| In the past three decades,phononic crystal(PC)has been widely concerned by researchers in different disciplines due to their unique physical phenomena,high designability of structures and materials,and extraordinary manipulation of wave/vibration.Many properties of PCs that are not possessed by the ordinary materials,such as bandgap,negative refraction,cloaking and subwavelength imaging,make them have a wide application prospect in various fields covering automotive industry,medical testing and military aviation.Recently,the discovery of topological edge states in PCs has once again overturned people’s understanding of the properties of traditional materials.Due to the topologically nontrivial nature of underlying band,edge states exhibit many extraordinary properties,such as lossless transmission,one-way transmission and stable backscattering suppression,which provide new methods to go beyond the traditional signal processing technology.At present,most of the related researches are focused on two-dimensional airborne acoustic system.Unfortunately,the only existing longitudinal wave mode for airborne acoustic system is limited in practical application.In fact,because of the coexistence of multiple modes and complex coupling mechanism,the two-dimensional and three-dimensional elastic wave/vibration systems are commoner in engineering and their applications are more extensive especially for the complicated working condition.The realization of the topological edge state for elastic wave with immunity to the backscattering caused by defects,bending angles and disturbances is extremely desirable,which can provide a theoretical and experimental guidance for reducing the manufacturing accuracy of equipment,improving the signal-to-noise ratio of signal system,and enhancing the detection performance and efficiency of devices in practical engineering.To meet the urgent requirements for the fast,stable and efficient techniques of signal processing,based on the theory of elastic wave propagation in PCs,topological theory and Weyl semimetals theory,this dissertation systematically investigates the elastic wave topological properties,edge states,directional transmission,robust transmission immune against the defect and the potential applications in novel ultrasonic devices.The main contents and innovations of this paper are as follows:(1)Based on the elastic analogy of quantum valley Hall effect(QVHE),simultaneous multi-band topological edge state and valley-protected backscattering suppression of out-of-plane bulk elastic wave are studied in the two-dimensional(2D)honeycomb PCs with veins.First,the finite element method(FEM)is employed to calculate the band structure and valley topological properties for the out-of-plane bulk elastic wave.It is indicated that adjusting the radius difference of adjacent cylinders can simultaneously induce the band inversion of multiple twofold Dirac cones and produce elastic valley topological phase transition.Then,it is demonstrated that multi-band valley topological edge states of the out-of-plane bulk elastic wave appear at the interface of supercell constructed by two kinds of solid PCs with different valley topological phases.Furthermore,through a full wave simulation,the path-selective characteristics of valley edge states are explored and the transmission coefficients of valley edge states under the introduction of bend angle and defect are calculated,which verifies the robustness and valley topological protection of edge states.Finally,the property of valley-protected backscattering suppression is demonstrated for out-of-plane bulk elastic wave in multiple frequency ranges.(2)Based on the elastic analogy of quantum spin Hall effect(QSHE),pseudospin topological edge states and one-way directional transmission of in-plane bulk elastic wave are studied in the 2D honeycomb PCs.First,the FEM is employed to calculate the band structure and pseudospin topological properties for the in-plane bulk elastic wave.It is indicated that shrinking and expanding the inserted scatterers can well induce the band inversion of fourfold Dirac cone and produce elastic pseudospin topological phase transition.Then,it is demonstrated that pseudospin topological edge states of the in-plane bulk elastic wave appear at the Zigzag and armchair interfaces of supercell constructed by two kinds of solid PCs with different pseudospin topological phases.Finally,through a full wave simulation,the one-way directional transmission and the robustness against the bending angles,defects and disorders for the pseudospin edge states of the in-plane bulk elastic wave are further demonstrated.(3)First,based on the elastic analogy of QVHE,the valley edge states and valley-protected transport of the coupled plate-mode wave are studied in 2D pillared honeycomb PC plate.The FEM is used to calculate the band structure and valley topological properties for the coupled plate-mode wave.It is indicated that adjusting the height difference of adjacent pillars can induce the band inversion of twofold Dirac cone and produce valley topological phase transition of coupled plate modes.The valley edge states of coupled plate modes are confirmed to appear at the Zigzag interface of supercell constructed by two kinds of PC plates with different valley topological phases.Then,based on the elastic analogy of QSHE,pseudospin topological edge states and unidirectional transmission of fundamental anti-symmetric Lamb wave are studied in 2D perforated honeycomb PC plate.The FEM is used to calculate the band structure and pseudospin topological properties for the anti-symmetric Lamb wave.It is indicated that rotating the angle of three-arm-column hole can induce the band inversion of fourfold Dirac cone and produce pseudospin topological phase transition of anti-symmetric Lamb wave.The pseudospin edge states of the in-plane bulk elastic wave appear at the armchair interfaces of supercell constructed by two kinds of PC plates with different pseudospin topological phases.Finally,the robust transport immune against the bending angle and defects for two categories of PC plates are proved by the calculation of the transmission coefficient.(4)Based on the elastic analogy of QVHE,the 2D robust valley transport and layer-selective transport for elastic wave are studied in three-dimensional(3D)monolayer-stacked and bilayer-stacked honeycomb PCs,respectively.First,the band structure and topological properties of the 3D monolayer-stacked PC without layer coupling are simulated by EFM.It is indicated that simultaneously changing the width difference of adjacent hexagonal blocks in each layer can induce the valley Hall phase transition of 3D monolayer-stacked PC and produce 2D elastic valley surface states at the interface of 3D PCs with different topological properties.Then,the PC samples of monolayer-stacked PC are fabricated and the experimental measure is carried out to obtain the transmission coefficient along the two spatial directions.Furthermore,by stacking the monolayer PC into bilayer with non-zero layer coupling,the 2D layer-polarized surface states are revealed.Finally,the PC samples of bilayer-stacked PC are fabricated and the layer-selective of 3D elastic wave are confirmed by experiment.(5)Based on the elastic analogy of Weyl semimetals,the ideal II-type Weyl points,Weyl surface states and anomalous chiral transport of elastic wave are studied in the 3D honeycomb PCs.First,by destroying the spatial inversion symmetry of 3D stacked PCs,two pairs of ideal Ⅱ-type Weyl points of elastic waves are discovered based on FEM,which carry topological charges of+1 and-1.Then,the transition process between the Weyl semimetal phase and the valley topological phase was revealed by adjusting the parameters of spatial inversion symmetry breaking.Furthermore,the surface states with opened arc trajectory are proved to appear the edges for Weyl semimetal and the surface states with closed circle trajectory are proved to appear at the interface of two distinct PCs with Weyl phase and valley topological phase by using supercell simulation.Finally,through a full wave simulation,the robust and unidirectional propagation of Fermi-arc surface state and kz-dependent robust propagation of Fermi-circle surface state are demonstrated. |
PDF Full Text Request