The Topological State Transport In Local Resonance Metamaterial

In recent years,the research of artificial periodic structures such as phononic crystals and metamaterials has made great progress.With the development of topologic band theory,the concepts related to topology have been gradually introduced into the research of periodic structures,including Quantum Hall Effect,Quantum Spin Hall Effect and Valley Hall Effect.Among them,the realization of the Valley Hall Effect only needs to break the spatial inversion symmetry of the structure,and because the model design is relatively simple,many researchers pay attention to it.They found that if the structures with different Valley topological phases were combined together,the edge state protected by topological properties would be observed at their contact interface.This special topological transport has good anti-scattering ability and energy concentration which can be used as an acoustic device,and has certain application value in the field of non-destructive testing and directional waveguide.Considering the small attenuation of elastic wave in solid system,it is more practical to construct solid topological materials.However,the working frequency of solid-state elastic phononic crystal is as high as several hundred MHz.In order to deal with the low-frequency problem,the lattice size of phononic crystal must be designed to be large,which is unrealistic and uneconomical.In this paper,we mainly study the topological transport of locally resonance metamaterials.By introducing the local resonance mechanism,we construct the topological materials with subwavelength band gap,which break the design limitations and can be used to deal with low-frequency problems.Specifically,in the second chapter of this paper,an Bloch-based isogeometric analysis for wave propagation is introduced as the theoretical formula for solving the band structure of metamaterials.In Chapter 3,we design an elastic metamaterial model with both negative effective mass and negative effective modulus based on translational resonance,which has subwavelength band gap and can be used as low-frequency sound insulation and vibration isolation material.In addition,by changing the material parameters of the model and calculating the Zak phase of the corresponding band,we construct a metamaterial structure with different topological phases.The interface state with the characteristics of energy concentration and robustness is observed at their contact interface by finite element simulation,which is expected to be used as acoustic devices in the future,such as acoustic switches,sensors,etc.In the fourth chapter,we constructs an elastic metamaterial plate with₃symmetry.This plate has two-dimensional periodicity and is composed of soft material and hard material.Based on the local resonance characteristics of soft materials,a low frequency Dirac cone is constructed at theand^?in the Brillouin region.Then,by breaking the spatial inversion symmetry of the model,the low-frequency band gap is opened,thus the valley topology material is constructed.In addition,the thin plate models with different topological phases are combined in this study,and the topological edge states are observed at their interfaces by using finite element simulation.This topological edge state has excellent anti-scattering characteristics.Even if there is corner,disorder or defect in the propagation path,it can smoothly propagate from one end to the other end,and the angle of refraction will be zero after the elastic wave is emitted from the interface.All of the above characteristics indicate that the elastic Valley topologic material will have a broad application prospect in the field of directional waveguide and non-destructive testing.