| Traditional base isolation is realized by adding base isolation systems between the structure and foundation. The principle is to lengthen the natural period of the structure. Based on the frequency band gap enjoyed by periodic structures, the present thesis proposes a brand new method of seismic isolation. The concept is to employ periodic foundation to block seismic wave whose frequency falls into the frequency gap. Due to the fact that the fundamental mode contributes most to structural dynamic response under seismic excitation, the key issue is to realize a low frequency gap that corresponds to the fundamental frequency of the concerned structure. So this thesis carries out a numerical analysis on periodic structures. The contents include:1. In order to realize low frequency gap, a systematic study is carried out on the first frequency gap of 2D periodic structure, which is formed by placing rubber coated steel cylinders periodically in concrete matrix. Different physical and geometrical parameters such as density, elastic modulus, filling fraction and core radius to coating thickness ratio have been investigated.2. By introducing Bloch-Floquet theorem and applying periodic boundary conditions, the present thesis extends the classical Kirchoff plate theory, derives the Finite Element Method formulae and Matlab codes for calculation of flexural vibration band gap. Compared with TPWE, the present FEM has better convergence and accuracy. Then, the present method is used to investigate the influence of geometrical parameters such as filling fraction, core to coating thickness ratio and plate thickness on the first frequency gap.3. Using MSC.Nastran, the thesis presents a transient response comparison between periodic and homogeneous concrete plate under forced ground acceleration. It is found that when the frequency falls into the gap, there is strong attenuation in periodic plate and its application in seismic isolation is pretty promising.
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