Periodic Structures And Periodic Seismic Isolation Foundations

Base isolation is an effective way to decrease structural responses under earthquake actions. However, because of the disadvantages of traditional base isolation systems, it is a hot topic to develop new seismic isolation systems. In1993, some investigations in the field of solid-state-physics show that phononic crystal, a novel periodic structure, can be designed as a filter for elastic wave. In some frequency regions, named band gap or attenuation zone, elastic waves cannot propagate in this type of periodic structure. Based on this idea, this work aims to investigate the filtering effect of this type of periodic structure and to study possible applications of periodic structure, named periodic seismic isolation foundation, in civil engineering.In this dissertation, attentions are focused on four topics:1, numerical method for the dispersion relationship of periodic structure;2, basic theory of periodic structure;3, numerical simulations of periodic foundations; A, experimental studies of periodic foundations. On the first topic, the convergence of the Fourier expansion method in calculating the band structures of elastic waves propagating in periodic composites is discussed based on its two mathematical backgrounds. And influences of the material parameters and the geometrical parameters on the convergence are analyzed. On the second topic, by using mass-spring models, the filtering effect of periodic structure for elastic wave is studied and the attenuation mechanism of energy flow in finite periodic structure is illustrated. To study the directional attenuation zone of local-resonant periodic structure, dispersion curves of local-resonant periodic structure are presented according to the vibration mode of the inner oscillator. On the third topic, numerical simulations are conducted to verify the efficiency of the attenuation zone of finite periodic structure and to show the filtering effect of periodic foundation for seismic waves. As using the improved layered periodic foundation or the two-dimensional periodic foundation with directional attenuation zones, seismic responses of upper-structures under different types of seismic waves are also simulated. On the fourth topic, shake table tests and free field tests are conducted for the layered periodic foundation and two-dimensional periodic foundation, respectively.Some conclusions are obtained:the convergence of the Fourier expansion method is influenced by the Gibbs oscillation and the uniform convergence formula for the product function. For the scattering periodic structure, the filtering effect is related to the interaction between different materials; for the local resonant periodic structure, the filtering effect is related to the resonance of the inner oscillator. Directional attenuation zones can be opened easily for non-symmetric periodic structures. Compared to symmetric periodic structures, the small-size non-symmetric periodic structures can open low-frequency broadband attenuation zones, which are much beneficial for engineering applications. Numerical simulation results show that vibrations in attenuation zones can be obviously lowered after three unit cells. Seismic simulation results show it is feasible to isolate seismic waves by using periodic foundations. Seismic responses of upper structure are decreased because the input energy is lowered by the periodic foundation. The improved layered periodic foundation and the two-dimensional periodic foundation with directional attenuation zones can be used to protect upper-structures in different sites. The efficiency of the layered periodic foundation is proved by the shaking table tests results, and the feasibility of two-dimensional periodic foundation is verified by the free field tests results.