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Article(id=1245390260985770253, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390255516397762, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0507, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1689350400000, receivedDateStr=2023-07-15, revisedDate=1704124800000, revisedDateStr=2024-01-02, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853776450, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853776450, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853776450, creator=13701087609, updateTime=1774853776450, updator=13701087609, issue=Issue{id=1245390255516397762, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='5', pageStart='1', pageEnd='231', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853775147, creator=13701087609, updateTime=1774854426342, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245392986884911753, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390255516397762, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245392986889106058, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390255516397762, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=71, endPage=81, ext={EN=ArticleExt(id=1245390261224845588, articleId=1245390260985770253, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Shaking table test study on suspended structure, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to investigate the seismic performance of the suspended structure with viscous damper during earthquakes, the shaking table tests were carried out on two 1/20 scaled models of suspended structures, which were equipped with rigid rods and viscous dampers respectively. The dynamic characteristics, damping ratio, structural response and damping effect of model structures were researched. The test results show that compared with the common suspended model structure, the natural frequency of the suspension damping model structure is reduced, while the damping ratio is improved, especially the first frequency and the corresponding damping ratio. The peak accelerations of the top of the main structure and the fifth suspended-floor of the suspension damping model structure are less than those of the common suspended model structure, but the damping amplitude of the peak acceleration of the fifth suspended-floor is even up to 94.34%. The maximum displacement of the top of the main structure is also distinctly smaller than that of the common suspended model structure. Different seismic wave input has different damping effect, in which the effect of Taft wave is the best, the El Centro wave is the second, and the last is artificial wave. However, the maximum relative displacement between the main structure and the suspended-floor is greater than that of the common suspended model structure, which shows that the stronger the connection between the main and secondary structures, the smaller the relative displacement. It also indicates that the suspension damping model structure takes advantage of the swing of the suspended-floors and the viscous dampers to consume energy, so that the suspended structure with viscous dampers has better effect of energy dissipation and vibration reduction.

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为研究设置黏滞阻尼器的悬挂结构在地震作用下的抗震性能，对采用刚性连接杆连接和采用黏滞阻尼器连接的悬挂结构进行了1/20比例缩尺模型振动台试验，主要研究了模型结构的动力特性、阻尼比、结构响应及其减振效果。研究结果表明：与普通悬挂模型结构相比，悬挂减振模型结构自振频率有所降低，结构的阻尼比得到提高，特别是第一阶频率和对应阻尼比；悬挂减振模型结构的主体结构顶部和第五层悬挂楼层的加速度峰值响应均小于普通悬挂模型结构，其中悬挂楼层的加速度峰值响应最佳减振幅度可达94.34%。悬挂减振结构主体结构顶部位移峰值响应较普通悬挂结构有明显地降低，且不同的地震波输入有着不同的减振效果，其中Taft波的减振效果最好，El Centro波次之，最后是人工波；主体结构与悬挂楼面的最大相对位移却大于普通悬挂结构，说明主次结构之间的连接越强，其相对位移就越小。同时也说明悬挂减振结构正是利用悬挂楼层的摆动和黏滞阻尼器来耗散能量，从而有着较好的耗能减振效果。

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蔡文华（1978—），女，副教授，博士，主要从事结构抗震性能研究。E-mail：

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蔡文华（1978—），女，副教授，博士，主要从事结构抗震性能研究。E-mail：

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蔡文华（1978—），女，副教授，博士，主要从事结构抗震性能研究。E-mail：

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Half-power bandwidth method and INV damping ration solver study[J]. Noise and Vibration Control, 2006, 26(2): 4-6. (in Chinese), articleTitle=Half-power bandwidth method and INV damping ration solver study, refAbstract=null)], funds=[Fund(id=1245390275397398635, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, awardId=51508491, language=CN, fundingSource=国家自然科学基金项目(51508491), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1245390268409688760, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, xref=1., ext=[AuthorCompanyExt(id=1245390268418077367, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, companyId=1245390268409688760, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.College of Civil Engineering, Yancheng Institute of Technology, Yancheng 224051, China), AuthorCompanyExt(id=1245390268422271672, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, 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language=CN, label=图12, caption=主结构和悬挂次结构地震加速度频率响应, figureFileSmall=gOVSojsFbnNnQv6zZw4DBw==, figureFileBig=lE+h0nisvlK8YH7kbeSYeA==, tableContent=null), ArticleFig(id=1245390273728065555, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=EN, label=Table 1, caption=

Main parameters of viscous dampers

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型号最大阻尼力/N阻尼系数/（kN•s/m）最大行程/mm
1×4D20055102
), ArticleFig(id=1245390273816145943, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=CN, label=表1, caption=

黏滞阻尼器的主要技术参数

, figureFileSmall=null, figureFileBig=null, tableContent=
型号最大阻尼力/N阻尼系数/（kN•s/m）最大行程/mm
1×4D20055102
), ArticleFig(id=1245390273954557984, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=EN, label=Table 2, caption=

Mechanical properties of reinforcement

, figureFileSmall=null, figureFileBig=null, tableContent=
直径/mm屈服强度/MPa抗拉强度/MPa弹性模量/（×105 MPa）
22403002.00
42403002.00
), ArticleFig(id=1245390274063609894, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=CN, label=表2, caption=

钢丝力学性能

, figureFileSmall=null, figureFileBig=null, tableContent=
直径/mm屈服强度/MPa抗拉强度/MPa弹性模量/（×105 MPa）
22403002.00
42403002.00
), ArticleFig(id=1245390274176856110, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=EN, label=Table 3, caption=

Similitude relations of test model

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物理量相似关系相似常数
长度SL1/20
弹性模量SE1/5
等效质量密度Sρ8/3
应力S1/5
时间St1/5.48
加速度3/2
), ArticleFig(id=1245390274281713715, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=CN, label=表3, caption=

模型主要相似关系

, figureFileSmall=null, figureFileBig=null, tableContent=
物理量相似关系相似常数
长度SL1/20
弹性模量SE1/5
等效质量密度Sρ8/3
应力S1/5
时间St1/5.48
加速度3/2
), ArticleFig(id=1245390274394959928, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=EN, label=Table 4, caption=

Seismic input condition

, figureFileSmall=null, figureFileBig=null, tableContent=
工况激振水平地震波加速度峰值/g
1白噪声0.0500
27度多遇El Centro波、Taft波、人工波0.0525
3白噪声0.0500
48度多遇El Centro波、Taft波、人工波0.1050
5白噪声0.0500
69度多遇El Centro波、Taft波、人工波0.2100
7白噪声0.0500
87度罕遇El Centro波、Taft波、人工波0.3300
9白噪声0.0500
108度罕遇El Centro波、Taft波、人工波0.6000
11白噪声0.0500
), ArticleFig(id=1245390274483040318, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=CN, label=表4, caption=

地震输入工况

, figureFileSmall=null, figureFileBig=null, tableContent=
工况激振水平地震波加速度峰值/g
1白噪声0.0500
27度多遇El Centro波、Taft波、人工波0.0525
3白噪声0.0500
48度多遇El Centro波、Taft波、人工波0.1050
5白噪声0.0500
69度多遇El Centro波、Taft波、人工波0.2100
7白噪声0.0500
87度罕遇El Centro波、Taft波、人工波0.3300
9白噪声0.0500
108度罕遇El Centro波、Taft波、人工波0.6000
11白噪声0.0500
), ArticleFig(id=1245390274613063747, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=EN, label=Table 5, caption=

Natural frequency and damping ratio of model

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振型普通悬挂结构悬挂减振结构
频率f/Hz阻尼比/%频率f/Hz阻尼比/%
1阶5.212.3011.509.254
2阶10.740.8133.715.879
3阶12.240.7106.243.362
), ArticleFig(id=1245390274701144138, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=CN, label=表5, caption=

模型自振频率及阻尼比

, figureFileSmall=null, figureFileBig=null, tableContent=
振型普通悬挂结构悬挂减振结构
频率f/Hz阻尼比/%频率f/Hz阻尼比/%
1阶5.212.3011.509.254
2阶10.740.8133.715.879
3阶12.240.7106.243.362
), ArticleFig(id=1245390274806001741, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=EN, label=Table 6, caption=

Peak acceleration response of top floors of main structure

, figureFileSmall=null, figureFileBig=null, tableContent=
地震波加速度峰值/g普通悬挂/（m/s2）悬挂减振/（m/s2）减幅/%
El Centro波0.05251.2631.2451.43
0.10502.5211.96522.05
0.21006.1935.7257.56
0.33009.6436.48832.72
0.600011.1219.07518.40
Taft波0.05250.9520.78717.33
0.10502.3922.1858.65
0.21006.1034.36428.49
0.33008.7706.73823.17
0.60009.4498.7807.08
人工波0.05251.0621.0451.60
0.10502.8612.54511.05
0.21007.3486.16916.05
0.33009.6318.53911.34
0.600011.23010.8813.11
), ArticleFig(id=1245390274885693523, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=CN, label=表6, caption=

主体结构顶点加速度峰值响应

, figureFileSmall=null, figureFileBig=null, tableContent=
地震波加速度峰值/g普通悬挂/（m/s2）悬挂减振/（m/s2）减幅/%
El Centro波0.05251.2631.2451.43
0.10502.5211.96522.05
0.21006.1935.7257.56
0.33009.6436.48832.72
0.600011.1219.07518.40
Taft波0.05250.9520.78717.33
0.10502.3922.1858.65
0.21006.1034.36428.49
0.33008.7706.73823.17
0.60009.4498.7807.08
人工波0.05251.0621.0451.60
0.10502.8612.54511.05
0.21007.3486.16916.05
0.33009.6318.53911.34
0.600011.23010.8813.11
), ArticleFig(id=1245390274977968214, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=EN, label=Table 7, caption=

Peak acceleration response of the fifth suspended floor

, figureFileSmall=null, figureFileBig=null, tableContent=
地震波加速度峰值/g普通悬挂/（m/s2）悬挂减振/（m/s2）减幅/%
El Centro波0.05250.5550.07985.77
0.10501.0430.18382.45
0.21003.9780.26893.26
0.33005.9220.50791.44
0.60006.8150.94086.21
Taft波0.05251.0310.12887.58
0.10502.1120.18391.34
0.21004.7540.26994.34
0.33006.1670.39793.56
0.60007.0340.60491.41
人工波0.05251.0730.17184.06
0.10502.1210.25687.93
0.21004.7910.45890.44
0.33006.5180.87386.61
0.60007.5411.08985.56
), ArticleFig(id=1245390275091214428, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=CN, label=表7, caption=

第5层悬挂楼层加速度峰值响应

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地震波加速度峰值/g普通悬挂/（m/s2）悬挂减振/（m/s2）减幅/%
El Centro波0.05250.5550.07985.77
0.10501.0430.18382.45
0.21003.9780.26893.26
0.33005.9220.50791.44
0.60006.8150.94086.21
Taft波0.05251.0310.12887.58
0.10502.1120.18391.34
0.21004.7540.26994.34
0.33006.1670.39793.56
0.60007.0340.60491.41
人工波0.05251.0730.17184.06
0.10502.1210.25687.93
0.21004.7910.45890.44
0.33006.5180.87386.61
0.60007.5411.08985.56
), ArticleFig(id=1245390275204460642, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=EN, label=Table 8, caption=

Peak strain response of key parts

, figureFileSmall=null, figureFileBig=null, tableContent=
地震波位置钢筋应变混凝土应变
普通/με减振/με减幅/%普通/με减振/με减幅/%
El Centro波柱底171417.6231821.7
梁端5340.011736.4
梁中8625.012925.0
Taft波柱底252020.0282221.4
梁端10640.015940.0
梁中7528.610730.0
人工波柱底282317.9201719.0
梁端8537.512833.3
梁中11827.37528.6
), ArticleFig(id=1245390275300929639, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390260985770253, language=CN, label=表8, caption=

关键部位应变响应峰值

, figureFileSmall=null, figureFileBig=null, tableContent=
地震波位置钢筋应变混凝土应变
普通/με减振/με减幅/%普通/με减振/με减幅/%
El Centro波柱底171417.6231821.7
梁端5340.011736.4
梁中8625.012925.0
Taft波柱底252020.0282221.4
梁端10640.015940.0
梁中7528.610730.0
人工波柱底282317.9201719.0
梁端8537.512833.3
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悬挂结构模拟振动台试验研究
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蔡文华 1 , 郁步军 2 , 吴发红 1 , 荀勇 1
地震工程与工程振动 | 2024,44(5): 71-81
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地震工程与工程振动 | 2024, 44(5): 71-81
悬挂结构模拟振动台试验研究
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蔡文华1 , 郁步军2, 吴发红1, 荀勇1
作者信息
  • 1.盐城工学院 土木学院，江苏 盐城 224051
  • 2.盐城工学院 基建处，江苏 盐城 224051

    • 蔡文华（1978—），女，副教授，博士，主要从事结构抗震性能研究。E-mail：

Shaking table test study on suspended structure
Wenhua CAI1 , Bujun YU2, Fahong WU1, Yong XUN1
Affiliations
  • 1.College of Civil Engineering, Yancheng Institute of Technology, Yancheng 224051, China
  • 2.Infrastructure Department, Yancheng Institute of Technology, Yancheng 224051, China
doi: 10.13197/j.eeed.2024.0507
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摘要
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为研究设置黏滞阻尼器的悬挂结构在地震作用下的抗震性能，对采用刚性连接杆连接和采用黏滞阻尼器连接的悬挂结构进行了1/20比例缩尺模型振动台试验，主要研究了模型结构的动力特性、阻尼比、结构响应及其减振效果。研究结果表明：与普通悬挂模型结构相比，悬挂减振模型结构自振频率有所降低，结构的阻尼比得到提高，特别是第一阶频率和对应阻尼比；悬挂减振模型结构的主体结构顶部和第五层悬挂楼层的加速度峰值响应均小于普通悬挂模型结构，其中悬挂楼层的加速度峰值响应最佳减振幅度可达94.34%。悬挂减振结构主体结构顶部位移峰值响应较普通悬挂结构有明显地降低，且不同的地震波输入有着不同的减振效果，其中Taft波的减振效果最好，El Centro波次之，最后是人工波；主体结构与悬挂楼面的最大相对位移却大于普通悬挂结构，说明主次结构之间的连接越强，其相对位移就越小。同时也说明悬挂减振结构正是利用悬挂楼层的摆动和黏滞阻尼器来耗散能量，从而有着较好的耗能减振效果。

悬挂减振结构  /  黏滞阻尼器  /  振动台试验  /  减振效果  /  减振幅度

In order to investigate the seismic performance of the suspended structure with viscous damper during earthquakes, the shaking table tests were carried out on two 1/20 scaled models of suspended structures, which were equipped with rigid rods and viscous dampers respectively. The dynamic characteristics, damping ratio, structural response and damping effect of model structures were researched. The test results show that compared with the common suspended model structure, the natural frequency of the suspension damping model structure is reduced, while the damping ratio is improved, especially the first frequency and the corresponding damping ratio. The peak accelerations of the top of the main structure and the fifth suspended-floor of the suspension damping model structure are less than those of the common suspended model structure, but the damping amplitude of the peak acceleration of the fifth suspended-floor is even up to 94.34%. The maximum displacement of the top of the main structure is also distinctly smaller than that of the common suspended model structure. Different seismic wave input has different damping effect, in which the effect of Taft wave is the best, the El Centro wave is the second, and the last is artificial wave. However, the maximum relative displacement between the main structure and the suspended-floor is greater than that of the common suspended model structure, which shows that the stronger the connection between the main and secondary structures, the smaller the relative displacement. It also indicates that the suspension damping model structure takes advantage of the swing of the suspended-floors and the viscous dampers to consume energy, so that the suspended structure with viscous dampers has better effect of energy dissipation and vibration reduction.

suspension damping structure  /  viscous dampers  /  shaking table test  /  damping effect  /  vibration reduction amplitude
蔡文华, 郁步军, 吴发红, 荀勇. 悬挂结构模拟振动台试验研究. 地震工程与工程振动, 2024 , 44 (5) : 71 -81 . DOI: 10.13197/j.eeed.2024.0507
Wenhua CAI, Bujun YU, Fahong WU, Yong XUN. Shaking table test study on suspended structure[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (5) : 71 -81 . DOI: 10.13197/j.eeed.2024.0507
正文
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0　引言
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高层建筑是一种应用广泛的建筑形式，但是，在地震作用下，建筑物的振动常常会使居住人群感到不适，甚至会造成结构的破坏。传统的方法是通过增强结构本身的强度、刚度和延性来提高结构的抗力。这种消极抗震措施不仅提高了工程的设防造价，也给工程结构带来了很大的局限性。为了改变这种状况，工程师们在积极探索新的抗震结构体系的同时，将结构控制理论融入结构设计之中[1-3]。悬挂结构体系[4-7]是一种新型抗震结构体系，其结构体系主要由三部分组成，分别为承重主构架、吊件和被悬挂的楼层。这种结构体系利用悬挂楼层，进行主动抗震，具有良好的抗震性能，同时承重主构架和悬挂楼层之间又便于控制设备的安装，是一种具有良好发展前景的高层建筑结构体系[4]。
目前研究较多的悬挂结构体系按主体结构的不同主要分为两类：核心筒体[5-7]和巨型框架[8-11]。本文主要针对单段巨型框架式悬挂结构进行了振动台试验[12-14]研究。
对于巨型框架悬挂结构，国内外学者做了不少的理论研究[15-17]。结果表明，巨型框架悬挂结构具有良好的减震性能，特别是在巨型框架柱与悬挂楼层之间安装阻尼器后，使得其具有更好地耗能能力，楼层地震反应明显减小，因而，使得实际工程的实现更具可行性。但是，试验研究很少，仅见报道的文献[15-16]中的模型是采用有机玻璃制作的，为4层巨型框架悬挂减振模型，且每根桁架仅悬挂一个楼层，并以海绵块作为巨型框架和悬挂楼层之间的阻尼器，这显然与实际的高层建筑结构相差比较大，并且此文献仅仅定性地研究了风洞试验条件下风振控制的效果。为了更好地研究巨型框架悬挂结构的减振特性，本文对安装黏滞阻尼器1/20缩尺的悬挂模型结构进行振动台试验，研究悬挂减振结构的动力特性，及其减振规律和减振效果。
1　试验概况
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1.1　模型设计
试验模型为10层CFRP索巨型框架悬挂结构，缩尺比为1/20。结构两端设有筒体巨型柱，第9、10层为巨型框架悬挂大梁所在楼层，两巨型柱之间设有悬挂楼层，第3~8层即为悬挂楼层，如图1所示。
模型平面尺寸为4.48 m×0.63 m，总高度2.28 m。悬挂楼层是通过设置于悬挂大梁上的钢索吊挂，各悬挂楼层与巨型框架柱之间留有一定空隙，用于布设黏滞阻尼器或刚性连接杆，如图2所示。悬挂楼层与巨型框架柱之间布设黏滞阻尼器的结构称为悬挂减振结构，布设刚性连接杆的结构称为普通悬挂结构。
主体结构与悬挂楼盖之间刚性连接采用的刚性连接杆两端与结构两端采用铰接的形式，刚性连接杆必须有足够的轴向刚度，以保证铁钩振动时连接处不发生相对位移。刚性连接杆采用直径为25 mm的中间带长度调节套筒的定制钢杆，如图2（a）所示。
试验选用的黏滞阻尼器是由美国Taylor公司负责设计和制造的线性速度型阻尼器，如图2（b）所示。该阻尼器主要是由一个不锈钢活塞杆、一个有孔青铜活塞头和装满硅油的圆柱形钢套管构成，具有线黏滞阻尼器的基本特征，尺寸较小。通过活塞杆与钢套管之间的相对运动，两油仓内的硅油受到挤压、剪切，从而耗散能量。根据前期研究成果[4，14]，结合模型需要选用了阻尼器的主要技术参数如表1所示。
模型采用微粒混凝土和镀锌钢丝制成。在模型浇筑过程中，预留了3组微粒混凝土立方体和棱柱体试块。实测微粒混凝土立方体抗压强度平均值为9.4 MPa，弹性模量为6×103 MPa。采用电液伺服万能试验机对镀锌钢丝进行了拉伸试验，得到模型钢筋的屈服强度和抗拉强度，如表2所示。
1.2　模型相似率
根据量纲分析法，先确定相似条件，然后由相似控制参数，推导其余的相似常数。基于地震模拟试验的一致相似率，根据振动台台面尺寸首先确定了试验模型几何相似比为1/20；考虑到试验模型实现的技术和条件，选用微粒混凝土，确定了弹性模量相似比为1/5；考虑到材料、配重等因素，综合考虑后取重力密度相似比为8/3。以上的3个相似比即为本次试验模型相似控制参数，一旦确定则可推导出模型其他的相似系数，模型主要相似关系如表3所示，试验模型如图3所示。
钢索采用直径为9 mm钢绞线、夹片式锚具制作而成。
1.3　配重方案
根据重力密度的相似关系计算出质量的相似关系，从而计算出模型各部分的质量，不足部分通过附加人工质量实现。选用试验专用试验块作为附加质量，用泡沫胶将其固定在主体结构和悬挂楼盖上。主体结构两侧框筒内，每层分别外加配重160 kg（共8块配重质量块），顶部每层悬挂转换梁外加配重240 kg（共12块配重质量块），每层悬挂楼盖外加配重240 kg（共12块配重质量块），主结构与次结构质量比为1/0.54，详细配重方案如图4所示。
1.4　测量设备及测点布置
本次试验在北京工业学城市与工程抗震减灾技术北京市国际科技合作基地进行，数据采集系统采用扬州晶明科技有限公司研发的动态信号采集仪，每个采集仪有16个通道，一共有4台采集仪，共64个通道。采集仪JM5938A和JM3823连接电阻应变片，采集仪JM5938连接位移传感器和加速度传感器，数据采集系统如图5所示。
试验模型上共布置有12个水平加速度传感器和5个水平位移激光传感器。加速度传感器主要布置在主体结构的第1、2、4、5、6、8、10层，以及悬挂楼面的第1、3、5、6层。位移传感器则布置在主体结构上，与第1、3、5、6层悬挂楼面相平齐处，以及结构顶部，如图6所示。
通过上述的位移、加速度传感器可测得结构关键位置处的加速度响应和位移响应。为了了解模型结构重点部位的受力情况，有选择地在模型结构的内部和表面粘贴了电阻应变片。具体为巨型柱与基础顶交接处的钢筋上粘贴钢筋应变片若干和结构相应表面混凝土上粘贴混凝土应变片若干；巨型柱、梁交接处和巨型框架梁跨中部位的钢筋上粘贴钢筋应变片若干和结构相应表面混凝土上粘贴混凝土应变片若干。
1.5　试验方案
试验采用电液伺服驱动的模拟地震振动台，其台面尺寸为2 m×2 m，最大载重量为10 t，最大位移为±125 mm，最大速度为500 mm/s，最大加速度为±2.0 g。
本次试验研究的是结构在弹性范围内的工作性能，故选用设计基本地震加速度为0.15 g地区的7度多遇、8度多遇、9度多遇、7度罕遇和8度罕遇5个地震作用水平进行试验。地震波沿结构长跨方向（即图6中的振动方向）输入。考虑不同场地条件的差异，以及脉冲效应对减振效果的影响。选取了3条典型地震波（El Centro波、Taft波及随机人工地震波）作为输入激励，如图7所示。试验时依次进行加载，通过对地震波数据的调整，将白噪声和3条地震波分别按照5个地震作用水平进行；为了对比分析3条地震波输入下结构的动力响应，各级地震波加速度峰值调整到同一值作为台面激励。表4为地震动输入工况，在试验开始前和各工况结束后，均采用白噪声激励，以量测动力特性及其变化。
本次地震模拟振动台试验按照先普通悬挂结构，后悬挂减振结构的顺序进行，且每组试验均按照表4所示的地震作用等级依次施加。
2　试验结果与分析
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2.1　试验现象
当输入的地震波峰值加速度小于0.105 g时，普通悬挂结构和悬挂减振结构的主体结构和悬挂楼面均没有肉眼可见的晃动；当输入的地震波峰值加速度为0.105 g时，2种悬挂结构均出现轻微的晃动。相比较而言，悬挂减振结构的悬挂楼面较普通悬挂结构的主体和悬挂楼面均晃动得明显，而悬挂减振结构的主体则较普通悬挂结构的晃动得不明显；当地震波加速度峰值达到0.21 g及以上时，两类结构均随着输入加速度峰值的增大，而出现越来越强烈的振动。普通悬挂结构的主体和悬挂楼面的振动基本是同步的，且无明显相对水平振动；而悬挂减振结构的悬挂楼面，其振动稍稍滞后于主体结构，且悬挂楼面与主体结构之间有相对水平振动。两类结构的主体结构和悬挂楼面从始至终均无裂缝产生，钢索也无受剪损伤的痕迹。但连接主次结构的刚性杆和阻尼器的螺丝有不同程度的变形。普通悬挂结构中，连接刚性连杆的螺丝有部分出现了松动，其中个别出现了螺杆的微微弯曲变形；而悬挂减振结构中，连接阻尼器的部分螺丝仅出现了松动，螺杆基本没有出现弯曲。
2.2　模型结构的动力特性
2　种结构在各种地震输入下，主体结构均无裂缝产生，钢索也没有受损的痕迹，可以初步断定，在整个试验过程中，结构处于弹性状态。
在各级地震荷载输入前后，均采用白噪声对两类结构进行扫频（见表4），可得测试点的加速度信号，求得模型结构的加速度响应幅频图。采用半功率带宽法[18-21]对所得的加速度幅频图进行分析，即可得结构在某阶自振频率下的阻尼比。白噪声激励下，测试分析得到结构x向（即沿结构纵向）前3阶自振频率见表5。
模型的动力特性在各级地震荷载作用前后无明显变化，已在表5中给出了其平均值。这也表明模型结构的主体结构在试验过程中一直处于弹性状态，从而达到主体结构保持弹性的设计目的。
由表5中数据的变化可知，对于2种模型结构，其各自的阻尼比均随着其X向自振频率的增加而降低，且悬挂减振模型结构的阻尼比比普通悬挂模型结构有很大的提高，分别从2.301%，0.813%和0.710%提高到9.254%，5.879%和3.362%。说明，主次结构之间采用不同的连接方式对结构的动力特性有较大的影响，在主次结构之间布设黏滞阻尼器可以有效地发挥其减振耗能作用，抑制结构的动力响应，提高悬挂建筑结构的阻尼比。
悬挂减振模型结构的前3阶自振频率明显小于普通悬挂模型结构，特别是第1阶频率，这说明当采用刚性连接时，主体结构与悬挂楼盖共同振动；而采用黏滞阻尼器连接时，以悬挂楼盖振动为主。普通悬挂结构的整体刚度大于悬挂减振结构，即悬挂减振结构较普通悬挂结构更“柔”一些，这有助于悬挂减振结构避开地震的卓越周期，提高结构的减振性能。
2.3　加速度响应
结构的加速度响应是一个反映结构动态响应的重要指标。表6给出了3种地震波激励下地震作用由弱到强时，普通悬挂模型结构和悬挂减振模型结构顶部最大加速度响应值，分析了结构的减振幅度（减振幅度简称减幅A=（R1-R2）/R1，其中，R1为普通悬挂结构的地震响应，R2为悬挂减振结构的地震响应）。
由表6可知，悬挂减振模型结构主体顶部的加速度比普通悬挂模型结构均小，减振幅度均在33%以内，某些工况下的减振效果较好，例如，El Centro波加速度峰值调整为0.330 g输入时，结构的减振效果可达32.72%；不同地震波作用下，2种模型结构顶部加速度峰值也有大差异，其中Taft波作用下，模型结构的减振效果较为明显。反映了结构对不同地震波的敏感程度不同，减振效果也不同，同时说明减振效果与输入地震波的频谱特性有关。
从表6中还可以看出，不同地震波作用下，模型结构的减幅不同；即使是同一地震波作用下，但地震作用水平不同，模型结构的减幅也不同。模型结构的减幅随着加速度响应峰值的变化而变化，没有明显的规律，不过这也正说明黏滞阻尼器对结构的加速度响应有一定的调节作用。
图8为9度多遇地震作用下普通悬挂结构和减振悬挂结构主体顶部加速度时程曲线。
悬挂楼层从下至上依次为第1~6层，在第5层布设的加速度传感器测得的模型结构的加速度响应峰值如表7所示。
由表7可知，悬挂减振模型结构的悬挂楼层加速度响应峰值远远小于普通悬挂模型结构，减振幅度最大达到了94.34%，最小也有82.45%。其中Taft波下的减振效果最明显，减振幅度为87.58%~94.34%。说明，模型结构的加速度响应对于不同地震波的输入敏感程度不同；悬挂楼面作为这类结构的主要活动场所，安装黏滞阻尼器后模型结构的加速度峰值响应急剧地下降，某些工况甚至能满足人体舒适度对加速度的要求。说明，黏滞阻尼器的布设在减小加速度响应方面发挥了巨大的作用；从表7还可以看出，随着地震烈度的增加，模型结构的加速度峰值响应也在不断地增大，但模型结构的减振效果则无明显变化，说明悬挂楼面的减振效果受地震烈度的强弱影响不大。另外，可以通过对黏滞阻尼器的布设、参数的优化等来实现最佳的减振效果。
2.4　位移响应
图9给出了各级地震荷载作用下，普通悬挂结构和悬挂减振结构主体顶部的位移反应。
由图9可知，3种地震波输入下，均是随着台面输入地震波峰值加速度的提高，2种模型结构顶部的位移峰值响应不断地增大，且在7度和8度罕遇地震作用时，模型结构顶部位移均显著增长；与主体框架柱和悬挂楼层采用刚性连接杆连接的普通悬挂模型结构相比，采用黏滞阻尼器连接的悬挂减振模型结构，其主体结构顶部位移峰值响应均有不同程度的降低，且对于不同的地震波降低的程度略有差异。经对比分析后发现，当台面输入地震加速度峰值为0.0525 g时，3种地震波作用下均有较好的减振效果；而当台面输入地震加速度峰值为0.210 g时，Taft波作用下减振效果最好，El Centro波作用下效果次之，而人工波作用下减振效果最差。说明不同台面地震加速度输入下，不同的地震波频谱特性对2种模型结构的位移响应影响较大。
图10给出了普通悬挂模型结构和悬挂减振模型结构的悬挂楼层与主体结构的最大相对位移。
由图10可知，随着地震荷载的加大，悬挂楼层与主体结构的最大相对位移增加；悬挂减振结构最大相对位移较普通悬挂模型结构大，说明悬挂楼层的摆动及黏滞阻尼器的耗能在减小结构的位移响应方面发挥了作用；同等级地震荷载，不同的地震输入，2种结构的最大相对位移稍有差异。另外，普通悬挂模型结构主次结构之间通过刚性连接杆连接，主次结构之间相对位移受到约束、限制，故当地震输入加速度较大时，只能有相对较为薄弱的刚性连接杆的螺杆产生了弯曲变形来实现，这与前文的试验现象相印证；而悬挂减振模型结构的主次结构的相对位移则可通过阻尼器实现。
2.5　应变响应
主体结构有些部位，如框架柱的底部、悬挂大梁的跨中及梁端等都是模型结构的关键部位，其应变响应也是值得关注的。对模型结构同一部位的不同应变片测得的最大应变响应峰值取均值，作为该部位的最大应变响应峰值。试验结果显示，模型结构应变峰值响应随着地震作用水平的增加而增大，但由于数据量庞大，没有详细给出，仅给出了具有代表性的一些。表8给出了8度多遇地震作用下，柱底、梁端以及梁跨中混凝土和钢筋应变响应峰值的均值及对应的动力响应减幅。
由表8可知，框架柱底（角部）的应变反应比框架大梁端部、跨中的应变反应均大一些。无论是钢筋的应变还是混凝土的应变，均是悬挂减振模型结构的应变响应峰值略小于普通悬挂模型结构，应变峰值响应减幅为17.6%~40.0%。整个试验过程中，模型未发现裂缝。从应变数据的观测来看，结构应变整体在小范围内变化。经计算，结构最大应力不超过模型材料（微粒混凝土和镀锌铁丝）的设计强度，说明整个试验过程中模型一直在弹性范围内工作。
3　悬挂减振结构能量耗散机理
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根据悬挂减振结构体系的建造原理，建立悬挂减振结构的动力分析模型如图11所示，是一个二自由度模型。
主体结构和悬挂次结构分别为一个单自由度系统，在地震作用下，其运动方程可表示为
式中：x、、分别为主体结构与地面的相对位移向量、相对速度向量和相对加速度向量；I为元素为1的单位向量；为地震动加速度；质量矩阵M、阻尼矩阵C、刚度矩阵K分别为
假定主体结构和悬挂次结构的固有频率分别为
主体结构和悬挂次结构的阻尼比分别为
悬挂次结构与主体结构的质量比和圆频率比分别为
激励频率与主体结构自振频率之比为
假设地震动为复简谐振动，幅值为1，即
可得：
令加速度响应为
式中，为加速度频率响应函数向量，则有：
由此可得：
将式（3）~式（6）代入式（1），得
由式（12）可求得地震加速度频率响应函数为
式中Ω= f2+2if（fξ1+ξ2）λ-[1+（1+μ）f2+4fξ1ξ2]λ2-2i [ξ1+（1+μ）fξ2]λ3+λ4。
影响结构地震加速度频率响应的因素很多，阻尼比是一个重要的影响因素。对于悬挂减振结构体系而言，主体结构的阻尼比ξ1通常变化不大，假定ξ1 = 0.05；悬挂次结构可以通过布置阻尼器等耗能减振装置，调节阻尼器参数的方法来影响其阻尼比ξ2。假定μ = 0.5，f = 1.0，图12给出了悬挂阻尼比ξ2对主体结构和悬挂次结构地震加速度频率响应的影响。
由图12可知，随着阻尼比ξ2的增大，主体结构和悬挂次结构的地震加速度响应都有显著减小。ξ2从0增加到0.2，地震加速度响应最大降幅达63%。可见，悬挂次结构的阻尼比ξ2越大，悬挂次结构的减振效果越好。当然，考虑到实际工程的成本等因素，不可能无限制地提高悬挂次结构的阻尼比，而应具体情况具体分析。
4　结论
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通过对悬挂减振模型结构和普通悬挂模型结构的模拟振动台试验研究和分析，得到以下结论：
1）与普通悬挂模型结构相比，采用黏滞阻尼器连接悬挂楼层和主体结构的悬挂减振模型结构，其结构的自振频率有所降低，结构的阻尼比得到了提高，特别是第一阶频率和阻尼比。
2）悬挂减振模型结构主体结构顶部的加速度峰值响应小于普通悬挂模型结构；悬挂减振模型结构第五悬挂楼层的加速度峰值也小于普通悬挂模型结构，最佳减振幅度达94.34%。说明黏滞阻尼器起到了较好的耗能减振效果。
3）与普通悬挂模型结构相比，采用黏滞阻尼器连接的悬挂减振模型结构主体结构顶部位移峰值响应有明显地降低。不同的地震波输入有着不同的减振效果。当台面输入地震加速度峰值为0.210 g时，Taft波的减振效果最好，El Centro波次之，最后是人工波。
4）采用黏滞阻尼器连接的悬挂减振模型结构，主体结构与悬挂楼面的最大相对位移大于普通悬挂结构结构，说明主次结构之间的连接越强，其相对位移就越小，更说明了悬挂减振结构正是因其悬挂楼层的摆动和黏滞阻尼器在耗能。当悬挂次结构阻尼比从0增加到0.2时，最大减振可达到63%。
基金
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  • 国家自然科学基金项目(51508491)
文献
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参考文献 引证文献
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2024年第44卷第5期
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doi: 10.13197/j.eeed.2024.0507
  • 接收时间：2023-07-15
  • 首发时间：2026-03-30
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  • 收稿日期：2023-07-15
  • 修回日期：2024-01-02
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国家自然科学基金项目(51508491)
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    1.盐城工学院 土木学院，江苏 盐城 224051
    2.盐城工学院 基建处，江苏 盐城 224051
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2种不同金属材料的力学参数
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Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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