Study On Band Gap Characteristics And Seismic Isolation Performance Of Periodic Structures

Periodic structure is a special artificial composite structure.The periodic structures,which are manually engineered and arranged in a certain way,exhibit dynamic properties that cannot be found in natural materials or structures.The study on phononic crystals in the field of solid-state-physics shows that periodic structures have unique filtering properties,that is,elastic waves in some frequency regions cannot propagate through the structures,and this specific frequency region is called band gap.In recent years,researchers have introduced the concept of periodic structure into the field of civil engineering,using its band gap characteristics to design and analyze the isolation structures,and gradually developed into a new seismic isolation technology.In this paper,the dispersion characteristics and isolation performance of one-dimensional periodic foundation,surface metabarrier and buried metabarrier were studied by theoretical analysis,numerical simulation and comparison with experimental results of other researchers.Firstly,based on elastic wave equation,the dynamic models and dispersion equations of three kinds of periodic structures were developed by transfer matrix method or effective medium method.Then,three types of unit cell finite element models,development in ABAQUS and COMSOL,were designed to confirm the analytical dispersion relation and get further insights into the attenuation characteristics of finite periodic structures.Finally,the transmission analysis model with finite periodic structures was performed,and the isolation performance of periodic structures was studied by frequency domain and transient analysis method.The conclusions can be drawn as follows:(1)A wider band gap can be obtained by reasonably designing unit cell with different thickness so that the band gap overlaps each other.Additionally,the existence of the superstructure will also change the position of the band gap,so it is more practical to calculate the dispersion relation by converting the superstructure into an equivalent layer.(2)Compared with reinforced concrete foundation,one-dimensional periodic foundation has good attenuation effect on horizontal and vertical seismic waves located in the frequency band gaps.Moreover,when the main frequency components of the input ground motion are outside the frequency band gaps,the dynamic response of the periodic foundation superstructure does not decrease obviously.(3)Due to the dispersion characteristics of Rayleigh waves in stratified half-space,the dispersion curves of the metabarrier arranged on the surface of stratified half-space also have multi-order modes.Simultaneously,it can be concluded that only the fundamental surface mode can strongly couple to the surface metabarrier owing to the significant disappearance of the vertical displacement component at the free surface.However,the other higher-order modes do no effect on the surface wave attenuation.(4)In the subwavelength range,the resonator composed of composite materials can be approximated as a frequency-dependent isotropic elastic homogeneous medium,and its elastic mechanical parameters can be expressed by the effective mass density,effective longitudinal wave velocity and effective shear wave velocity of the resonator.(5)In the frequency range above the surface wave band gap in the fully resonant half-space,the apparent phase velocity of the surface mode is greater than that of the shear wave,and the internal surface waves exist in the form of leaky wave modes,which leads to the band gap widening.