基于耦合效应的主—附结构体系地震响应研究
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摘要
随着经济发展和科技进步,越来越多土木工程结构物的形式趋向于大型化和复杂化,由多个子结构构成的组合结构体系在工程中日益频繁出现,如大量装饰性和功能性的建筑类非结构构件依附于建筑物主体结构安置,现代化进程的推进使得重要精密仪器和机电设备在生产生活中逐渐开始广泛应用,为抵抗复杂环境荷载阻尼器装置在建筑结构中的采用等,诸如此类的结构体系都可归于由具备不同动力特性、存在主次关系的多个子结构组合而成,并具有独特动力特性的主—附结构体系,其中建筑物称为主体结构,建筑物上附加的建筑类非结构构件、机电设备非结构构件以及阻尼器减振装置统称为附属结构。鉴于附属结构在地震中的损坏往往会造成巨大的经济损失,国内外学者对其十分关注,自上世纪八十年代开始,持续进行了较系统的研究工作。近年来,随着基于性能抗震设计理念的发展,附属结构的抗震设防以及减振控振成为目前抗震领域研究的热点。由于主一附结构体系具有明显区别于一般建筑结构形式的动力特性,从严格意义上来说,传统的实模态振型分解以及以此为基础的抗震设计反应谱等动力分析方法在理论上不再适用,依赖于传统分析方法必然会引入不必要的误差甚至是错误,因此,有必要针对此类结构形式进行专门的研究,扩展和改进已有分析手段并引入新方法,以建立兼顾精度和效率要求的适合于主—附结构体系的动力分析方法。根据以上几点需要,本文开展了相关研究工作,工作内容以建筑物主体结构和附属结构动力耦合特性为基础,分别从主一附结构体系的地震响应特性、数值分析方法和减振控振策略等方面对主—附结.构体系进行研究,作者所做的工作如下:
(1)基于主—附结构体系的动力耦合特性,对非线性主体结构上附属结构的地震响应特性进行了研究。文中建立了由建筑物主体结构与附属结构组合而成的主—附结构耦合体系的随机分析模型,通过数值实验分析了影响附属结构动力响应的几个重要因素:建筑物主体结构的非线性情况、主体结构和附属结构各自的模型参数、附属结构所在楼层位置以及多个附属结构之间的动力相互影响等,其中重点分析了主体结构非线性对附属结构的影响。文中通过以上的参数影响研究,得到了一些有益的结论,借此探究非线性情况下主一附结构体系的耦合响应特征。
(2)研究了多维地震动输入下具有偏心特性的建筑物主体结构上附属结构的地震响应特性,并对偏心楼板反应谱的变化情况进行了分析和探讨。文中建立了偏心主体结构—附属结构的耦合动力模型,基于此偏心模型对附属结构进行了分析,研究了偏心情况下影响附属结构地震响应的主要因素。进一步计算了附属结构响应评估的重要参数一楼板反应谱,分析了参数影响规律,文中计算考虑了主—附结构之间的耦合特性,将其结果与基于规范方法的结果相对比,指出了规范方法的适用范围和误差情况。
(3)基于动力耦合效应,对主—附结体系的整体可靠度进行了研究。文中首先指出了在主—附结构体系中对附属结构进行整体可靠度分析的必要性,研究了地震激励下考虑建筑物主体结构损坏情况时附属结构整体可靠度的计算方法,进一步分析了建筑物主体结构参数变化对附属结构可靠度的影响规律和影响程度。此外,文中还对比了相关失效模式和基于独立重复试验的结构体系可靠度,分析了基于独立重复试验假定的串联可靠度计算方法的误差。
(4)推导了适用于主—附结构体系随机响应计算的快速迭代公式。不同于之前提出的迭代方法,本文方法是基于虚拟激励法所提出,其结合了虚拟激励法和迭代法各自的优点,计算效率较高,并可避免复数运算和矩阵求逆运算,借以避免矩阵病态可能导致的数值问题,得到随机响应分析的精确解。文中从数值理论上分析了该方法的计算效率,并采用数值算例验证了其计算准确性,证明了该方法是一种具有高计算效率的准确随机分析方法。
(5)提出了适用于主—附结构体系反应谱分析的摄动反应谱方法。该方法是基于与传统的完全平方组合(CQC)方法类似的假定展开的随机推导,是对传统反应谱组合方法的改进,可提高主—附结构体系反应谱分析的精度,避免非比例阻尼情况下强迫解耦可能会带来的过大误差。文中通过数值算例进行验证,可知其相对于传统的CQC方法具有更高的精度。鉴于当前工程设计中采用的往往是能体现概率统计特性同时具备较高实用性的反应谱理论,该方法具有一定的工程应用价值。
(6)提出了临近多个附属结构协同减振的控制策略,并进行了相关研究。文中对协同减振装置参数进行了优化设置,分析了多个附属结构的协同减振效果,从而确切指出可以在多个附属结构之间设置连接粘滞阻尼器和共享调谐阻尼器来实现共同减振,并分析了二者的适用范围。此外,文中给出了调谐质量阻尼器(TMD)和调谐液体阻尼器(TLD)的统一运动方程,提出了将TLD转化为TMD的建模方法,其可统一调谐阻尼器的数值建模,具有工程实用意义。
In recent years, more and more civil engineering structures tend to be large-scale and complicated along with technological progress and economic development, which lead to plenty of coupled system composed by a number of sub-structures, such as a lot of decorative and functional building non-structural components attached to the main structure of the building, important mechanical and electrical equipments comprehensively adopted in the production and life, damper devices installed in buildings in order to resist complex environment loads, et al. As be shown above, such complicated system can be grouped into primary-secondary system which is composed by multiple subsystems with different dynamic characteristics and exicsts the relationship between primary and secondary. The structure is referred to as primary system, and the mechanical and electrical equipments, structural appendages and damper devices are collectively referred to as secondary system. Because the secondary systems damaged in the earthquake would cause huge economic losses, a lot of researchers have been devoted to the seismic response of such systems since 80s of the last century, and some meaningful research work are in progress. Especially in recent years, with the development of performance-based seismic design, aseicmis design and seismic control of secondary systems attract more and more researchers' attention. Primary-secondary systems have significantly different dynamic characteristics distinguished with the ordinary building structures, the traditional real modal decomposition method as well as the response spectrum theory, because of failing to properly account for the distinctive characteristic, would introduce unnecessary errors or mistakes and are no longer applicable in theory. Therefore, it is necessary to carry out specialized research and improve existing analytical tools and introduce new methods for dynamic analysis of such system. According to the demand mentioned above, the research in the thesis is carried out based on the coupled dynamic characteristics of primary-secondary system, and the work includes 3 asepct of research content: seismic characteristics, numercical analysis method and seismic control strategy. The main findings of the research work are listed as follows:
(1) The primay-secondary coupled system consisted of the nonlinear structure and secondary systems is established, and based on the dynamic coupling effect several important factors affecting the seismic response of secondary systems are studied, which is helpful for the estimating the seismic performance of secondary systems. The stochastic analysis model of primary-secondary system is established in the thesis, and the the coupling characteristics between the two subsystems are included, the corresponding parameters of the study include in the research: the random model corresponding to different types of ground site, the nonlinear situation of the structure, the model parameters of the nonlinear model, the postion of the secondary systems and dynamic interaction between multiple secondary systems.
(2) The eccentric characteristic of the structure and multiple-dimensional seismic input ae considered and studied for the seismic response of secondary systems, and the effect of some important parameters are analyzed. The floor response spectrum of the eccentric structure to two horizontal earthquake input is also studied and some important parameters related with the floor response spectrum were also discussed, and the conventional method in the current aseismatic criterion is also discussed, consequently the shortcomings are indicated in the thesis.
(3) Considering the dynamic coupling effect of the primary-secondary system, the united dynamic reliability of the primary-secondary system are computed and studied. In the thesis, firstly the necessity of the united dynamic reliability analysis of secondary system is explained, and then the calculation method is presented. By numerical research, the effect of parameters' varieties on the realiability of secondary systems is studied. Furthermore, the approximate solution based on the independent repeated trials and the exact solution based on general Rice formula are compared, and the research indicates that the approximate solution is inaccurate and conservative in some cases.
(4) A new fast stochastic method for seismic analysis of the non-proportionally damped structure is presented, which can be used in the primary-secondary systems. In the new method, the dynamic equilibrium equation of non-proportionally damped structure is expressed in the iteration form, based on which the inverse operation of the matrices is avoided. Moreover, the new method also does not need the solution of any complex eigenvalue problem, in contrast to other methods found in the literature. The new method is based on fundamental principles from structural dynamics, pseudo excitation method and pseudo force method, so it is more efficient in computation and can give the exact solution. Furthermore, several numerical examples corresponding to different types of prmary-secondary systems are utilized to verify the accuracy and computational efficiency of the new method.
(5) A new response spectrum combination rule for the seismic analysis of non-classically damped systems such as primary-secondary systems are developed. The approach, which is denoted the perturbation spectrum method, can provide a more accurate evaluation of non-classically damped system's mean peak response in terms of the ground response spectrum, and avoid the error introcued by ignoring the off-diagonal elements of modal damping matrix. Given the response spectrum which can possess statistical properties is often used in the current engineering design, the method has engineering application value. Finally, the computation efficiency and accuracy of the proposed method is examined by numerical examples.
(6) A new strategy which can be used for the vibration absorbtion of multiple adjacent secondary systems is presented in the thesits. By setting viscous damper and shared mass damper connecting adjacent secondary systems, the vibration of all the systems can be reduced, and the corresponding numerical research are carried out. The parameters of the two measures are optimized for obtaining a good vibration control effect. In the paper, the effect of two strategies of STMD and VD on reducing the seismic response of secondary systems is studied and so is the application scope of the two seismic control strategies. Moreover, the author also gives the unified motion equations of the TMD and TLD, and proposes the modeling method to simulate TLD utilizing the TMD model, which can facilitate the model establishment of the tuned damper and has practical significance in engineering.
(1)基于主—附结构体系的动力耦合特性,对非线性主体结构上附属结构的地震响应特性进行了研究。文中建立了由建筑物主体结构与附属结构组合而成的主—附结构耦合体系的随机分析模型,通过数值实验分析了影响附属结构动力响应的几个重要因素:建筑物主体结构的非线性情况、主体结构和附属结构各自的模型参数、附属结构所在楼层位置以及多个附属结构之间的动力相互影响等,其中重点分析了主体结构非线性对附属结构的影响。文中通过以上的参数影响研究,得到了一些有益的结论,借此探究非线性情况下主一附结构体系的耦合响应特征。
(2)研究了多维地震动输入下具有偏心特性的建筑物主体结构上附属结构的地震响应特性,并对偏心楼板反应谱的变化情况进行了分析和探讨。文中建立了偏心主体结构—附属结构的耦合动力模型,基于此偏心模型对附属结构进行了分析,研究了偏心情况下影响附属结构地震响应的主要因素。进一步计算了附属结构响应评估的重要参数一楼板反应谱,分析了参数影响规律,文中计算考虑了主—附结构之间的耦合特性,将其结果与基于规范方法的结果相对比,指出了规范方法的适用范围和误差情况。
(3)基于动力耦合效应,对主—附结体系的整体可靠度进行了研究。文中首先指出了在主—附结构体系中对附属结构进行整体可靠度分析的必要性,研究了地震激励下考虑建筑物主体结构损坏情况时附属结构整体可靠度的计算方法,进一步分析了建筑物主体结构参数变化对附属结构可靠度的影响规律和影响程度。此外,文中还对比了相关失效模式和基于独立重复试验的结构体系可靠度,分析了基于独立重复试验假定的串联可靠度计算方法的误差。
(4)推导了适用于主—附结构体系随机响应计算的快速迭代公式。不同于之前提出的迭代方法,本文方法是基于虚拟激励法所提出,其结合了虚拟激励法和迭代法各自的优点,计算效率较高,并可避免复数运算和矩阵求逆运算,借以避免矩阵病态可能导致的数值问题,得到随机响应分析的精确解。文中从数值理论上分析了该方法的计算效率,并采用数值算例验证了其计算准确性,证明了该方法是一种具有高计算效率的准确随机分析方法。
(5)提出了适用于主—附结构体系反应谱分析的摄动反应谱方法。该方法是基于与传统的完全平方组合(CQC)方法类似的假定展开的随机推导,是对传统反应谱组合方法的改进,可提高主—附结构体系反应谱分析的精度,避免非比例阻尼情况下强迫解耦可能会带来的过大误差。文中通过数值算例进行验证,可知其相对于传统的CQC方法具有更高的精度。鉴于当前工程设计中采用的往往是能体现概率统计特性同时具备较高实用性的反应谱理论,该方法具有一定的工程应用价值。
(6)提出了临近多个附属结构协同减振的控制策略,并进行了相关研究。文中对协同减振装置参数进行了优化设置,分析了多个附属结构的协同减振效果,从而确切指出可以在多个附属结构之间设置连接粘滞阻尼器和共享调谐阻尼器来实现共同减振,并分析了二者的适用范围。此外,文中给出了调谐质量阻尼器(TMD)和调谐液体阻尼器(TLD)的统一运动方程,提出了将TLD转化为TMD的建模方法,其可统一调谐阻尼器的数值建模,具有工程实用意义。
In recent years, more and more civil engineering structures tend to be large-scale and complicated along with technological progress and economic development, which lead to plenty of coupled system composed by a number of sub-structures, such as a lot of decorative and functional building non-structural components attached to the main structure of the building, important mechanical and electrical equipments comprehensively adopted in the production and life, damper devices installed in buildings in order to resist complex environment loads, et al. As be shown above, such complicated system can be grouped into primary-secondary system which is composed by multiple subsystems with different dynamic characteristics and exicsts the relationship between primary and secondary. The structure is referred to as primary system, and the mechanical and electrical equipments, structural appendages and damper devices are collectively referred to as secondary system. Because the secondary systems damaged in the earthquake would cause huge economic losses, a lot of researchers have been devoted to the seismic response of such systems since 80s of the last century, and some meaningful research work are in progress. Especially in recent years, with the development of performance-based seismic design, aseicmis design and seismic control of secondary systems attract more and more researchers' attention. Primary-secondary systems have significantly different dynamic characteristics distinguished with the ordinary building structures, the traditional real modal decomposition method as well as the response spectrum theory, because of failing to properly account for the distinctive characteristic, would introduce unnecessary errors or mistakes and are no longer applicable in theory. Therefore, it is necessary to carry out specialized research and improve existing analytical tools and introduce new methods for dynamic analysis of such system. According to the demand mentioned above, the research in the thesis is carried out based on the coupled dynamic characteristics of primary-secondary system, and the work includes 3 asepct of research content: seismic characteristics, numercical analysis method and seismic control strategy. The main findings of the research work are listed as follows:
(1) The primay-secondary coupled system consisted of the nonlinear structure and secondary systems is established, and based on the dynamic coupling effect several important factors affecting the seismic response of secondary systems are studied, which is helpful for the estimating the seismic performance of secondary systems. The stochastic analysis model of primary-secondary system is established in the thesis, and the the coupling characteristics between the two subsystems are included, the corresponding parameters of the study include in the research: the random model corresponding to different types of ground site, the nonlinear situation of the structure, the model parameters of the nonlinear model, the postion of the secondary systems and dynamic interaction between multiple secondary systems.
(2) The eccentric characteristic of the structure and multiple-dimensional seismic input ae considered and studied for the seismic response of secondary systems, and the effect of some important parameters are analyzed. The floor response spectrum of the eccentric structure to two horizontal earthquake input is also studied and some important parameters related with the floor response spectrum were also discussed, and the conventional method in the current aseismatic criterion is also discussed, consequently the shortcomings are indicated in the thesis.
(3) Considering the dynamic coupling effect of the primary-secondary system, the united dynamic reliability of the primary-secondary system are computed and studied. In the thesis, firstly the necessity of the united dynamic reliability analysis of secondary system is explained, and then the calculation method is presented. By numerical research, the effect of parameters' varieties on the realiability of secondary systems is studied. Furthermore, the approximate solution based on the independent repeated trials and the exact solution based on general Rice formula are compared, and the research indicates that the approximate solution is inaccurate and conservative in some cases.
(4) A new fast stochastic method for seismic analysis of the non-proportionally damped structure is presented, which can be used in the primary-secondary systems. In the new method, the dynamic equilibrium equation of non-proportionally damped structure is expressed in the iteration form, based on which the inverse operation of the matrices is avoided. Moreover, the new method also does not need the solution of any complex eigenvalue problem, in contrast to other methods found in the literature. The new method is based on fundamental principles from structural dynamics, pseudo excitation method and pseudo force method, so it is more efficient in computation and can give the exact solution. Furthermore, several numerical examples corresponding to different types of prmary-secondary systems are utilized to verify the accuracy and computational efficiency of the new method.
(5) A new response spectrum combination rule for the seismic analysis of non-classically damped systems such as primary-secondary systems are developed. The approach, which is denoted the perturbation spectrum method, can provide a more accurate evaluation of non-classically damped system's mean peak response in terms of the ground response spectrum, and avoid the error introcued by ignoring the off-diagonal elements of modal damping matrix. Given the response spectrum which can possess statistical properties is often used in the current engineering design, the method has engineering application value. Finally, the computation efficiency and accuracy of the proposed method is examined by numerical examples.
(6) A new strategy which can be used for the vibration absorbtion of multiple adjacent secondary systems is presented in the thesits. By setting viscous damper and shared mass damper connecting adjacent secondary systems, the vibration of all the systems can be reduced, and the corresponding numerical research are carried out. The parameters of the two measures are optimized for obtaining a good vibration control effect. In the paper, the effect of two strategies of STMD and VD on reducing the seismic response of secondary systems is studied and so is the application scope of the two seismic control strategies. Moreover, the author also gives the unified motion equations of the TMD and TLD, and proposes the modeling method to simulate TLD utilizing the TMD model, which can facilitate the model establishment of the tuned damper and has practical significance in engineering.
引文
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