Research On Topological Insulator And Device Design Of Acoustic Artificial Materials

The emergence of acoustic artificial materials(including phononic crystals and acoustic metamaterials)provides a new way for manipulating acoustic and elastic waves.Artificial acoustic materials are composite structures designed by human,By designing different structural units,a number of unique physical properties that cannot be found in natural materials can be obtained,such as band gap,negative effective mass and negative effective modulus.With the development of the topological band theory,the study of topological states has been extended from condensed matter to acoustics.In topological insulators,topologically protected interface states and edge states can be observed,which are robust to defects and perturbations.Topological acoustics provides an avenue for the design and development of novel wave devices.In this thesis,we construct one-and two-dimensional topological insulators using acoustic artificial structures,study the topological properties and wave characteristics of these topological insulators by theoretical analysis,numerical simulation and experimental test,and then explore their potential device applications.The main research contents are as follows:1?One-dimensional hierarchical acoustic metamaterials are constructed based on the Su-Schrieffer-Heeger(SSH)model and then the topological properties of these metamaterials are analyzed.The spring-mass model is extended to the continuum medium model.The results show that the equivalent mass of the system is negative for some frequencies due to the introduction of hierarchical resonators,which leads to the locally resonant band gaps in the band structure.The topological properties of the metamaterials vary as the stiffness of the internal and external springs connecting mass-in-mass resonators on the sublattices changes.When the external spring stiffness is larger than the internal spring stiffness,the structure is topologically non-trivial.When the external spring stiffness is smaller than the internal spring stiffness,the structure is topologically trivial.The topologically protected edge states or interface states can be formed at the boundary of topologically non-trivial structures or the interface between topologically non-trivial and trivial structures,and show robustness against defects or perturbations.Because the metamaterials contain hierarchical resonators,the topologically protected edge states or interface states can appear simultaneously in multiple Bragg band gaps.2?A phononic crystal plate with a band gap for flexural waves is designed.The cavities are constructed by introducing point defects into the phononic crystal,and the cavity mode with high symmetry can be generated in the band gap.Based on the SSH model,the one-dimensional diatomic chains of phononic crystal cavities are constructed and their topological properties are then analyzed.The results show that the coupling strength between the cavities can be described by the tight-binding model.And the closer the distance between the resonators is,the higher the coupling strength will be;otherwise,the lower the coupling strength will be.The relationship between the internal and external coupling strengths of the cavities affect the topological properties of the structures.When the external coupling strength is larger than the internal coupling strength,the structure is topologically non-trivial.And when the external coupling strength is smaller than the internal coupling strength,the structure is topologically trivial.The topologically protected edge state can be observed at the boundary of topologically non-trivial structures and are robust against perturbations.3?An acoustic metamaterial with three Helmholtz resonators in each scatterer is designed.This results in a subwavelength scale band gap appearing in the band structure.The acoustic metamaterial has C_3Vsymmetry.Similar to the quantum valley Hall effect,the topological phase transition at the subwavelength scale is realized by rotating the scatterers.The waveguide transmission with topological protection is formed at the interface of structures with different topological phases and shows backscattering suppression.The energy harvesting of acoustic waves is realized by using a waveguide-cavity coupled structure that is topologically protected.Compared with the reference specimen,the performance of energy harvesting is significantly improved,and the amplification ratio of energy harvesting is up to more than 100 times.