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基于动力特性的混合结构地震响应复模态叠加法

孙攀旭 杨红 刘庆林

孙攀旭, 杨红, 刘庆林. 基于动力特性的混合结构地震响应复模态叠加法[J]. 工程力学, 2020, 37(11): 69-82. doi: 10.6052/j.issn.1000-4750.2019.12.0723
引用本文: 孙攀旭, 杨红, 刘庆林. 基于动力特性的混合结构地震响应复模态叠加法[J]. 工程力学, 2020, 37(11): 69-82. doi: 10.6052/j.issn.1000-4750.2019.12.0723
Pan-xu SUN, Hong YANG, Qing-lin LIU. COMPLEX MODE SUPERPOSITION METHOD OF HYBRID STRUCTURE SEISMIC RESPONSES BASED ON DYNAMIC CHARACTERISTICS[J]. Engineering Mechanics, 2020, 37(11): 69-82. doi: 10.6052/j.issn.1000-4750.2019.12.0723
Citation: Pan-xu SUN, Hong YANG, Qing-lin LIU. COMPLEX MODE SUPERPOSITION METHOD OF HYBRID STRUCTURE SEISMIC RESPONSES BASED ON DYNAMIC CHARACTERISTICS[J]. Engineering Mechanics, 2020, 37(11): 69-82. doi: 10.6052/j.issn.1000-4750.2019.12.0723

基于动力特性的混合结构地震响应复模态叠加法

doi: 10.6052/j.issn.1000-4750.2019.12.0723
基金项目: 国家自然科学基金项目 (51578343);重庆市研究生科研创新项目 (CYB18036)
详细信息
    作者简介:

    孙攀旭 (1990−),男,河南许昌人,博士生,从事结构抗震设计与计算的研究 (E-mail: sunpanxu@163.com)

    刘庆林 (1969−),男,湖南衡山人,高工,博士,从事结构分析、计算与设计理论 (E-mail: liu2xa@vip.163.com)

    通讯作者:

    杨 红 (1969−),男,浙江平湖人,教授,博士,博导,从事结构抗震设计理论与方法的研究 (E-mail: yangh@cqu.edu.cn)

  • 中图分类号: TU311.3

COMPLEX MODE SUPERPOSITION METHOD OF HYBRID STRUCTURE SEISMIC RESPONSES BASED ON DYNAMIC CHARACTERISTICS

  • 摘要: 混合结构由不同阻尼特性的材料组成,确定其阻尼矩阵存在困难。分块Rayleigh阻尼模型由于数学上的简易性,被广泛用于构建混合结构的阻尼矩阵,但分块Rayleigh阻尼模型的计算精度与参考频率的选择方法直接相关。针对参考频率的选择问题,依据结构动力响应的组成和特点,提出了一种确定Rayleigh阻尼系数的计算方法,进而实现基于分块Rayleigh阻尼模型的复模态叠加法。求解结构的瞬态反应时,根据结构前两阶振型的自振频率确定阻尼系数;求解结构的稳态反应时,选择结构的基频、与外激励频率接近的结构自振频率确定阻尼系数。依据地震波的频谱特性,提出了基于地震波卓越频率的分块Rayleigh阻尼模型,并结合地震加速度的分段线性假定,建立了混合结构的复模态叠加法。在此基础上,利用三角级数展开得到组成地震波的谐波频率,进一步提出了基于谐波频率的分块Rayleigh阻尼模型和对应的复模态叠加法。算例分析结果表明:所提方法误差更小,且克服了传统方法因振型选择不唯一导致的计算结果具有不确定性的问题;与基于地震波卓越频率的复模态叠加法相比,基于谐波频率的复模态叠加法计算量更大,但计算精度更高、适用范围更广。
  • 图  1  试件动力响应的试验系统

    Figure  1.  Test system of specimens’ dynamic responses

    图  2  试件的尺寸 /mm

    Figure  2.  Size of specimen

    图  3  拾振点的位置 /mm

    Figure  3.  Locations of vibration receiving points

    图  4  试件CP-1的随机激励

    Figure  4.  Random external excitation of specimen CP-1

    图  5  试件CP-1的速度响应时程

    Figure  5.  Velocity time-history responses of specimen CP-1

    图  6  试件CP-2的随机激励

    Figure  6.  Random external excitation of specimen CP-2

    图  7  试件CP-2的速度响应时程

    Figure  7.  Velocity time-history responses of specimen CP-2

    图  8  模型示意图

    Figure  8.  Schematics of structural models

    图  9  天津地震波的加速度时程和傅里叶谱

    Figure  9.  Acceleration time-history and Fourier amplitude spectrum of Tianjin seismic wave

    图  10  迁安地震波的加速度时程和傅里叶谱

    Figure  10.  Acceleration time-history and Fourier amplitude spectrum of Qian'an seismic wave

    图  11  天津波作用下模型A的顶层时程响应

    Figure  11.  Top floor time-history responses of Model A under Tianjin wave

    图  12  迁安波作用下模型A的顶层时程响应

    Figure  12.  Top floor time-history responses of Model A under Qian'an wave

    图  13  天津波作用下模型B的顶层时程响应

    Figure  13.  Top floor time-history responses of Model B under Tianjin wave

    图  14  迁安波作用下模型B的顶层时程响应

    Figure  14.  Top floor time-history responses of Model B under Qian'an wave

    表  1  试件的材料参数

    Table  1.   Material parameters of specimen

    材料参数基层材料阻尼层材料
    Q235钢板Air++3104阻尼胶片
    弹性模量/Pa$2.1 \times {10^{11}}$$4.0 \times {10^7}$
    密度/(kg/m3)75001600
    泊松比0.300.49
    损耗因子0.0030.59
    下载: 导出CSV

    表  2  试件CP-1的动力响应对比

    Table  2.   Comparisons of dynamic responses of specimen CP-1

    速度CP-1-TestCRSCRZCRX
    ${I_{\rm{A}}}$/(mm/s) 39.2692 23.8258 35.1506 36.0660
    ${\delta _{\rm{A}}}$/(%) 39.3300 10.4900 8.1600
    ${I_{\rm{B}}}$/(mm/s) 38.1542 25.8730 32.1342 33.6120
    ${\delta _{\rm{B}}}$/(%) 32.1900 15.7800 11.9000
    下载: 导出CSV

    表  3  试件CP-2的动力响应对比

    Table  3.   Comparisons of dynamic responses of specimen CP-2

    速度CP-2-TestCRSCRZCRX
    ${I_{\rm{A}}}$/(mm/s) 63.4593 48.5796 55.1387 58.4345
    ${\delta _{\rm{A}}}$/(%) 23.4500 13.1100 7.9200
    ${I_{\rm{B}}}$/(mm/s) 75.2177 39.4871 60.7179 66.8291
    ${\delta _{\rm{B}}}$/(%) 47.5000 19.2800 11.1500
    下载: 导出CSV

    表  4  不同材料的参数

    Table  4.   Parameters of different materials

    材料类别弹性模量/Pa密度/(kg/m3)阻尼比
    钢筋混凝土$3.5 \times {10^{10}}$25000.05
    钢材$2.0 \times {10^{11}}$79000.02
    阻尼器$1.0 \times {10^{11}}$50000.40
    下载: 导出CSV

    表  5  模型A的顶层响应对比

    Table  5.   Comparisons of top floor responses of Model A

    响应天津地震波迁安地震波
    RYCRZCRXRYCRZCRX
    位移峰值/cm 16.5223 15.9200 16.5802 1.1064 0.8875 1.1094
    相对误差/(%) 3.6500 0.3500 19.7800 0.2700
    加速度峰值/
    (cm/s2)
    356.7642 347.9600 357.8498 97.1007 111.6260 96.9218
    相对误差/(%) 2.4700 0.3000 14.9600 0.1800
    下载: 导出CSV

    表  6  模型B的顶层响应对比

    Table  6.   Comparisons of top floor responses of Model B

    响应天津地震波迁安地震波
    RYCRZCRXRYCRZCRX
    位移峰值/cm 0.5488 0.6193 0.6047 0.2666 0.2074 0.2989
    相对误差/(%) 12.8500 10.1900 22.2100 12.1200
    加速度峰值/
    (cm/s2)
    184.2694 225.0049 215.8834 162.0321 143.2617 181.4360
    相对误差/(%) 22.1100 17.1600 11.5800 11.9800
    下载: 导出CSV
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  • 收稿日期:  2019-12-05
  • 修回日期:  2020-05-20
  • 刊出日期:  2020-11-25

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