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Article(id=1245390012028666067, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390004252426256, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0312, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1682438400000, receivedDateStr=2023-04-26, revisedDate=1685548800000, revisedDateStr=2023-06-01, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853717094, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853717094, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853717094, creator=13701087609, updateTime=1774853717094, updator=13701087609, issue=Issue{id=1245390004252426256, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='3', pageStart='1', pageEnd='230', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853715241, creator=13701087609, updateTime=1774854338522, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245392618545332491, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390004252426256, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245392618545332492, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390004252426256, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=127, endPage=135, ext={EN=ArticleExt(id=1245390012339044584, articleId=1245390012028666067, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Performance design method of a new combined isolation system based on passive variable damping variable stiffness device, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Passive variable damping and stiffness device is a device that does not require external energy input and feedback control, and has the functions of variable damping energy consumption and variable stiffness limit. By combined with isolation bearings, this device forms a new isolation system that can effectively control seismic waves of different types and intensities. Based on the theory of performance-based design, a design method for composite isolation systems has been proposed. Through this method, the parameter design of passive variable damping and stiffness devices and isolation bearings in the isolation layer can be completed. The study also provided a complete design process and detailed explanation of the design process, and verified the feasibility and effectiveness of the design method through engineering examples. This performance design method can be widely applied in the engineering design field of composite isolation new systems, providing a reliable design method and technical support for related engineering. Through this advanced design method, the structure can better cope with disasters caused by earthquakes, ensuring the safety and stability of the structure.

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被动变阻尼变刚度装置是一种无需外部能源输入和反馈控制的装置，具有变阻尼耗能和变刚度限位功能。当与隔震支座组合使用时，这种装置构成了一种新的隔震体系，能够有效控制不同类型和烈度大小的地震波。根据性能化设计理论，提出了针对组合隔震体系的设计方法，通过该方法可以完成隔震层中被动变阻尼变刚度装置和隔震支座的参数设计工作。研究还提供了完整的设计流程和详细的设计过程说明，并通过工程实例验证了设计方法的可行性和有效性。这种性能设计方法可以广泛应用于组合隔震新体系的工程设计领域，为相关工程提供了一种可靠的设计方法和技术支持。通过这种先进的设计方法，可使结构能够更好地应对地震带来的灾害，保障结构的安全性和稳定性。

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付伟庆（1976—），男，教授，博士，主要从事结构振动控制研究。E-mail：
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李铮（1994—），男，硕士研究生，主要从事结构振动控制研究。E-mail：

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李铮（1994—），男，硕士研究生，主要从事结构振动控制研究。E-mail：

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(in Chinese), articleTitle=null, refAbstract=null)], funds=[Fund(id=1245390025148448821, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, awardId=52178488, language=CN, fundingSource=国家自然科学基金项目(52178488), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1245390018060075680, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, xref=null, ext=[AuthorCompanyExt(id=1245390018064269985, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, companyId=1245390018060075680, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=School of Civil Engineering, Qingdao University of Technology, Qingdao 266033, China), AuthorCompanyExt(id=1245390018068464290, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, companyId=1245390018060075680, language=CN, country=null, 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Performance design objectives of new combined isolation system

, figureFileSmall=null, figureFileBig=null, tableContent=
地震作用水准性能水准
水准1水准2水准3
多遇地震A——
设防地震BA—
罕遇地震CBA
), ArticleFig(id=1245390024003403783, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, language=CN, label=表1, caption=

组合隔震新体系性能设计目标

, figureFileSmall=null, figureFileBig=null, tableContent=
地震作用水准性能水准
水准1水准2水准3
多遇地震A——
设防地震BA—
罕遇地震CBA
), ArticleFig(id=1245390024112455690, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, language=EN, label=Table 2, caption=

Performance levels and expected post-earthquake performance status

, figureFileSmall=null, figureFileBig=null, tableContent=
性能水准预期震后性能状态
水准1充分运行隔震装置外观无损伤，功能完好，可正常工作
水准2基本运行隔震装置可能发生轻度损伤，无需维修可继续工作，隔震层功能基本不受影响
水准3生命安全隔震装置发生中度损伤，极少数装置破坏，但整体仍具承载力，隔震层功能受扰
), ArticleFig(id=1245390024225701902, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, language=CN, label=表2, caption=

各性能水准及预期震后性能状态

, figureFileSmall=null, figureFileBig=null, tableContent=
性能水准预期震后性能状态
水准1充分运行隔震装置外观无损伤，功能完好，可正常工作
水准2基本运行隔震装置可能发生轻度损伤，无需维修可继续工作，隔震层功能基本不受影响
水准3生命安全隔震装置发生中度损伤，极少数装置破坏，但整体仍具承载力，隔震层功能受扰
), ArticleFig(id=1245390024326365204, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, language=EN, label=Table 3, caption=

Displacement limit of isolation layer at different levels

, figureFileSmall=null, figureFileBig=null, tableContent=
性能指标性能水准
水准1水准2水准3
隔震层位移0.05D0.20D0.45D
), ArticleFig(id=1245390024439611415, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, language=CN, label=表3, caption=

不同水准下的隔震层位移限值

, figureFileSmall=null, figureFileBig=null, tableContent=
性能指标性能水准
水准1水准2水准3
隔震层位移0.05D0.20D0.45D
), ArticleFig(id=1245390024624160795, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, language=EN, label=Table 4, caption=

Acceleration limit of floor at different levels

, figureFileSmall=null, figureFileBig=null, tableContent=
性能指标性能水准
水准1水准2水准3
楼层加速度0.250.652.50
), ArticleFig(id=1245390024741601310, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, language=CN, label=表4, caption=

不同水准下的楼层加速度限值

, figureFileSmall=null, figureFileBig=null, tableContent=
性能指标性能水准
水准1水准2水准3
楼层加速度0.250.652.50
), ArticleFig(id=1245390024833876002, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, language=EN, label=Table 5, caption=

Structural parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
层数质量/（×103 kg）刚度/（kN/m）
一层9806430000
二层9805626250
三层9804822500
四层9804018759
五层9803215000
), ArticleFig(id=1245390024947122217, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390012028666067, language=CN, label=表5, caption=

结构参数

, figureFileSmall=null, figureFileBig=null, tableContent=
层数质量/（×103 kg）刚度/（kN/m）
一层9806430000
二层9805626250
三层9804822500
四层9804018759
五层9803215000
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基于被动变阻尼变刚度装置组合隔震新体系性能化设计方法
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李铮 , 付伟庆 , 王浩哲
地震工程与工程振动 | 2024,44(3): 127-135
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地震工程与工程振动 | 2024, 44(3): 127-135
基于被动变阻尼变刚度装置组合隔震新体系性能化设计方法
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李铮 , 付伟庆 , 王浩哲
作者信息
  • 青岛理工大学 土木工程学院，山东 青岛 266033

    • 李铮（1994—），男，硕士研究生，主要从事结构振动控制研究。E-mail：

通讯作者:

付伟庆（1976—），男，教授，博士，主要从事结构振动控制研究。E-mail：
Performance design method of a new combined isolation system based on passive variable damping variable stiffness device
Zheng LI , Weiqing FU , Haozhe WANG
Affiliations
  • School of Civil Engineering, Qingdao University of Technology, Qingdao 266033, China
doi: 10.13197/j.eeed.2024.0312
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摘要
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被动变阻尼变刚度装置是一种无需外部能源输入和反馈控制的装置，具有变阻尼耗能和变刚度限位功能。当与隔震支座组合使用时，这种装置构成了一种新的隔震体系，能够有效控制不同类型和烈度大小的地震波。根据性能化设计理论，提出了针对组合隔震体系的设计方法，通过该方法可以完成隔震层中被动变阻尼变刚度装置和隔震支座的参数设计工作。研究还提供了完整的设计流程和详细的设计过程说明，并通过工程实例验证了设计方法的可行性和有效性。这种性能设计方法可以广泛应用于组合隔震新体系的工程设计领域，为相关工程提供了一种可靠的设计方法和技术支持。通过这种先进的设计方法，可使结构能够更好地应对地震带来的灾害，保障结构的安全性和稳定性。

被动变阻尼变刚度装置  /  组合隔震体系  /  性能设计方法  /  控制效果

Passive variable damping and stiffness device is a device that does not require external energy input and feedback control, and has the functions of variable damping energy consumption and variable stiffness limit. By combined with isolation bearings, this device forms a new isolation system that can effectively control seismic waves of different types and intensities. Based on the theory of performance-based design, a design method for composite isolation systems has been proposed. Through this method, the parameter design of passive variable damping and stiffness devices and isolation bearings in the isolation layer can be completed. The study also provided a complete design process and detailed explanation of the design process, and verified the feasibility and effectiveness of the design method through engineering examples. This performance design method can be widely applied in the engineering design field of composite isolation new systems, providing a reliable design method and technical support for related engineering. Through this advanced design method, the structure can better cope with disasters caused by earthquakes, ensuring the safety and stability of the structure.

passive variable damping variable stiffness device  /  combined isolation system  /  performance design method  /  control effect
李铮, 付伟庆, 王浩哲. 基于被动变阻尼变刚度装置组合隔震新体系性能化设计方法. 地震工程与工程振动, 2024 , 44 (3) : 127 -135 . DOI: 10.13197/j.eeed.2024.0312
Zheng LI, Weiqing FU, Haozhe WANG. Performance design method of a new combined isolation system based on passive variable damping variable stiffness device[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (3) : 127 -135 . DOI: 10.13197/j.eeed.2024.0312
正文
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0　引言
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常规被动隔震技术存在最优控制频域窄和需限位的局限性[1-6]，采用磁流变阻尼器的半主动隔震控制效果好，但需外部能源输入和响应数据反馈控制[7-10]。被动变阻尼装置是一种在黏滞阻尼器的基础上改进发展而来的新型耗能装置，其采用机械方式随速度变化动态改变流孔面积，实时调节阻尼系数的方式实现可变阻尼力的输出[11-13]。但其在使用中存在位移反应过大的问题，如无法对超限位移进行控制会造成装置损坏。针对这一问题，在被动变阻尼装置的基础上，设计制作了一种新型被动变阻尼变刚度装置，该装置由变阻尼系统和变刚度系统两部分组成，兼具耗能和限位的功能。
将被动变阻尼装置与隔震支座组成组合隔震新体系，可对不同类型和烈度地震波进行有效控制。研究基于性能设计方法理论，提出一种适用于该组合隔震新体系的设计方法，给出满足各级控制目标的完整设计流程，通过工程实例验证设计方法的有效性。
1　被动变阻尼变刚度装置构造原理
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1.1　装置设计构造
被动变阻尼变刚度装置（图1）由变阻尼耗能系统和变刚度限位系统两部分组成。变阻尼耗能系统和变刚度限位系统通过法兰转接架组装成一个整体，变阻尼耗能系统的活塞杆与变刚度限位系统的碟簧杆同轴心，并且通过螺纹连接在一起协同工作。为了方便拆卸维修，装置其他零部件也均通过螺纹、法兰等机械方式组装在一起。
1.2　装置工作原理
根据装置由变阻尼耗能系统和变刚度限位系统两部分组成的构造特点，装置的工作状态可分为变阻尼耗能状态和变刚度限位状态。
1.2.1　变阻尼耗能状态
设定变刚度碟簧组首次发挥作用时的距离为预留距离d，如图1所示。当活塞相对缸筒位移小于预留距离时，装置处于变阻尼耗能状态。活塞将缸筒分为左右2个腔体，2个腔体内充满黏滞流体阻尼材料。活塞上不设阻尼通道，当阻尼器工作时，随着活塞相对油缸往复运动，黏滞流体材料从高压腔体经过外置油管控制阀流往低压腔体。在黏滞流体流经控制阀时，受到控制阀交叉孔的约束产生阻尼力，随着交叉孔大小的改变输出可变阻尼力。当活塞移动速度增大到一定阈值，流入口处的液体压力大于弹簧的预压力时，活动阀芯后的弹簧被压缩，交叉孔的面积开始变小。当活塞移动速度变小时，流入口处的液体压力也变小，弹簧压力得到释放，交叉孔的面积相应变大，阻尼器的黏滞系数变小，输出的阻尼力变小。这样就实现了阻尼力输出随速度响应的连续可变[11-13]。
1.2.2　变刚度限位状态
以装置受拉为例介绍装置的工作状态：装置活塞相对缸筒往复运动中，当位移超出限位预留距离时，变阻尼系统继续发挥作用的同时，变刚度限位系统开始发挥作用，固定于碟簧杆支座上的第一阶碟簧组端面与连接法兰接触，压缩第一阶碟簧组发挥第一阶段变刚度限位作用。随着位移继续增加，第一阶碟簧组端面接触的同时，第二阶碟簧组也与连接法兰接触，此时2组并联在一起的碟簧组共同发挥作用，发挥第二阶限位作用。
1.3　装置性能试验
为研究被动变阻尼变刚度装置变阻尼系统和变刚度系统设计的可行性，以及2个系统的协同工作情况对装置进行了性能试验。试验采用位移控制的正弦曲线加载。频率为0.01 Hz、位移幅值为30~90 mm加载工况下的滞回曲线如图2所示；频率为0.06 Hz、位移幅值为30~90 mm加载工况下的滞回曲线如图3所示。
由图2可知，在往复加载过程中，滞回曲线发生倾斜，说明装置变刚度系统能够附加刚度，且随着加载位移幅值的提高，图中滞回曲线的斜率也随之继续增大，试验结果所反映趋势与装置设计中2个阶段变刚度设计目标基本一致。因此实现了装置变刚度的预期功能。
由图3可知，试验设计中阀芯弹簧不存在预压力，加载后滞回曲线逐渐出现凸起，此时活动阀芯运动，交叉孔面积减小，黏滞阻尼系数增大引起阻尼力变大。在相同加载频率下，随着输入位移幅值的增加或者在相同加载幅值下，随着加载频率的增加，交叉孔面积不断减小，滞回曲线逐渐饱满，这与变阻尼系统随速度增大阻尼力逐渐增大的设计想法一致，试验结果表明，装置变阻尼系统实现了设计要求的变阻尼耗能功能。
2　组合隔震新体系性能化设计方法
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2.1　组合隔震新体系的组成
被动变阻尼变刚度装置组合隔震体系是将被动变阻尼变刚度装置作为隔震系统的一部分，与隔震支座共同组成新的隔震体系，如图4所示。体系中的两部分协同工作，来实现隔震效能，达到保护上部结构的目的。
2.2　性能目标和性能水准的设定
组合隔震新体系的抗震性能目标应综合考虑地震作用水准、建筑结构的重要性和经济效益等各项因素选定。参考GB/T 51408—2021《建筑隔震设计标准》[14]中给出的性能目标，设定组合隔震新体系抗震性能目标如表1所示，其中每个性能目标均与指定地震地面运动下的结构抗震性能水准相对应。设定各级抗震性能水准所要求性能状态如表2所示。
表1中给出了三类性能目标：
1）性能目标A为基本性能目标，即在多遇地震作用水准下能够充分运行、设防地震作用水准下能够基本运行、大震作用水准下确保生命安全。该性能目标是最基本的性能目标，适用于大多数一般使用条件下的建筑。
2）性能目标B为重要性能目标，即在设防地震作用下能够充分运行，罕遇地震作用下保证能够基本运行。该性能目标适用于重要性程度高或遭受地震破坏后产生较大危害的建筑。
3）性能目标C为特殊性能目标，即在罕遇地震作用下也要保证充分运行。该性能目标是最高等级的性能目标，适用于对安全需求极高的建筑。
2.3　性能目标和性能水准隔震量化值
具体实施性能设计方法，用于工程设计，需要将定性描述的性能水准转化为具体的设计参数。性能目标的量化直接影响性能设计方法的有效性和可行性。力、能量、位移和加速度等可以反映结构性能水准。组合隔震新体系控制主要与地震作用下隔震层的变形和上部结构的使用舒适度有关。在现有规范、规程的基础上，结合被动变阻尼变刚度组合隔震新体系性能特点，选择隔震层位移和楼层加速度作为控制指标，将定性的性能目标进行如下定量描述。
1）隔震层位移限值
参考规范GB/T 51408—2021《建筑隔震设计标准》[14]、CES 126—2001《叠层橡胶支座隔震技术规程》[15]、对隔震支座最大水平位移所做规定，同时考虑新型组合隔震体系中隔震支座和新型阻尼器的协同工作特点，对隔震层在不同性能水准下的隔震层位移限值的建议取值如表3所示。其中D为隔震支座直径。
2）楼层加速度限值
GB/T 17742—2020 《中国地震烈度表》[16]对不同水平方向地震动参数下人的感觉做出了规定，JGJ 3—2010《高层建筑混凝土结构技术规程》[17]给出了不同风振加速度下人的舒适度感受。参考以上规范规程中影响建筑使用舒适度的加速度数值，考虑组合隔震新体系的特点，建议组合隔震新体系楼层最大加速度的限值如表4所示。
2.4　组合隔震体系性能化设计方法
根据被动变阻尼变刚度装置的性能特点和性能化设计理论，提出了组合隔震体系满足不同控制目标的性能化设计方法。首先对结构进行初步设计，主要依照现有规范规程中的设计方法，把被动变阻尼变刚度装置作为提高结构性能的一种手段，根据已经明确的性能目标来完成装置和支座的参数设计。整个设计过程进行了装置各级阻尼系数和限位刚度参数的设计，设计流程如图5所示。
根据所给设计流程，设计过程主要分为4步，主要步骤如下：
1）综合考虑技术、经济、建筑安全性与使用性能确定设防目标和性能水准及其量化值。根据我国GB/T 51408—2021《建筑隔震设计标准》、CESC 126—2001《叠层橡胶支座隔震技术规程》对叠层支座竖向平均压应力限值的要求，初定隔震层布置方案。为便于后续迭代计算建立整体隔震模型，针对普通隔震结构，可根据实际情况采用多自由体系进行迭代。根据地震烈度、场地类别、设计地震分组选择地震波。
2）选取表3中水准1“充分运行”时的位移限值作为限位装置发挥作用限位预留距离dmax0，输入阻尼系数计算程序如图5，通过迭代确定使结构满足设防地震作用下水准1“充分运行”目标下的阻尼系数C0。
3）选取表3中水准2“基本运行”时的隔震位移限值作为限位装置发挥作用的第一阶限位距离dmax1；选取表4中水准2“基本运行”时的层加速度限值amax1，通过静力平衡，按式（1）计算第一阶限位刚度k1。
将dmax1和k1输入阻尼系数计算程序，通过迭代确定使结构满足设防地震作用下“基本运行”目标的阻尼系数C1。
4）选取表3中水准3“生命安全”指标时的隔震位移限值作为第二阶限位距离dmax2；选取表4“生命安全”指标时的层加速度限值amax2，通过静力平衡，按式（2）计算第二阶限位刚度k2。
将dmax1、dmax2、k1、k2输入阻尼系数计算程序，通过迭代确定结构满足设防地震作用下“基本运行”目标的阻尼系数C2。
装置数量的确定受到隔震层空间的影响，变阻尼部分的控制阀的数量增减受空间影响小，变刚度限位弹簧组受空间影响大，最终决定装置数量。因此，按照GB/T 1972—2005《碟形弹簧》[18]中的要求考虑弹簧组的数量和个数。
图6为阻尼系数计算程序，通过MATLAB/Simulink平台搭建。整个程序包括前处理子模块、状态空间子模块、装置力学模型子模块和结果输出子模块。在结构已选定的条件下，前处理子模块调用地震波数据，结构参数以及装置力学模型参数dmaxi，ki，输入到采用状态方程的状态空间子模块，最后通过结果输出子模块输出各阶段阻尼系数Ci的数值。
3　组合隔震体系性能化设计方法应用
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3.1　工程概况
采用日本建筑学会《建筑隔震设计指南》[19]中给出的结构。该结构为5层隔震钢框架结构（图7），结构质量分布均匀，刚度分布为梯形，最上层刚度为下层刚度的1/2，基本周期为0.3 s。结构各层具体参数如表5所示。
3.2　设计方法应用
1）根据表1确定性能设防目标及其量化值，给出当该建筑遭遇本地区8度地震时，基本性能目标A，即在多遇地震作用水准下能够充分运行、设防地震作用水准下能够基本运行、大震作用水准下确保生命安全。
隔震层设计最大位移设定为35 cm，橡胶支座最小直径为设计位移的2倍，即取隔震支座直径700 mm，最大载荷处采用直径900 mm橡胶支座，各橡胶支座承受的压应力约为12 N/mm2。设计直径700 mm和900 mm支座各4个，支座压应力验算：9 600 kN×5层/（6 362×4+3 848×4）= 11.8 N/mm2。因此满足支座竖向应力12 MPa控制要求。直径700 mm支座的水平刚度为1130 kN/mm，直径900 mm支座水平刚度为1870 kN/mm。
隔震层总水平刚度为
隔震结构基本周期为
2）根据表3给出的“充分运行”时性能指标，限位预留距离装置dmax0 = 0.05D = 35 mm；通过阻尼系数计算程序，最终选取初始阻尼系数C0 =1.54×102（kN•s/m）。多遇地震作用下隔震层及上部结构响应如图8和图9所示，装置耗能滞回曲线如图10所示。
3）根据表3、表4给出的“基本运行”时位移dmax1、加速度amax1性能指标，第一阶限位距离dmax1 = 0.2D = 140 mm，由静力平衡，计算第一阶限位刚度k1为
将dmax1、k1输入阻尼系数计算程序，评估是否满足预设性能目标，通过迭代计算，最终选取第一阶段变阻尼系数C1 = 4.62×102（kN•s/m）。设防地震作用下隔震层及上部结构响应如图11和图12所示，装置耗能滞回曲线如图13所示。
4）根据表3、表4给出的“生命安全”时位移dmax2、加速度amax2性能指标，第二阶限位距离dmax2 = 0.45D = 315 mm；由静力平衡得到第二阶限位刚度：
将dmax1、dmax2、k1、k2输入阻尼系数计算程序，评估是否满足预设性能目标，通过迭代计算，最终选取第二阶段变阻尼系数C2 = 1.23×103（kN•s/m）。罕遇地震作用下隔震层及上部结构响应如图14和图15所示，装置耗能滞回曲线如图16所示。
按照设计说明要求，根据以上限位刚度系数计算值，参考GB/T 1972—2005《碟形弹簧》中对碟簧尺寸、数量和载荷大小的要求，综合考虑变阻尼部分数量，最终设计被动变阻尼变刚度装置数量为12个。
4　结论
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1）针对被动变阻尼变刚度装置组合隔震体系能够有效控制不同类型和烈度地震波的特点，基于性能设计理论提出了一种适用于组合隔震新体系的性能化设计方法。这一方法的关键在于通过合理设计被动变阻尼变刚度装置和隔震支座的参数，使其在地震发生时能够发挥最佳效果，提高建筑物或结构的抗震性能。
2）详细描述了性能化设计方法的完整流程和相关说明。通过对一个工程实例进行的性能化设计过程，证明了该设计方法的可行性和有效性。实践证明，通过这种设计方法，可以实现预先设定的各级抗震性能目标，从而为建筑物或结构在地震中的安全性提供可靠保障。
3）这种性能化设计方法的优势在于其针对性强，能够根据具体的工程需求和地震环境特点进行定制化设计，从而最大程度地提升隔震体系的整体性能。通过该方法，可以更加有效地应对不同类型和烈度的地震波，确保结构在地震中具有更好的抗震性能和安全性。这种性能化设计方法在组合隔震新体系的工程设计应用中具有广泛的应用前景和重要意义。
基金
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  • 国家自然科学基金项目(52178488)
文献
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参考文献 引证文献
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2024年第44卷第3期
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doi: 10.13197/j.eeed.2024.0312
  • 接收时间：2023-04-26
  • 首发时间：2026-03-30
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  • 收稿日期：2023-04-26
  • 修回日期：2023-06-01
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国家自然科学基金项目(52178488)
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    青岛理工大学 土木工程学院，山东 青岛 266033

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付伟庆（1976—），男，教授，博士，主要从事结构振动控制研究。E-mail：
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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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