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Article(id=1245390148230299866, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390147664068826, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0404, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1680883200000, receivedDateStr=2023-04-08, revisedDate=1683734400000, revisedDateStr=2023-05-11, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853749567, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853749567, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853749567, creator=13701087609, updateTime=1774853749567, updator=13701087609, issue=Issue{id=1245390147664068826, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='4', pageStart='1', pageEnd='233', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853749433, creator=13701087609, updateTime=1774854381443, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245392798560662150, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390147664068826, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245392798560662151, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390147664068826, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=37, endPage=45, ext={EN=ArticleExt(id=1245390148456792283, articleId=1245390148230299866, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Simulation analysis of shaking table iterative control based on surrogate specimen model, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The specimen-table interaction effects can significantly affect the accuracy of shaking table acceleration time history. Iterative control is often an important means to improve the reliability of test data. However, masonry, reinforced concrete and other structures are prone to enter the nonlinear mechanical state due to cracking, which is often not suitable for iterative loading. A simulation study is carried out on the iterative control method of the shaking table based on the surrogate specimen model. First, a surrogate specimen model with similar dynamic characteristics to the specimen was constructed, after completing the iterative loading of the shaking table and obtaining the driving command with the surrogate specimen model, a real specimen-shaking table test was carried out. The simulation results show that the shaking table iterative control based on the surrogate specimen model effectively reduces the influence of the specimen-table interaction on the system control performance, and realizes the high precision reproduction of the acceleration time history of the table.

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试件-台面相互作用会显著影响振动台加速度时程复现精度，迭代控制常常成为提高试验数据可靠性的重要手段。然而，砌体、钢筋混凝土等结构易于因开裂而进入非线性力学状态，往往不适合迭代加载。文中开展了基于替代试件模型的振动台迭代控制方法仿真研究，先构建一个与试件动力特性相近的替代试件模型，利用替代试件模型完成振动台迭代加载获得驱动命令后，再开展真实试件的振动台试验。仿真结果表明：基于替代试件模型的振动台迭代控制有效降低了试件-振动台相互作用对系统控制性能的影响，实现了台面加速度时程的高精度复现。

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吴斌（1970—），男，教授，博士，主要从事结构抗震试验方法和结构振动控制研究。E-mail：
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王贞（1983—），男，研究员，博士，主要从事结构抗震试验方法研究。E-mail：

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王贞（1983—），男，研究员，博士，主要从事结构抗震试验方法研究。E-mail：

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王贞（1983—），男，研究员，博士，主要从事结构抗震试验方法研究。E-mail：

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Shaking table control technology and software research[J]. Chinese Hydraulics & Pneumatics, 2011(6): 98-101. 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Parameters of the three degrees of freedom surrogate specimen

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物理参数第一层（阶）第二层（阶）第三层（阶）
质量/kg192023301180
刚度/（kN/m）630640500
频率/Hz1.373.714.96
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三自由度替代试件物理参数

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物理参数第一层（阶）第二层（阶）第三层（阶）
质量/kg192023301180
刚度/（kN/m）630640500
频率/Hz1.373.714.96
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Acceleration history reproduction results of three degrees of freedom specimen-shaking table system

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输入命令波形相关系数
空载线性三自由度试件非线性三自由度试件
2.6 Hz正弦曲线99.3195.7697.12
7.2 Hz正弦曲线98.5492.1595.70
10.5 Hz正弦曲线95.8191.5691.56
El Centro波92.0985.0185.99
Taft波93.0787.9887.96
), ArticleFig(id=1245390161081647900, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390148230299866, language=CN, label=表2, caption=

三自由度试件-振动台系统波形复现结果

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输入命令波形相关系数
空载线性三自由度试件非线性三自由度试件
2.6 Hz正弦曲线99.3195.7697.12
7.2 Hz正弦曲线98.5492.1595.70
10.5 Hz正弦曲线95.8191.5691.56
El Centro波92.0985.0185.99
Taft波93.0787.9887.96
), ArticleFig(id=1245390161178116895, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390148230299866, language=EN, label=Table 3, caption=

Acceleration history reproduction results of linear specimen-shaking table system

, figureFileSmall=null, figureFileBig=null, tableContent=
输入命令波形相关系数/%波形归一化均方根
期望信号89.80.398
空载迭代命令95.40.186
替代试件迭代命令99.40.111
), ArticleFig(id=1245390161345889061, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390148230299866, language=CN, label=表3, caption=

线性试件-振动台系统波形复现结果

, figureFileSmall=null, figureFileBig=null, tableContent=
输入命令波形相关系数/%波形归一化均方根
期望信号89.80.398
空载迭代命令95.40.186
替代试件迭代命令99.40.111
), ArticleFig(id=1245390161488495404, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390148230299866, language=EN, label=Table 4, caption=

Acceleration history reproduction results of nonlinear specimen-shaking table system

, figureFileSmall=null, figureFileBig=null, tableContent=
输入命令波形相关系数/%波形归一化均方根
期望信号92.10.393
空载迭代命令95.80.172
替代试件迭代命令99.10.129
), ArticleFig(id=1245390161631101745, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390148230299866, language=CN, label=表4, caption=

非线性试件-振动台系统波形再现精度结果

, figureFileSmall=null, figureFileBig=null, tableContent=
输入命令波形相关系数/%波形归一化均方根
期望信号92.10.393
空载迭代命令95.80.172
替代试件迭代命令99.10.129
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基于替代试件模型的振动台迭代控制仿真分析
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王贞 1 , 陆文龙 1 , 吴斌 1 , 贾学军 2
地震工程与工程振动 | 2024,44(4): 37-45
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地震工程与工程振动 | 2024, 44(4): 37-45
基于替代试件模型的振动台迭代控制仿真分析
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王贞1 , 陆文龙1, 吴斌1 , 贾学军2
作者信息
  • 1.武汉理工大学 土木工程与建筑学院，湖北 武汉 430070
  • 2.中国建筑第二工程局有限公司，湖北 武汉 430070

    • 王贞（1983—），男，研究员，博士，主要从事结构抗震试验方法研究。E-mail：

通讯作者:

吴斌（1970—），男，教授，博士，主要从事结构抗震试验方法和结构振动控制研究。E-mail：
Simulation analysis of shaking table iterative control based on surrogate specimen model
Zhen WANG1 , Wenlong LU1, Bin WU1 , Xuejun JIA2
Affiliations
  • 1.School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China
  • 2.China Construction Second Engineering Bureau Co., Ltd., Wuhan 430070, China
doi: 10.13197/j.eeed.2024.0404
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摘要
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试件-台面相互作用会显著影响振动台加速度时程复现精度，迭代控制常常成为提高试验数据可靠性的重要手段。然而，砌体、钢筋混凝土等结构易于因开裂而进入非线性力学状态，往往不适合迭代加载。文中开展了基于替代试件模型的振动台迭代控制方法仿真研究，先构建一个与试件动力特性相近的替代试件模型，利用替代试件模型完成振动台迭代加载获得驱动命令后，再开展真实试件的振动台试验。仿真结果表明：基于替代试件模型的振动台迭代控制有效降低了试件-振动台相互作用对系统控制性能的影响，实现了台面加速度时程的高精度复现。

振动台  /  试件-台面相互作用  /  替代试件模型  /  迭代控制

The specimen-table interaction effects can significantly affect the accuracy of shaking table acceleration time history. Iterative control is often an important means to improve the reliability of test data. However, masonry, reinforced concrete and other structures are prone to enter the nonlinear mechanical state due to cracking, which is often not suitable for iterative loading. A simulation study is carried out on the iterative control method of the shaking table based on the surrogate specimen model. First, a surrogate specimen model with similar dynamic characteristics to the specimen was constructed, after completing the iterative loading of the shaking table and obtaining the driving command with the surrogate specimen model, a real specimen-shaking table test was carried out. The simulation results show that the shaking table iterative control based on the surrogate specimen model effectively reduces the influence of the specimen-table interaction on the system control performance, and realizes the high precision reproduction of the acceleration time history of the table.

shaking table  /  specimen-table interaction effects  /  surrogate specimen model  /  iterative control
王贞, 陆文龙, 吴斌, 贾学军. 基于替代试件模型的振动台迭代控制仿真分析. 地震工程与工程振动, 2024 , 44 (4) : 37 -45 . DOI: 10.13197/j.eeed.2024.0404
Zhen WANG, Wenlong LU, Bin WU, Xuejun JIA. Simulation analysis of shaking table iterative control based on surrogate specimen model[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (4) : 37 -45 . DOI: 10.13197/j.eeed.2024.0404
正文
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0　引言
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随着科技进步，地震模拟振动台试验与振动台混合试验得到了更广泛的应用[1]，对振动台加载控制精度也提出更高的要求[2]。试验中存在的试件-台面相互作用会显著影响波形复现精度，DYKE等[3]在结构主动控制研究中考虑了结构对系统控制性能的影响，建立了作动器-结构相互作用模型。MAOULT等[4]对试件与台面的边界条件进行了有限元分析，验证了试件-台面相互作用的影响。李振宝等[5]研究了试件质量、频率和阻尼等因素对振动台系统性能的影响，指出试件与台面间的相互作用不可忽视。目前三参量控制[6]是大多数地震模拟振动台[7]研究中采用的伺服控制方法，其中位移反馈能够调节系统整体增益，速度和加速度反馈可以有效拓展系统工作频宽和提高系统阻尼比。同时，迭代控制[8]常常成为提高试验数据可靠性不可或缺的手段。刘一江等[9]在振动台液压作动器位移比例-积分-微分（proportional-integral-derivotive，PID）控制[10]的基础上，应用迭代学习控制理论构建了外部加速度控制闭环。许国山等[11]提出了基于位移-加速度迭代学习控制方法，建立实测加速度输出与位移命令输入之间的传递函数，通过输出加速度与期望加速度之间的偏差求取新的振动台位移输入命令。栾强利等[12]采用驱动信号修正迭代算法开展了通信设备的波形复现试验，得到了较高精度的地震时域波形复现效果。然而，砌体、钢筋混凝土等结构易于因开裂而进入非线性力学状态，往往不适合迭代加载。文献[13]提出了基于替代试件模型的振动台迭代控制方法，其思想是构建一个与试件动力特性相近的替代试件模型，利用该替代模型完成振动台迭代加载获得驱动命令后，再开展真实试件的振动台试验。
文献[13]阐述了基于替代试件模型的迭代控制方法基本原理，提出了求解替代试件模型参数的方法。本文在此基础上，建立试件-振动台耦合系统模型，引入三参量伺服控制和迭代控制策略，分析试件与台面间的相互作用对系统频响特性的影响；以六自由度试件和三自由度替代试件模型为例，开展基于替代试件模型的迭代控制方法仿真分析，验证该方法对于提高振动台波形复现精度的有效性。
1　振动台迭代控制原理
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三参量控制是一种基于位移闭环控制系统的极点配置控制策略[14]，包括三参量前馈和三参量反馈。其中三参量前馈部分用于对消振动台系统位移闭环传递函数中距离虚轴较近的极点，拓展系统频宽；三参量反馈是在位移闭环的基础上，分别采用加速度反馈和速度反馈提高系统的阻尼比和固有频率，保证系统稳定性的同时拓展工作频宽。
仅采用三参量伺服控制往往难以得到满意的振动台波形复现精度[15]。考虑到振动台系统本质上是非常复杂的非线性系统，难以用准确的数学模型来描述，因此迭代学习控制[16]常被用于在三参量控制基础上进一步改善台面波形复现精度。它是一种不依赖于精确的系统模型，仅需根据上一轮的控制命令和误差信号，即可修正下一轮控制命令的控制方法。然而迭代加载过程常对试件造成损伤，进而改变试件的力学性能[17]。
针对上述问题，本文提出基于替代试件模型的振动台迭代控制方法，基本原理如图1所示。在使用试件开展振动台试验之前，先构建一个与试件动力特性相近的替代试件模型，使替代试件模型和试件在地震波输入下对台面有相同的作用力；利用替代试件模型完成多轮迭代加载，修正输入信号直至台面加速度时程与期望信号之间的偏差足够小，得到迭代修正输入信号后，再使用试件开展正式的振动台试验。该方法既避免了试件在迭代加载中受损，又考虑了试件-台面相互作用对振动台系统控制性能的影响。
替代试件模型可使用梁、柱、板钢构件以及配重块制作成标准化模块，为便于组装和拆卸，宜采用具备可重复性使用特性的材料如钢材制作，各构件之间宜采用螺栓连接。文献[13]中已经表明，已知原试件的前几阶频率和振型，可以求得与其动力特性相近的替代试件模型的质量和刚度信息，由此可以选择不同截面参数和长度的柱构件，分配不同的层间质量，从而组装得到满足刚度和质量参数要求的替代试件模型。替代试件模型迭代加载试验的目的是修正振动台驱动命令，因此也不需要布置太多传感器，能够大幅降低仪器选型、传感器安装和数据采集等环节耗时。
2　振动台迭代控制仿真方法
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以往的振动台系统研究和算法设计中，常常考虑试件为刚性负载，忽略了试件-振动台相互作用对系统频率特性的影响[18-19]。本节首先建立多自由度试件与振动台耦合的系统模型，然后开展以六自由度原试件及其三自由度替代试件模型为例的振动台迭代控制仿真。
2.1　多自由度试件-振动台耦合系统
限于篇幅，仅以三自由度线性试件为例，建立多自由度试件-振动台相互作用系统模型，如图2所示。下面根据动力学特性建立运动方程。
分别建立三自由度试件和台体的运动学方程，并进行拉普拉斯变换，得
式中：M、C和K分别为试件的质量矩阵、阻尼矩阵和刚度矩阵；x={x1，x2，x3}为试件各自由度相对台面的位移向量；l={1，1，1}T为单位列向量；s为拉普拉斯算子；mp为台体质量；xp为台体位移；FI为试件对台面的作用力。由振型分解法可得各质点相对台面的位移为
式中：φi ={φ1i，φ2i，φ3i}为试件的第i阶振型向量；ωi和ζi分别为试件的第i阶频率和阻尼比。则试件的绝对位移xtp为
由式（3）和式（4）可得试件绝对位移xtp与台面位移xp之间的传递函数Htp（s）为
则三自由度试件底部对台面产生的反力等于各自由度水平惯性力之和，得
液压系统流量连续性方程[20]为
式中：kq为滑阀增益；xv为伺服阀阀芯位移；PL为负载压力；Kc和Ctc分别为液压缸泄露系数和流量压力系数；Ap为活塞有效面积；Vt为油腔总体积。令Mef=mp+lTMHtp，联立式（2）、式（6）、式（7）和式（8），消去流量QL和负载压力PL，可得负载为三自由度线性试件时台面位移与阀芯位移之间的传递函数为
2.2　振动台迭代控制仿真流程
为验证基于替代试件模型的振动台迭代学习控制方法的控制效果，采用文献[20]中的3 m×3 m地震模拟振动台模型开展仿真研究[21]。以El Centro波作为期望加速度时程，以六自由度弹簧质量阻尼原试件，三自由度替代试件模型为例，利用Matlab/Simulink建立试件-振动台耦合系统模型如图3所示，以开展仿真分析。
取六自由度试件第一至第五层质量均为1000 kg，各层间刚度为1200 kN/m；第六层质量为800 kg，层间刚度为900 kN/m；各层阻尼比为0.03，采用瑞雷阻尼。基于替代试件模型的振动台迭代控制方法仿真步骤如下：
1）求解替代试件模型物理参数。根据文献[1]中原试件模态参数的反解法求解得到该六自由度试件的三自由度替代模型参数如表1所示。
2）利用三自由度替代试件模型开展迭代加载，修正振动台驱动命令。具体步骤如下：
步骤1：首先采用白噪声激励X（t）作为输入命令，测得系统输出信号Y（t），根据输入、输出信号的傅里叶变换X（f）、Y（f）计算系统的频率响应估计，得到系统频率响应函数H（f）=Y（f）/X（f）。
步骤2：求解初始输入信号。将期望信号yd（t）傅里叶变换为yd（f），与系统逆模型H-1（f）相乘得到频域上的初始输入信号u0（f）=yd（f）•H-1（f），再经过逆傅里叶变换得到时域上的初始输入信号u0（t）。
步骤3：求取系统响应偏差。测得初始输入下的系统输出信号y0（t），计算系统响应与期望信号之间的偏差e0（t）=yd（t）-y0（t），再经过傅里叶变换为频域表示e0（f）。
步骤4：求解输入信号修正量。将系统响应偏差与逆模型相乘计算下一轮迭代的输入命令修正量Δu0（f）=e0（f）•H-1（f），再经过逆傅里叶变换为时域表示Δu0（t）。
步骤5：修正下一轮迭代的输入信号。根据当前步骤的输入信号以及求得的输入信号修正量计算下一轮迭代输入命令u1（t）=u0（t）+KΔu0（t），K为迭代增益。
步骤6：反复执行步骤3、步骤4、步骤5开展多轮修正迭代，直至振动台系统台面输出加速度波形达到满意的复现精度。迭代学习流程如图4所示。
3）利用上一步骤使用三自由度替代试件模型迭代加载得到的驱动命令作为振动台输入，完成六自由度试件的振动台试验。
3　仿真结果分析
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3.1　试件-振动台耦合系统频响特性
考虑三自由度线性试件参数如下，各自由度质量m1=m2=m3=2 000 kg；各层层间刚度K1=K2=K3=4000 kN/m；一阶频率f1 =2.6 Hz，二阶频率f2=7.2 Hz，三阶频率f3=10.5 Hz；各阶振型阻尼比ζ1=ζ2=ζ3=0.03。考虑三自由度非线性试件参数的各层屈服后刚度为弹性刚度的0.5倍，屈服位移为0.002 m。分别采用三自由度试件各阶频率处的正弦波信号，以及El Centro地震波和Taft地震波对振动台进行频率带宽和时域波形再现精度测试，分析三参量控制条件下，多自由度试件-振动台耦合系统在试件自振频率附近的波形复现精度、高频信号的追踪能力，仿真结果如表2所示。
图5为基于三参量控制的三自由度试件-振动台系统伯德图，显然试件自振频率处出现了不同程度的峰值和陷波。由表2三参量控制的三自由度试件-振动台系统波形再现结果可见，无论是三自由度线性试件还是非线性试件，相对台面空载而言均会降低输入信号的波形复现精度。对于试件各阶自振频率附近的输入信号，线性试件-振动台耦合系统的波形复现精度会出现差于台面试件为非线性的情况，主要原因在于试件屈服产生塑性变形消耗了一部分能量，从而降低了台面的共振响应，削弱了伯德图中试件自振频率处的共振峰值。另外试件屈服后刚度退化导致自振频率改变，一定程度上引起了共振峰的偏移。
3.2　振动台迭代控制仿真结果
利用三自由度替代试件模型-振动台系统开展迭代加载的输出结果如图6所示，仅需经过两轮迭代，三自由度替代模型-振动台耦合系统的输出加速度时程响应与期望信号之间的相关系数即可由89.8%提升至99.63%。图7为在三自由度替代试件模型迭代得到的驱动命令输入下，六自由度线性试件-振动台耦合系统的加速度时程输出结果。为了对比本文提出方法对于提升振动台波形复现精度的效果，分别以期望信号和空载迭代得到的振动台加载命令作为控制信号，输入到六自由度线性试件-振动台系统，仿真结果如图8和图9所示。
通过波形相关系数和波形归一化均方根来评价波形复现精度，计算结果如表3所示。波形相关系数表示为
式中：和分别为系统输出信号和期望信号均值；n为采样点数。波形归一化均方根J计算式为
对比表3数据可知，利用替代试件模型迭代更新后的振动台加载命令作为输入，相比以期望信号和空载迭代命令而言，相关系数分别增加了9.6%和4.0%，而归一化均方根分别降低了0.287和0.075。
考虑非线性试件的情况，以双线性滞回模型为例进行分析。取六自由度试件质量和弹性刚度与线性试件情况相同，屈服后刚度为弹性刚度的0.5倍，各层层高取1 m，由钢框架结构最大弹性层间位移角限值1/250 m，可得各层最大弹性位移为4 mm。采用含阻尼器的三自由度线性替代试件模型，代替双线性六自由度试件开展振动台迭代学习控制。此时在期望信号输入下，试件1~5层进入了屈服状态，第6层仍然保持弹性。仿真结果如表4所示，可知，六自由度非线性试件-振动台耦合系统在不同输入命令下的波形再现精度稍低于试件为线性的情况。整体上来看，相对于单纯三参量控制和空载迭代控制，基于替代试件模型的振动台迭代控制方法的控制效果是最优的，波形相关系数分别提升了7.0%和3.3%，而归一化均方根分别降低了0.264和0.043。
在迭代修正后的振动台加载命令输入下，六自由度线性试件、非线性试件以及三自由度替代试件对台面的作用力对比如图10所示。可见，三自由度线性试件与六自由度线性试件的底部剪力时程基本吻合，由此验证了替代试件模型的替代效果和有效性，而六自由度试件屈服之后的底部剪力总体上小于线性试件的情况，说明试件屈服之后的塑性变形消耗了一部分地震能量，由此降低了非线性试件的加速度响应。根据台面分别为线性与非线性试件的振动台作动缸活塞杆出力对比，如图11所示。图11可知，针对线性试件和非线性试件施加给台面的不同反作用力，在三参量反馈控制作用下，为了实现期望的台面加速度时程输出，作动器的出力也会有所调整。总体而言，当试件处于线性时的活塞杆出力更大，对振动台控制系统动态特性的要求更高。基于上述分析可知，尽管试件特性在试验过程中发生变化，本文提出的基于替代试件模型的振动台迭代学习控制方法仍然可以获得较高的波形复现精度，具有较强的适用性。
4　结论
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本文从三参量和迭代双闭环控制策略角度出发，针对试件与振动台台面之间的耦合作用会影响系统控制性能的问题，在提出替代试件模型求解方法的基础上，开展了基于替代试件模型的振动台迭代学习控制仿真研究。主要研究结论如下：
1）建立了多自由度试件与振动台耦合的系统模型，分析了耦合系统频率特性。仿真结果表明：无论是线性试件还是非线性试件，均会对台面波形复现精度造成较大影响，尤其是试件自振频率附近的输入波分量实现效果较差；非线性试件屈服耗能会在一定程度上抑制幅频特性图中的共振峰，相对于线性试件而言会提高试件自振频率附近的输入波分量再现精度。
2）相比于使用期望信号或台面空载迭代得到的振动台加载命令作为输入信号，利用本文提出的替代试件模型开展迭代学习获得的驱动信号作为输入，能有效地消除试件动力响应对台面产生的反力干扰，从而更大程度地提高试件-振动台耦合系统的加速度时程复现精度。
为进一步验证基于替代试件模型的振动台迭代控制方法的有效性，下一步需开展试验研究。另外，针对非线性特性复杂的试件模型，本文方法还存在一定局限性。后续将为替代试件模型引入半主动控制、主动控制元件，使其能够更好替代原型试件，并具有更好的适用性。
基金
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  • 国家自然科学基金面上项目(52078398)
  • 海南省重大科技计划项目(ZDKJ2021024)
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2024年第44卷第4期
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doi: 10.13197/j.eeed.2024.0404
  • 接收时间：2023-04-08
  • 首发时间：2026-03-30
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  • 收稿日期：2023-04-08
  • 修回日期：2023-05-11
基金
国家自然科学基金面上项目(52078398)
海南省重大科技计划项目(ZDKJ2021024)
作者信息
    1.武汉理工大学 土木工程与建筑学院，湖北 武汉 430070
    2.中国建筑第二工程局有限公司，湖北 武汉 430070

通讯作者:

吴斌（1970—），男，教授，博士，主要从事结构抗震试验方法和结构振动控制研究。E-mail：
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