开口的中厚圆柱壳随机振动响应. 该过程保证了空间上的精确性, 高效获得壳内随机振动响应的分布, 结果可作为基准解验证其他数值方法. 通过与ABAQUS软件、蒙特卡洛模拟结果及文献结果比较, 展示了离散解析法的高精度和高效性. 最后, 阐明了圆柱壳厚径比、载荷形式、非平稳性特性等因素对随机振动响应的显著影响.

     

  • 图  1  中厚圆柱壳几何模型及载荷情况

    Figure  1.  Geometric model and load cases for moderately thick cylindrical shell

    图  2  开口中厚壳的自振频率(Hz)及振型(精确解和有限元解)

    Figure  2.  Natural frequencies (Hz) and modal functions of open moderately thick shells (exact solutions and FEM results)

    图  3  随机点激励下封闭中厚壳(L/2, 0)处径向位移响应功率谱密度曲线

    Figure  3.  Deflection response PSD curves of (L/2, 0) for the closed moderately thick shells under random point excitation

    图  4  随机点激励(case 2)下封闭中厚壳(L/2, 0)处薄膜内力Nx和弯矩Mx功率谱密度曲线

    Figure  4.  Response PSD curves of membrane force Nx and bending moment Mx of (L/2, 0) for the closed moderately thick shells under random point excitation (case 2)

    5  随机环形线激励下中厚壳(L/2, 0)处弯矩响应功率谱密度曲线

    5.  Bending moment response PSD curves of (L/2, 0) for the closed moderately thick shells under random annular line excitation

    图  6  两类随机分布载荷的空间分布形式

    Figure  6.  Spatial distribution forms of two random distributed loads

    图  7  两类分布载荷作用下开口圆柱壳的位移响应均方根分布

    Figure  7.  RMS distributions of deflection for open shell under two distributed random loads

    图  9  两类分布载荷作用下开口壳的加速度响应均方根分布

    Figure  9.  RMS distributions of acceleration for open shell under two distributed random loads

    图  8  两类分布载荷作用下开口壳的速度响应均方根分布

    Figure  8.  RMS distributions of velocity for open shell under two distributed random loads

    图  10  时间调制函数f(t)

    Figure  10.  Time-modulated function f(t)

    11  非平稳随机激励下中厚壳中心点位移响应均方根

    11.  Stochastic deflection responses RMSs of the center of moderately thick shell under nonstationary random excitations

    11  非平稳随机激励下中厚壳中心点位移响应均方根(续)

    11.  Stochastic deflection responses RMSs of the center of moderately thick shell under nonstationary random excitations (continued)

    12  非平稳随机激励下中厚壳中心点位移响应功率谱密度

    12.  Stochastic deflection responses PSD curves of the center of moderately thick shell under nonstationary random excitations

    12  非平稳随机激励下中厚壳中心点位移响应功率谱密度(续)

    12.  Stochastic deflection responses PSD curves of the center of moderately thick shell under nonstationary random excitations (continued)

    表  1  封闭中厚壳的前5阶自振频率(Hz)

    Table  1.   The first 5 natural frequencies (Hz) of closed moderately thick cylindrical shells

    Order1st2nd3rd4th5th
    exact 713.3 1218.1 1558.7 1694.2 1816.1
    Ref. [12] 713.5 1218.3 1558.8 1695.1 1817.4
    FEM (500, S4 R) 729.6 1209.1 1712.7 1730.9 1969.3
    FEM (1000, S4 R) 714.5 1217.4 1596.6 1702.5 1846.6
    FEM (2000, S4 R) 714.2 1215.6 1597.1 1694.4 1846.0
    FEM (4000, S4 R) 712.3 1216.2 1582.3 1691.5 1832.1
    FEM (6000, S4 R) 710.5 1217.3 1566.3 1690.2 1817.3
    FEM (8000, S4 R) 710.4 1217.2 1566.3 1689.6 1817.2
    FEM (500, S8 R) 709.4 1217.8 1558.4 1688.7 1810.6
    FEM (1000, S8 R) 709.2 1217.7 1556.4 1688.1 1808.0
    FEM (2000, S8 R) 709.2 1217.7 1556.4 1688.0 1808.0
    FEM (4000, S8 R) 709.2 1217.7 1556.2 1688.0 1807.8
    FEM (6000, S8 R) 709.2 1217.7 1556.2 1688.0 1807.8
    FEM (8000, S8 R) 709.2 1217.7 1556.2 1688.0 1807.8
    下载: 导出CSV

    表  2  径向随机点激励作用下封闭中厚壳(L/2, 0)处响应均方根

    Table  2.   Response RMSs of (L/2, 0) for the closed moderately thick shells under random point excitation

    CasesMethodsElements (nodes)Response RMSs of (L/2, 0)CPU time/s
    Def./μmAcc./(m·s−2)Mx/(N·m)
    case 1 AM − (1)* 0.574 4 20.494 1.577 13.4
    DAM 4000 (4141) 0.574 4 20.494 1.577 0.01
    ABAQUS 4000 (12080) 0.574 0 19.148 1.517 0.02
    case 2 AM − (1) * 0.309 8 6.652 0.545 13.5
    DAM 4000 (4141) 0.309 8 6.652 0.545 0.01
    ABAQUS 4000 (12080) 0.309 6 5.601 0.519 0.02
    * “−” indicates that the analytical method do not implement element discretization, and (1) means the number of nodes is 1
    下载: 导出CSV

    表  3  随机环形线激励作用下封闭中厚壳(L/2, 0)处径向响应均方根

    Table  3.   Radial response RMSs of (L/2, 0) for the closed moderately thick shells under random annular line excitation

    h/RRadial response RMSs of (L/2,0)
    Def./μmVel./cmAcc./(m·s−2)
    1/362.8732.449217.893
    1/201.5961.361121.041
    1/100.7980.68060.496
    下载: 导出CSV

    表  4  非平稳随机均布激励下中厚壳中心点响应均方根 (t = 4.8 s)

    Table  4.   Stochastic response RMSs of the center of moderately thick shell under nonstationary random distributed excitations (t = 4.8 s)

    h/RMethodsΔt/sRadial response RMSsCPU time/s
    Def./cmVel./(m·s−1)Acc./(km·s−2)
    1/20AM10.8710.901.85860.5
    DAM0.210.8610.901.8570.1
    MCS0.000510.8410.981.8639.2
    1/10AM2.533.920.94031.6
    DAM0.22.523.910.9400.1
    MCS0.00052.503.930.9444.2
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-10-21
  • 录用日期:  2022-02-17
  • 网络出版日期:  2022-02-18
  • 刊出日期:  2022-03-18

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