Laminated Rubber Bearings With Cantilever Columns In Series To The System Dynamic Stability Analysis

At present, the laminated rubber bearings are often mounted on the top of the basement cantilever columns in most of projects in china and abroad. In order to guarantee the engineering security, the dynamic stability of serial system is analyzed. Highlighting this topic, the thesis tries to investigate the following essential aspects:1. Structure vibration control is classified and explained and the current researching situation and the tendency of base-isolated control system in china and abroad are mainly detailed. The definition and classification of the theory of dynamic stability are provide and the brief but overall introduction to its research approach is given and its research history is reviewed; Lastly, questions such as proposing of the problem, current research-situation and the meanings of the problem are discussed.2. A comprehensive introduction to the theory of dynamic stability is given. The concept of parametric resonance is introduced. The system differential equations(Mathieu-Hill equations)for dynamic stability analysis is derived. Floquet's theory is introduced. The application of finite element method(FEM) to dynamic stability analysis is described emphatically. The Lagrangian equations is used to derive the necessary element matrices(element stiffness matrix, element mass matrix and element geometric stiffness matrix). It is also shown that system equations for static structural mechanics, structural dynamics and static buckling are only a special case of the system equations of dynamic instability. Finally, Floquet's theory is used to generate- dynamic stability system equations for the purpose of determining both undamped and damped instability regions.3. A investigation review of static stability of the laminated rubber bearings are presented according to the documents of J.M.Kelly et al. and Zhou Xiyuan et al.. The serial isolation system consisting of laminated rubber bearing and R/C column and the combined bearing consisting of an up small one and down larger one are introduced and their calculation formulas of static stability is derived. With the latter calculation formula, the static stability formula of the serial system considering P-A effect of R/C column can be acquired.4. The FEM program DSA(Dynamic Stability Analysis) developed on the basis of the dynamic stability theory, the basic theory of spectrum analysis and the Fast Fourier Transform (FFT) algorithm is introduced. The spectral analyses of three earthquake waves are made using FFT algorithm. All the process is realized by programming in Matlab5.3.5. The dynamic stability of serial system of laminated rubber bearing with column is calculated on the basis of FEM Analysis program DSA. The first example indicates thatthough adopting the simple dispersed unit, the calculation result can still meet the project request. The second one discusses the rules of dynamic instability regions of serial system with different static load factor and different column cross-section size. Through the frequency spectrum analysis of earthquake waves and the dynamic instability regions analysis, the dynamic stability of serial system can be judged under a certain earthquake wave. Finally, the range of least column cross-section size meeting the dynamic stability condition is provided at the third example.