Theoretical And Numerical Analysis Of Two Dimensional Periodic Seismic Metamaterials

As an innovative isolation technology,seismic metamaterial has the functions of isolating the main frequency part of seismic waves,attenuating most energy of the seismic waves or directly guiding the seismic waves to propagate bypass the buildings,so as to realize the effective protection of buildings in the event of earthquakes.This external isolation structure also has many advantages that are not entailed by traditional isolation measures,such as the integrity characteristics of the structures will not be affected,the applicability is strong for various site types,the costs of construction and maintenance are relatively low,different and separate design for each building are not needed,and the protection to a group of buildings can be realized.In order to push forward the engineering applications of this new isolation technology,the study on the control of elastic waves in these seismic metamaterials is imperative.Therefore,this thesis aims at two dimensional periodic seismic metamaterials and carries out the following investigations in order to obtain a band gap with low center frequency and large bandwidth,so that the attenuation zone can cover a wide range of frequencies of seismic waves and the functions including the wave isolation,attenuation and guidance of seismic metamaterials can be fully employed.Firstly,based on the classical vibration theory and Floquet-Bloch principle of periodic structures,the influences of multiple parameters on the center frequency and bandwidth of the first band gap are studied,which supplements the deficiency of current literatures which usually study the influences of relevant parameters on band gap characteristics by altering a single variable at one time.Obviously,the variation of multiple parameters at one time accord more closely with the practical fact that material parameters are correlative.Secondly,two essential parameters that are easy to calculate are summarized to synthetically reflect the influence of material and geometrical parameters of scatterers and matrix on band gap properties.This theoretical analysis is further verified by numerical simulation.These results provide guiding reference for rapid engineering design in selecting parameters and comparing schemes.Thirdly,based on the above obtained results,a structure which has a first band gap with relatively low center frequency and wide band width is designed.The numerical simulation results of the dynamic responses in both frequency and time domains prove that the structure has good attenuation effect on the elastic waves within its band gap frequency range.Finally,considering the disadvantage that the elastic waves in waveguides of traditional seismic metamaterial are sensitive to local defects(disorders),here in this thesis a waveguide of seismic metamaterial with the property of topological insulator is realized by combining the theory of topological insulators with that of elastic systems.The topological properties of the structure are verified from two aspects,i.e.the phenomenon of band inversion and the alteration of topological invariants.Then,the numerical simulation results show that the seismic metamaterial waveguide of topological insulator designed here does have a strong disorder-immune property as contrasting to the waveguide of traditional seismic metamaterial.