Seismic Response Analysis And Smart Control Of Serial System With Distributed Parameters

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.