Research On Topological Edge States Of Two-dimensional Tunable Phononic Crystals

Effective control the propagation of acoustic signal is a hot issue in current acoustic research.In recent years,a lot of achievemets have been made in the research of new acoustic functional structural materials such as acoustic metamaterials and phononic crystals,including many novel characteristics that traditional acoustic materials do not have.These are provid brand-new way for regulating sound waves.Both Acoustic metamaterials and phononic crystals belong to the category of acoustic artificial structural materials,which broadens people’s research on the properties of elastic waves in acoustic materials,and there is no particularly obvious boundary of them.In contrast,the main research direction of phononic crystals is the Bloch acoustic wave in the periodic structure,and The propagation properties of acoustic waves are affected by the energy band structure of the momentum space.Acoustic metamaterials are more inclined to study the design of the internal structure of the materials.For the structure whose size is much smaller than the wavelength of the sound wave,it can be regarded as an isotropic homogeneous medium with local resonance response and dynamic negative elastic parameters,so as to realize the acoustic stealth,acoustic super transmission and other interesting acoustic phenomena.In recent years,with people’s research on topological states of matter in the quantum and electromagnetic fields in condensed matter physics,topological effect in acoustic systems is starting to get widespread attention,and realized acoustic topological states under different conditions,including acoustic quantum Hall effect,acoustic topological insulators,the Valley Hall effect,and high-order topological states,etc.The research in the field of topological acoustics improves people’s ability to manipulate acoustic waves.In this paper,based on the theory of acoustic Valley Hall effect,we study the influence of the degree of freedom of rotation in a two-dimensional phononic crystal on the energy band,the properties of topological boundary states and its regulation on acoustic signals.The specific content is as follows:1.We introduce the theoretical basis for calculating the energy band of phononic crystals based on the perturbation method and the finite element method,then we construct the unit cell structure of the two-dimensional phononic crystals:the hexagonal primordial cells composed of triangular rigid columns are tightly arranged in two-dimensional air space according to the honeycomb lattice.the cross section is a triangle.When the angle of rotation of the triangular columnar structure is the same as the highly symmetric direction of the hexagonal cell,the entire system shows C_3vsymmetry.Then we study and calculate the energy bands of phononic crystals with different rotation angles.2.In Chapter 3,we first calculate the projected energy bands of two adjacent phononic crystals with different topological phases to obtain the topological boundary states,and then calculat the projected energy bands under different scatterer rotation angles.Furthermore,the robustness that immunity to bending defects of acoustic wave propagating in topological boundary states are verified by simulation and experimental design.Finally,by adjusting the rotation angle of the scatterer,we could control the sound wave propagation in the topological boundary state:using the bending defect immunity of the phononic crystal boundary state to realize the control of the sound wave propagation path,and the sound wave can be efficiently propagated according to a specific path;By analyzing the band gap characteristics of different boundary states and the propagation of sound waves,it is found that the diffusion of the acoustic wave on different topological boundary states which is perpendicular to the sound propagation direction is different,and the rotation angle of the scatterer can be adjusted to receive the sound wave at a specific incident angle;the bending defect immunity that extends the topological boundary state realizes the control of the transmission intensity of the sound wave.In terms of experiments,we use three-dimensional printing technology and mechanical processing technology to produce the required triangular scatterers and scaled substrates,and we could control the rotation Angle by a stepping motor with an external integrated relay circuit board.