Research On Topological States And Refraction Properties Of Elastic Waves In Solid Phononic Crystals

With the rapid development of modern information technology,the energy consumption of electronic integrated devices has become a technical bottleneck to be solved.To this end,researchers are committed to studying new information carriers and artificial bandgap materials.Phononic crystals have the advantages of adjustable structure,controllable defects,easy processing and observation,which provide an effective means to solve this problem.Recently,topological phononic crystals have attracted extensive attention because of their unique robust edge states.Protected by the nontrivial topological properties of the energy band,the phononic edge states can exhibit excellent characteristics such as immunity to structure defects,backscattering suppression and lowloss unidirectional propagation,which have great application prospects in the fields of acoustic signal processing,acoustic communication and ultrasonic medical diagnosis.So far,most studies of phononic topological states mainly focus on airborne acoustic system,and its practical application is limited to a great extent.Due to the conversion and coupling of various elastic wave modes,the one-dimensional and two-dimensional elastic solid systems have greater advantages in engineering applications under complicated working conditions.Therefore,the study of the topological edge states and topological protected refraction characteristics of elastic waves in solid phononic crystals can realize high-efficiency,lowloss and stable elastic wave propagation,which is not only expected to be applied to the design of chip-level elastic wave devices,but also has important theoretical guiding significance and practical value in the fields of the high-sensitivity sensing,high signal-to-noise ratio information processing and structural health detection.Based on the wave theory and topological band theory of elastic waves in one-dimensional and two-dimensional solid phononic crystals,this dissertation focuses on the topological edge state propagation and topological protected refraction characteristics of elastic waves in solid phononic crystals by means of numerical simulation and experimental measurement.The main innovations and research contents of this dissertation are as follows:(1)Based on Su-Schrieffer-Heeger(SSH)model,a one-dimensional solid phononic crystal plate is constructed to study the multiple topological interface states of shear horizontal(SH)guided waves.It is found that the band dispersion and Zak phase of phononic crystals can be tuned by changing geometric parameters and utilizing the inversion symmetry of unit cells,which induces band inversion and topological phase transition.Then,the phononic crystal supercell structure composed of two configurations with different Zak phases is constructed.The transmission spectrums calculated by combining the finite element method and the eigenmode matching theory method show that there are topological interface states at the phononic band gaps opened at the center of the Brillouin zone,or at the zone boundary,or both.By calculating the eigenfrequency spectrums and displacement field distributions of the phononic crystal supercell structures with defects,it is demonstrated that the topological interface state is robust to various defects and perturbations.Finally,the coexistence of topological interface states and trivial defect states is realized in the phononic crystal system caused by Bragg scattering and local resonance.The results show that these highly localized and energy enhanced multiple topological interface modes can be empolyed to design new acoustic functional devices such as adjustable filters and vibration isolators,and are expected to be applied to the fields of high-sensitivity sensing,nondestructive testing and acoustic focusing.(2)Based on the topological theory of defects and homotopy theory,a two-dimensional composite solid phononic crystal composed of elliptical scatterers and epoxy resin matrix is designed.Combined with simulation calculation and experimental measurement,the pseudospin topological edge state propagation of in-plane bulk elastic waves is studied.It is found that the fourfold Dirac point degeneracy at the Γ point can be lifted by inhomogeneously changing the direction of the elliptical scatterers,which leads to the band inversion and topological phase transition of the pseudospin dipole modes and quadrupole modes of the in-plane bulk elastic waves.Then,by calculating the projected band structure of a supercell comsisting of two phononic crystals with different topological properties,the pseudospin-dependent topological edge states are obtained,and a pseudospin-selective waveguide coupler is designed by utilizing the selective excitation of elastic pseudospin and the unidirectional propagation characteristics of edge states.Finally,the topological robustness of pseudospin edge states to bending defects is demonstrated by simulation and experiments.The results show that the elastic topological insulator is independent of the number of elliptical cylinders within the unit cell,breaks through the limits of point-group symmetry and lattice structure to realize the pseudospin-orbit coupling edge state,which opens up a new way to study the new topological phononic phase in the elastic wave system.(3)Based on elastic pseudospin-Hall phononic crystals,the topologically protected zero refraction with arbitrary angles of incidence and wide working frequency range is experimentally studied.Firstly,an elastic near-zero refractive index metamaterial is constructed.On this basis,a three wave beam splitter and an elastic straight waveguide are designed,whose directional collimation characteristics and tunable mode conversion phenomena around the Dirac point frequency are analyzed by simulation.Then,it is found that the fourfold Dirac point degeneracy at the Γ point can be lifted by inhomogeneously changing the direction of the elliptical scatterers,which induces the band inversion and topological phase transition of the pseudospin multipole modes of the in-plane bulk elastic waves.By calculating the projected band structure of supercells composed of two phononic crystals with different topological phases,the highly localized pseudospin polarized edge states are obtained.Combined with simulation calculation and experimental measurement,the topological zero refraction of edge states entering into free space and its robustness to various structural defects and perturbations are studied.The tunable mode conversion phenomena of zero angle refraction waves are revealed by the wave mode separation and equifrequency curve analysis.The results show that this topological elastic wave platform can simultaneously realize topological zero refraction of in-plane and out-of plane elastic waves at different frequency ranges,and enables the highly efficient and stable control of longitudinal and transverse waves in various fluid and solid environments,which is not only expected to be applied to the design of integrated topological elastic wave antenna,but also has great application prospects in the fields of signal processing and underwater communication.(4)Based on ternary valley-Hall topological insulators at the deep subwavelength scale,the topological negative refraction of in-plane bulk elastic waves is studied.Firstly,a graphene-like phononic crystal with lattice constant of0.06 times wavelength is constructed,and the band structure and valley topology of in-plane bulk elastic waves are calculated by finite element method.It is found that the double local resonance Dirac point degeneracy at the K point can be lifted by changing the direction of the elliptical scatterers,which induces the band inversion and topological phase transition of different valley vortex states.Then,by constructing a supercell composed of phononic crystals with opposite valley-Hall phase,the topological valley projected edge states induced by locally resonant state are obtained.The topological negative refraction hosted by the edge states outcoupling into free space and its topological robustness to defects are studied by simulation.Moreover,the wave mode separation and equifrequency curve analysis indicates that the in-plane bulk elastic waves can realize the total mode conversion from longitudinal to transverse waves in the case of topological positive/negative refraction.Finally,utilizing the valley-selective excitation,a topological elastic valley filter is designed by coupling the topological valley edge states with bulk valley states.The results show that this ternary valley-Hall topological insulator based on local resonance mechanism extends the research of elastic wave manipulation to the deep subwavelength scales and may bring significant breakthrough for the compact engineering applications in super-resolution sensors,in-plane wave superlens and structural health monitoring.