Study Of Valley Topological States And Transport Properties In Elastic Phonon Crystals

In recent years,new developments have been made in the study of phononic crystals.With the development of topological theory,the study of topological properties has also been introduced in acoustic systems,which have received a lot of attention from researchers due to their novel physical properties such as transmission protection,energy free loss and defect immunity.Much progress has been made in the realisation of topological states in acoustic systems in fluid media,but the existence of multiple modes coupled in elastic waves in solids and the complexity of their modes makes research on the realisation of topological states in elastic waves still in the early stages of development.However,elastic waves have their unique advantages over acoustic waves in fluids.Elastic waves have almost no attenuation when transmitted in solid materials and are more practically applicable,so research into the implementation of topological states in elastic waves becomes necessary.The emergence of the valley state concept presents one of the simplest solutions for implementing topological states in elastic waves.The introduction of the valley state concept into elastic materials allows the design of a variety of superior acoustic topological devices such as nondestructive probes and acoustic sensors with higher energy transfer efficiency.This paper mainly studies the propagation properties of elastic waves in phononic crystals and valley topological edge transport,including the following three parts:In the 2nd chapter,the main discussion focuses on the design of a honeycomb hexagonal lattice phonon crystal in a two-dimensional elastic material.When the system is protected by inverse symmetry,three pairs of linear simplex Dirac points appear at point K,corresponding to different frequency bands,and the inverse symmetry of the system can be broken simply by adjusting its geometry so that the Dirac points at point K open up the band gap to form a valley.By calculating the projected energy band structure of two different valley Hall materials combined into a strip supercell,it is found that edge states appear in all three band gaps,and symmetric and antisymmetric modes are defined by judging the eigenfields of the edge states.This section focuses on the use of multiple boundary states containing positive and antisymmetric modes to achieve valley topological transport,We have found that positively incident SV waves are more likely to couple to the boundary states of the antisymmetric modes.In the 3rd chapter,design of a honeycomb hexagonal elastic phonon crystal with trigonal scatterers adsorbed on the top and bottom surfaces of the thin plate.When the scatterer does not rotate the system has₃symmetry,and numerical simulations reveal that at the corner points of the Brillouin zone,Dirac points are created.By simply choosing the angle of the scatterer,the Dirac point can be made to open up the band gap to form a valley.The topological phase transition of the system is relation to the angle of the rotating scatterer,by using6)?theory analysis of the topological characteristics of the system.Using two different Valley Hall phonon crystals,the existence of edge states connecting the upper and lower bulk bands was discovered,and the modulation of the edge state frequency was realized by adjusting the scatterer height.Finally,the existence of corner states was discovered by constructing triangular supercells.In the 3rd chapter,this chapter focuses on the realization of valley topological transport using boundary states and the design of some acoustic devices.The chapter introduces the idea of tunable edge state frequencies to achieve topological transport at wider frequencies and confirms the excellent anti-scattering properties of the edge transport protected by the valley topology.This section also explores the phenomenon of positive and negative refraction when elastic waves are radiated into a thin unstructured plate,at the same time the design of the sandwich structure allows the interference of the two trains of waves radiating in the unstructured thin plate.It is discussed that by adjusting the geometry,it is achievable to artificially control the position at which the two trains of radiation waves meet.Finally,the selective excitation phenomenon of multi-channel design is discussed,and it is found that the energy flow entering a specific channel depends only on the Angle between the channel and the source channel,independent of the position of the source channel and the length of the channel.