带有分布参数的串联体系地震响应分析及智能控制
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摘要
带分布参数的串联体系是土木工程中常见的结构体系,比如：高压电气设备支架串联结构、高层框架结构、高层框架-剪力墙结构等。由于这类串联体系既有集中参数又有分布参数,而且集中参数与分布参数的节点又有柔性连接的情形,同时在地震作用下会产生较大的倾覆弯矩,因此在地震作用下带分布参数的串联体系地震响应求解、被动隔震及智能隔震比较复杂。为此本文针对带分布参数的串联体系地震响应求解、被动隔震及智能隔震的几个热点、难点问题展开研究,其中主要的工作有以下几方面：
(1)首先以单节柔性节点高压电气设备为研究对象建立单节分布参数串联体系的动力分析模型,通过分布参数梁振动理论,避免对结构的离散,集中参数通过边界条件的引入,推导出其频率方程,根据Betti定律,推导出具有单节带分布参数柔性节点串联体系的正交条件,应用此正交条件对集中参数与分布参数的振动方程解耦,推导出该单节带分布参数串联体系的广义质量及广义荷载,进一步通过振型叠加的方法求解结构的地震响应。仿真结果表明,该半解析法与有限元法计算结果相一致,说明该半解析法的正确性。最后将上述方法应用于多节柔性节点带分布参数串联体系,求解多节柔性节点高压电气设备支架串联体系的地震响应。
(2)建立了高层剪力墙结构动力分析简化模型,仿照推导柔性节点带分布参数串联体系地震响应半解析解的方法,推导出多节刚性节点带分布参数串联体系——高层剪力墙结构地震响应的半解析解；进一步建立了高层框架-剪力墙结构的动力分析模型,框架结构部分对整体结构的影响通过边界条件的引入,然后通过应用求解多节刚性节点带分布参数地震响应的求解方法求解框架-剪力墙结构的地震响应。仿真结果显示,建立的高层结构动力分析简化模型优于悬臂梁模型,而且本文推导的求解地震响应的半解析解是正确的及计算工作量小。
(3)通过并联橡胶隔震支座,实现以带分布参数的高架电气设备支架串联体系的隔震,然后建立高架电气设备支架串联隔震体系的力学模型,通过串联体系集中参数与分布参数的振动方程,推导出该串联隔震体系的频率方程、振型正交条件、广义质量与广义刚度,由于该串联隔震体系为非比例阻尼体系,通过把该串联隔震体系的非比例阻尼分解为比例阻尼部分和非比例阻尼部分,非比例阻尼部分由隔震支座的阻尼所引起,应用Hamilton原理推导出非比例阻尼部分等效振型阻尼,从而实现该体系运动方程的解耦,通过振型叠加法进行该串联隔震体系地震响应的求解。最后进行有限元软件数值积分法求解的地震响应与该半解析法求解地震响应的比较,分析半解析法求解地震响应的正确性及隔震技术的有效性。
(4)针对以高层建筑为研究对象的带分布参数串联体系,研制出双向抗拔滑动装置,该双向抗拔滑动装置既能抵抗拉力又能承受压力。将该装置设置于隔震层较大拉力的位置,与夹层橡胶隔震垫同时使用,当高层建筑在地震作用下倾覆力矩较大时,该双向滑动装置可以抵抗倾覆力矩产生的拉力,使夹层橡胶隔震垫处于受压状态。然后建立刚性节点带分布参数串联隔震体系力学模型,用推导多节柔性节点带分布参数串联隔震体系地震响应求解的方法进行推导求解刚性节点带分布参数串联隔震体系地震响应的半解析解。
(5)针对带分布参数的串联体系,借用本课题组提出的序列最优控制算法,推导出序列最优模态控制算法,然后用该算法进行带分布参数串联体系的智能隔震。由于序列最优模态控制算法振动控制时需要结构全状态,在工程应用中难于实现,因此,提出了针对序列最优模态控制算法的全维状态观测器,实现在振动控制时只要测量容易测量的状态,然后通过全维状态观测器重构结构的全部状态,从而实现序列最优模态控制算法用于带分布参数串联体系的振动控制。由于在线实时控制过程中,结构响应测量、在线计算和驱动器响应都需要消耗时间,因此时滞是不可避免的,为了解决时滞问题,提出了将径向基神经网络和序列最优模态控制算法有机结合而形成的序列最优预测模态控制器,仿真结果表明,在无时滞与有时滞情况下该控制器的控制效率良好。
(6)在双向抗拔滑动装置的基础上,设计出双向压电变摩擦控制装置,该控制装置可以在两个方向滑动产生控制力,进一步推导出该控制装置应用于结构振动控制的半主动控制算法。最后设计出一压电变摩擦控制装置,进行数值仿真,根据仿真结果,将该控制装置应用于带分布参数串联体系的智能隔震,显示出良好的控制效果。
(7)对目前进行地震响应分析及振动控制仿真软件Simulink作了详细介绍,讲述了Simulink仿真地震响应及振动控制的技术。讲述Simulink的扩展工具——S-函数的工作原理,用Simulink/S-函数实现序列最优模态控制算法变增益矩阵的技术,实现序列最优模态控制算法的模块化。最后通过Simulink软件分别建立经典最优控制算法、线性二次型高斯算法和序列最优控制算法及基于状态观测器的序列最优模态控制算法的仿真模块图。
(8)在理论研究和计算机仿真的基础上,进行了带分布参数体系的动力响应、隔震的扫频振动台试验。设计出压电变摩擦控制装置,并进行力学性能试验,然后将该控制装置用于带分布参数隔震体系,分别进行应用Passive-on与Passive-off算法的带分布参数串联隔震体系振动控制的扫频振动台试验,为该控制器的工程应用奠定了基础。
(9)将本文带分布参数地震响应分析理论及隔震技术应用于实际工程,进行了完整的带分布参数串联体系隔震分析及设计,通过计算与分析,采用本文的并联橡胶隔震支座进行带分布参数体系的隔震技术具有较好的减震效果。通过讲述该隔震技术的设计过程,为该技术广泛应用于实际工程奠定了基础。
Serial system with concentrated and distributed parameters is usually used in civil engineering, for instance serial electrical equipment and supporter with distributed parameters, tall shear-wall structure, tall frame-shear-wall structure and so on. Due to the serial system with concentrated and distributed parameters, flexible node between concentrated and distributed parameters and large overturning moment produced under earthquake, it is rather difficult to solve the seismic response of serial system with concentrated and distributed parameters, make passive and smart isolation for this serial system. Therefore, this paper is to aim to the some focuses and difficult points in the research of the solution of seismic response of this serial system, passive and smart isolation for this serial system, and mainly focuses on the following aspects:
(1) Firstly, the dynamic analysis model of serial system with concentrated and distributed parameters is presented by taking single level flexible node electric porcelain high-voltage equipments as the research object and the frequency equation of this serial system is derived by the vibration theory of beam with distributed parameters and introducing the boundary conditions of concentrated parameters, then frequency and mode shape can be obtained by the numerical method. According to the Betti law, the orthogonal conditions of modes of serial system with concentrated and distributed parameters are deduced. Then we can use these orthogonal conditions to decouple vibration equation of concentrated and distributed parameters and obtain the generalized mass and stiffness. Therefore the responses of serial system under earthquake excitation can be solved by the mode superposition method. The simulation results show the responses obtained by two methods are basically consistent, which indicated the correctness of this semi-analytical method. Finally, the semi-analytical solution of the seismic response for several levels serial system with distributed parameters and flexible nodes is deduced by imitating the process to deduce the seismic response of the single level serial system, and then the seismic response of serial system of the supporter and high-place electrical equipment with the flexible nodes and electric porcelains is solved by the semi-analytical solution.
(2) The dynamic modal of tall shear-wall building is presented and the semi-analytical solution of several levels serial system with distributed parameters and rigid nodes is deduced by imitating the process to deduce the seismic response of the several levels serial system with flexible nodes, namely,tall shear-wall building. Finally, the dynamic modal for tall frame-shear-wall building is presented and the influence of the part of frame structure to frame-shear wall building is considered by boundary conditions, then we can obtain the seismic response of frame-shear wall building by the method to solve the seismic response of several levels serial system with distributed parameters and rigid nodes.
(3) Serially isolated electrical equipment and supporter with distributed parameters is presented by in-parallel laminated rubber bearings and mechanics model of this system is built. Based on the vibration theory of beam with distributed parameters and the boundary conditions of concentrated parameters, the frequency equation of this serially isolated system is derived, and the frequencies and mode shapes are obtained by the numerical method. According to the Betti law, the orthogonal conditions of modes of this serially isolated system with concentrated and distributed parameters are deduced and the generalized mass and stiffness can be obtained. By decomposing the non-proportional damping of serially isolated system to the party of proportional damping and non-proportional damping, which is induced by laminated rubber bearings, the equivalent mode damping ratio of the non-proportional damping is derived by Hamilton principle. Therefore the vibration equation of the non-proportional damping of the isolated system is decoupled, and the responses of structure under earthquake excitation can be solved by the mode superposition method. Then validity of the semi-analytical method to solve the seismic response of serially isolated system with distributed parameters and effectiveness of isolated system designed by author are proved by comparison the seismic response of isolated system with ordinary system solved by the semi-analytical method and numerical integration of finite element method, separately.
(4) Aimed to serial system with distributed parameters and rigid nodes taken the tall building as the research object, the bidirectional anti-pulling sliding device which can resist tension and bear pressure is developed. This device is set at the place of isolation layer where the large tension exists, and the laminated rubber bearings are used at isolation layer at the same time. This device can resist tension produced by over-turning moment and make laminated rubber bearings confine in pressured state when the large over-turning moment at the bottom of tall building is generated under earthquake. Then the mechanics model of serial isolated system with distributed parameters and rigid nodes is presented, and the semi-analytical solution of serial isolated system is deduced by imitating the process to deduce the seismic response of the serial isolation system with distributed parameters and rigid nodes.
(5) The Sequential Optimal Mode Control (SOMC) algorithm for serial system with distributed parameters is presented by expanding the Sequential Optimal Control (SOC) algorithm. Then SOMC algorithm is used to the smart isolation of serial system with distributed parameters. For it is difficult to obtain the full state of structural response needed by SOMC in engineering application, the SOMC based on state observer which can realize the vibration control of structure by partial state of structure measured easily is presented. Due to time consumed by the measure of response of structures, on-line calculation and reaction of actuators in the process of on-line real-time control, time lag always exists in the control system. In order to solve the problem of time lag, Sequentialoptimal predicted mode controller is founded by organically combining RBF neural network with sequential optimal control algorithm. The simulation results show that control effect of this predicted mode controller is better in the case of time lag and no time lag.
(6) Based on the bidirectional anti-pulling sliding device, the bidirectional piezoelectric variable friction control device which can produce control force in two orthogonal directions is designed. Then semi-active control algorithm which is used to the vibration control of structure by this control device is presented. Finally one piezoelectric variable friction control device is designed and simulated numerically, and according to mechanical properties of this control device obtained by numerical simulation, this control device is used to smart isolation of serial system with distributed parameters and simulation results show the smart isolation is of excellent control effect.
(7) The simulation technique of Simulink software which is always used to make the analysis of seismic response and vibration control of structure is described in detail. Especially working principle of S-function, namely, the extended tool of Simulink software is emphatically introduced, and at the same time the technique of realizing the variable gain matrix of SOMC is presented, therefore the modularization of SOMC is realized. Finally, the simulation modules of SOC, COC, LQG and SOMC based on state observer of Simulink which are used to make vibration control of structure are designed.
(8) Based on the research of theoretical research and computer simulation, the sweep frequency shaking table test of dynamic response and isolation for serial system with distributed parameters is carried out. The actual piezoelectric variable friction control device is designed and the mechanical properties of the actual control device are test. Then this control device is used to isolation of serial system with distributed parameters and the sweep frequency shaking table test of vibration control for isolation of serial system with distributed parameters is performed under the control of Passive-on and Passive-off control algorithms. So the foundation of engineering application of this control device is established.
(9) The analysis theory of seismic response and isolation technique for serial system with distributed parameters are applied for the actual project and the process of analysis and design of serially isolated system with distributed parameters is presented. The serially isolated system adopted the in-parallel laminated rubber bearings has a better effect of seismic reduction by the calculation and analysis and All those have laid solid foundation for the wide application of this isolation technique.
(1)首先以单节柔性节点高压电气设备为研究对象建立单节分布参数串联体系的动力分析模型,通过分布参数梁振动理论,避免对结构的离散,集中参数通过边界条件的引入,推导出其频率方程,根据Betti定律,推导出具有单节带分布参数柔性节点串联体系的正交条件,应用此正交条件对集中参数与分布参数的振动方程解耦,推导出该单节带分布参数串联体系的广义质量及广义荷载,进一步通过振型叠加的方法求解结构的地震响应。仿真结果表明,该半解析法与有限元法计算结果相一致,说明该半解析法的正确性。最后将上述方法应用于多节柔性节点带分布参数串联体系,求解多节柔性节点高压电气设备支架串联体系的地震响应。
(2)建立了高层剪力墙结构动力分析简化模型,仿照推导柔性节点带分布参数串联体系地震响应半解析解的方法,推导出多节刚性节点带分布参数串联体系——高层剪力墙结构地震响应的半解析解；进一步建立了高层框架-剪力墙结构的动力分析模型,框架结构部分对整体结构的影响通过边界条件的引入,然后通过应用求解多节刚性节点带分布参数地震响应的求解方法求解框架-剪力墙结构的地震响应。仿真结果显示,建立的高层结构动力分析简化模型优于悬臂梁模型,而且本文推导的求解地震响应的半解析解是正确的及计算工作量小。
(3)通过并联橡胶隔震支座,实现以带分布参数的高架电气设备支架串联体系的隔震,然后建立高架电气设备支架串联隔震体系的力学模型,通过串联体系集中参数与分布参数的振动方程,推导出该串联隔震体系的频率方程、振型正交条件、广义质量与广义刚度,由于该串联隔震体系为非比例阻尼体系,通过把该串联隔震体系的非比例阻尼分解为比例阻尼部分和非比例阻尼部分,非比例阻尼部分由隔震支座的阻尼所引起,应用Hamilton原理推导出非比例阻尼部分等效振型阻尼,从而实现该体系运动方程的解耦,通过振型叠加法进行该串联隔震体系地震响应的求解。最后进行有限元软件数值积分法求解的地震响应与该半解析法求解地震响应的比较,分析半解析法求解地震响应的正确性及隔震技术的有效性。
(4)针对以高层建筑为研究对象的带分布参数串联体系,研制出双向抗拔滑动装置,该双向抗拔滑动装置既能抵抗拉力又能承受压力。将该装置设置于隔震层较大拉力的位置,与夹层橡胶隔震垫同时使用,当高层建筑在地震作用下倾覆力矩较大时,该双向滑动装置可以抵抗倾覆力矩产生的拉力,使夹层橡胶隔震垫处于受压状态。然后建立刚性节点带分布参数串联隔震体系力学模型,用推导多节柔性节点带分布参数串联隔震体系地震响应求解的方法进行推导求解刚性节点带分布参数串联隔震体系地震响应的半解析解。
(5)针对带分布参数的串联体系,借用本课题组提出的序列最优控制算法,推导出序列最优模态控制算法,然后用该算法进行带分布参数串联体系的智能隔震。由于序列最优模态控制算法振动控制时需要结构全状态,在工程应用中难于实现,因此,提出了针对序列最优模态控制算法的全维状态观测器,实现在振动控制时只要测量容易测量的状态,然后通过全维状态观测器重构结构的全部状态,从而实现序列最优模态控制算法用于带分布参数串联体系的振动控制。由于在线实时控制过程中,结构响应测量、在线计算和驱动器响应都需要消耗时间,因此时滞是不可避免的,为了解决时滞问题,提出了将径向基神经网络和序列最优模态控制算法有机结合而形成的序列最优预测模态控制器,仿真结果表明,在无时滞与有时滞情况下该控制器的控制效率良好。
(6)在双向抗拔滑动装置的基础上,设计出双向压电变摩擦控制装置,该控制装置可以在两个方向滑动产生控制力,进一步推导出该控制装置应用于结构振动控制的半主动控制算法。最后设计出一压电变摩擦控制装置,进行数值仿真,根据仿真结果,将该控制装置应用于带分布参数串联体系的智能隔震,显示出良好的控制效果。
(7)对目前进行地震响应分析及振动控制仿真软件Simulink作了详细介绍,讲述了Simulink仿真地震响应及振动控制的技术。讲述Simulink的扩展工具——S-函数的工作原理,用Simulink/S-函数实现序列最优模态控制算法变增益矩阵的技术,实现序列最优模态控制算法的模块化。最后通过Simulink软件分别建立经典最优控制算法、线性二次型高斯算法和序列最优控制算法及基于状态观测器的序列最优模态控制算法的仿真模块图。
(8)在理论研究和计算机仿真的基础上,进行了带分布参数体系的动力响应、隔震的扫频振动台试验。设计出压电变摩擦控制装置,并进行力学性能试验,然后将该控制装置用于带分布参数隔震体系,分别进行应用Passive-on与Passive-off算法的带分布参数串联隔震体系振动控制的扫频振动台试验,为该控制器的工程应用奠定了基础。
(9)将本文带分布参数地震响应分析理论及隔震技术应用于实际工程,进行了完整的带分布参数串联体系隔震分析及设计,通过计算与分析,采用本文的并联橡胶隔震支座进行带分布参数体系的隔震技术具有较好的减震效果。通过讲述该隔震技术的设计过程,为该技术广泛应用于实际工程奠定了基础。
Serial system with concentrated and distributed parameters is usually used in civil engineering, for instance serial electrical equipment and supporter with distributed parameters, tall shear-wall structure, tall frame-shear-wall structure and so on. Due to the serial system with concentrated and distributed parameters, flexible node between concentrated and distributed parameters and large overturning moment produced under earthquake, it is rather difficult to solve the seismic response of serial system with concentrated and distributed parameters, make passive and smart isolation for this serial system. Therefore, this paper is to aim to the some focuses and difficult points in the research of the solution of seismic response of this serial system, passive and smart isolation for this serial system, and mainly focuses on the following aspects:
(1) Firstly, the dynamic analysis model of serial system with concentrated and distributed parameters is presented by taking single level flexible node electric porcelain high-voltage equipments as the research object and the frequency equation of this serial system is derived by the vibration theory of beam with distributed parameters and introducing the boundary conditions of concentrated parameters, then frequency and mode shape can be obtained by the numerical method. According to the Betti law, the orthogonal conditions of modes of serial system with concentrated and distributed parameters are deduced. Then we can use these orthogonal conditions to decouple vibration equation of concentrated and distributed parameters and obtain the generalized mass and stiffness. Therefore the responses of serial system under earthquake excitation can be solved by the mode superposition method. The simulation results show the responses obtained by two methods are basically consistent, which indicated the correctness of this semi-analytical method. Finally, the semi-analytical solution of the seismic response for several levels serial system with distributed parameters and flexible nodes is deduced by imitating the process to deduce the seismic response of the single level serial system, and then the seismic response of serial system of the supporter and high-place electrical equipment with the flexible nodes and electric porcelains is solved by the semi-analytical solution.
(2) The dynamic modal of tall shear-wall building is presented and the semi-analytical solution of several levels serial system with distributed parameters and rigid nodes is deduced by imitating the process to deduce the seismic response of the several levels serial system with flexible nodes, namely,tall shear-wall building. Finally, the dynamic modal for tall frame-shear-wall building is presented and the influence of the part of frame structure to frame-shear wall building is considered by boundary conditions, then we can obtain the seismic response of frame-shear wall building by the method to solve the seismic response of several levels serial system with distributed parameters and rigid nodes.
(3) Serially isolated electrical equipment and supporter with distributed parameters is presented by in-parallel laminated rubber bearings and mechanics model of this system is built. Based on the vibration theory of beam with distributed parameters and the boundary conditions of concentrated parameters, the frequency equation of this serially isolated system is derived, and the frequencies and mode shapes are obtained by the numerical method. According to the Betti law, the orthogonal conditions of modes of this serially isolated system with concentrated and distributed parameters are deduced and the generalized mass and stiffness can be obtained. By decomposing the non-proportional damping of serially isolated system to the party of proportional damping and non-proportional damping, which is induced by laminated rubber bearings, the equivalent mode damping ratio of the non-proportional damping is derived by Hamilton principle. Therefore the vibration equation of the non-proportional damping of the isolated system is decoupled, and the responses of structure under earthquake excitation can be solved by the mode superposition method. Then validity of the semi-analytical method to solve the seismic response of serially isolated system with distributed parameters and effectiveness of isolated system designed by author are proved by comparison the seismic response of isolated system with ordinary system solved by the semi-analytical method and numerical integration of finite element method, separately.
(4) Aimed to serial system with distributed parameters and rigid nodes taken the tall building as the research object, the bidirectional anti-pulling sliding device which can resist tension and bear pressure is developed. This device is set at the place of isolation layer where the large tension exists, and the laminated rubber bearings are used at isolation layer at the same time. This device can resist tension produced by over-turning moment and make laminated rubber bearings confine in pressured state when the large over-turning moment at the bottom of tall building is generated under earthquake. Then the mechanics model of serial isolated system with distributed parameters and rigid nodes is presented, and the semi-analytical solution of serial isolated system is deduced by imitating the process to deduce the seismic response of the serial isolation system with distributed parameters and rigid nodes.
(5) The Sequential Optimal Mode Control (SOMC) algorithm for serial system with distributed parameters is presented by expanding the Sequential Optimal Control (SOC) algorithm. Then SOMC algorithm is used to the smart isolation of serial system with distributed parameters. For it is difficult to obtain the full state of structural response needed by SOMC in engineering application, the SOMC based on state observer which can realize the vibration control of structure by partial state of structure measured easily is presented. Due to time consumed by the measure of response of structures, on-line calculation and reaction of actuators in the process of on-line real-time control, time lag always exists in the control system. In order to solve the problem of time lag, Sequentialoptimal predicted mode controller is founded by organically combining RBF neural network with sequential optimal control algorithm. The simulation results show that control effect of this predicted mode controller is better in the case of time lag and no time lag.
(6) Based on the bidirectional anti-pulling sliding device, the bidirectional piezoelectric variable friction control device which can produce control force in two orthogonal directions is designed. Then semi-active control algorithm which is used to the vibration control of structure by this control device is presented. Finally one piezoelectric variable friction control device is designed and simulated numerically, and according to mechanical properties of this control device obtained by numerical simulation, this control device is used to smart isolation of serial system with distributed parameters and simulation results show the smart isolation is of excellent control effect.
(7) The simulation technique of Simulink software which is always used to make the analysis of seismic response and vibration control of structure is described in detail. Especially working principle of S-function, namely, the extended tool of Simulink software is emphatically introduced, and at the same time the technique of realizing the variable gain matrix of SOMC is presented, therefore the modularization of SOMC is realized. Finally, the simulation modules of SOC, COC, LQG and SOMC based on state observer of Simulink which are used to make vibration control of structure are designed.
(8) Based on the research of theoretical research and computer simulation, the sweep frequency shaking table test of dynamic response and isolation for serial system with distributed parameters is carried out. The actual piezoelectric variable friction control device is designed and the mechanical properties of the actual control device are test. Then this control device is used to isolation of serial system with distributed parameters and the sweep frequency shaking table test of vibration control for isolation of serial system with distributed parameters is performed under the control of Passive-on and Passive-off control algorithms. So the foundation of engineering application of this control device is established.
(9) The analysis theory of seismic response and isolation technique for serial system with distributed parameters are applied for the actual project and the process of analysis and design of serially isolated system with distributed parameters is presented. The serially isolated system adopted the in-parallel laminated rubber bearings has a better effect of seismic reduction by the calculation and analysis and All those have laid solid foundation for the wide application of this isolation technique.
引文
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