The Research On Multidimensional Topological Properties Of Elastic Phononic Crystal

The appearance of phononic crystals provides a new way to artificially manipulate the elastic wave propagation in elastic media and structures.Developed from phononic crystals,the phononic topological insulator,due to its fantastic functions in wave controlling,have attract vast attentions.As the research further develops,multiple topological states have been realized in phononic topological insulator,such as the topological edge state,topological surface state and higher-order corner state.Meanwhile,as researchers have a better understanding of topological defects,a series of topological states have been successively realized by using topological defects,such as topological interface states and topological localized states.However,in the field of elastic wave,the band dispersion is complicated due to the coupling of various vibration modes,so the study of topological wave properties in this field is relatively lagged.In this paper,we have investigated multidimensional elastic topological states.The topological edge state,topological surface state and topological corner state of three different dimensions are realized in the same system,and the topological interface state and localized state based on defects are also obtained.This paper shows great prospect in the fields of elastic wave regulation,energy recovery and so on.The thesis mainly includes the following contents:(1)One-dimensional edge state and two-dimensional surface states are realized in the same bilayer phononic elastic plates.The Dirac cone at the corner point of the Brillouin zone is lifted by changing the radius of the oblique column.A nd we observed the lifted-opened-lifted process of the Dirac cone,which means topological phase transition is formed.We then calculated the band structure of the supercell composed of unit cells(γ=0.2 andγ=-0.2).Two edge bands were observed in the bandgap.At last,topological edge states were observed in the elastic plate composed of these unit cells.Then,the two-layer elastic plate is stacked along the Z direction,and the structure becomes a three-dimensional system of chiral Weyl phononic crystals.When k_z≠0,the Weyl point is lifted and the topological band gap is formed.Also,we observed edge bands in the bandgap of the supercell’s band structure.The topologically protected two-dimensional surface state without gap is observed by excitation of two excitation sources with 90 degrees phase difference.(2)The higher-order topological corner state is achieved using the same bilayer phononic crystal plates.A double Dirac point is obtained at the center of the Brillouin zone by analyzing the composite cell’s band structure.By adjusting the coupling that between and inside the composite cells respectively,we obtained topological nontrivial elastic plate consisted of shrunken cells and topological trivial plate consisted of expanded cells.the double Dirac point of the shrunken cell is lifted,resulting in a topological phase transition,which enables the second order topological state.We observed edge states exist in the bandgap of the supercell,which means the higher-order topological states would appear.Then,we obtained corner state in a parallelogram plate consisting of shrunken cells.(3)Topological defects are introduced into the phononic crystal elastic plate to realize valley interface states.Bring the disclination defects into the valley-polarized hexagonal phononic crystal elastic plates and the plates change into a pentagonal pla te with negative topological charge and a heptagonal plate with positive topological charge.Different from previous topological charges derived from the energy band structure of momentum space,such topological charges are derived from real space.Due to the valley polarization topological phase transition at the interface of the pentagonal elastic plate,the interface generated by disclination defects becomes a n elastic topological waveguide.Then,connecting the pentagonal plate with the heptagonal plate,the waveguide based on dislocation is obtained.Furthermore,the robustness of elastic wave propagation in the waveguide is verified via artificially fabricating structure defects.(4)The localized state of elastic phononic crystal plate is also obtained based on the disclination defect,which is introduced into a honeycomb lattice elastic phononic crystal plate.Due to the existence of disclination defect,the original hexagonal structure becomes into a pentagonal plate with a pentagonal center.In the pentagonal plate composed of shrunk composite cells,there are fractional charges at the pentagonal center,which supports the topological state.While the pentagonal plate consisting of enlarged composite cells owns integer charges and is in a trivial state.Through modal analysis,five local ized states are observed in the pentagonal plate with shrunk composite cells,and the elastic wave energy is highly concentrated on the boundary of the pentagonal center.Such local state is stable and immune to defect s.In this paper,the topological states of elastic phononic crystal plate is systematically studied.We will show 4 different elastic wave prop agations in the same system,namely the wave propagation in the bulk,surface,edge and corner.Besides,by using topological defects,we realized the topological interface state and local ized state for the first time.