The Research On Wave Characteristics Of Topological Elastic Metamaterials Induced By Lattice Deformation

The term"topological insulator"refers to a novel substance that has been produced in recent years.It is capable of breaking the structure’s symmetry and generating a nontrivial bandgap to actualize the edge state of topology protection.This topology-protected interface state is resistant to disturbances and faults and has a high degree of robustness.At the moment,the majority of topological insulators explored are based on a periodic structure.The periodic structure enables the realization of a two-dimensional surface state,a one-dimensional edge state,and a zero-dimensional corner state.However,when the crystal structure is altered significantly,the topological state vanishes.There is less research on the topological properties of lattice-distorted materials than there is on periodic crystal materials.Currently,the optical system is the primary focus of relevant research.Because of the intricate coupling and dispersion relationship of elastic systems,realizing elastic topological states in lattice-distorted structures will be more difficult.The production of elastic topological States in lattice-distorted materials would enrich the relevant mechanism of elastic wave control and provide ideas for creating amorphous topological insulators in different physical contexts.As a result,the research on achieving the topological state of an elastic wave in an lattice-distorted structure will take on new significance.In this article,we add lattice disclinations into three-dimensional elastic phononic crystals and demonstrate excellent elastic wave transmission at the interface of lattice-distorted Valley-polarized three-dimensional elastic phononic crystals.Additionally,by randomly shifting lattice points,the effect of disorder on lattice-distorted topological Valley-spin and pseudospin structure is investigated in detail.We demonstrate the transmission of large-scale and long-range topological edge states associated with amorphous deformation.Finally,we extend our research to two-dimensional high-order central bound states.The topological protected bound states persist robustly through a wide range of lattice deformations.The research presented in this article offers applicable prospects for regulating elastic wave energy and developing elastic topology devices.This paper’s primary research content includes the following:(1)This article describes the creation of a three-dimensional elastic phononic crystal cell with a degenerate energy band in the K-H direction of the Brillouin zone.By varying the radius of the unit cells R_aand R_b,the energy band undergoes a process of opening,closing,and reopening,reversing the valley vortex mode.A valley-polarized three-dimensional elastic phononic crystal with periodic structure is produced using this principle.By introducing the lattice disclinations into the valley polarized three-dimensional elastic phononic crystal,the lattice deformation causes the valley-polarized unit cell’s topological phase to invert,forming an interface and thus enabling the robust interface transmission of elastic waves in the three-dimensional elastic phononic crystal.(2)A two-dimensional elastic phononic plate with periodic topological Valley propagation is designed using the quantum Valley Hall effect.We fabricate amorphous Valley polarized two-dimensional elastic phonon plates with deformation ranges of r=1mm,1.2mm,1.4mm,and 1.6mm by randomly moving lattice points.The investigation of the valley-polarized two-dimensional elastic phononic plate’s eigenstates and topological transmission characteristics reveals that it is still capable of robust topological Valley edge state propagation under large-scale and long-range amorphous deformation.A two-dimensional elastic phononic plate with periodic topological pseudospin propagation is developed using the quantum spin Hall effect.We investigate the eigenstates and interfacial transmission properties of amorphous deformed topological pseudospin two-dimensional elastic phononic plates with r=0.2mm,0.8mm,1mm,and 1.4mm.When the lattice deformation is sufficiently large,the elastic wave retains a high transmission efficiency along with the topological interface.(3)A two-dimensional elastic phononic plate with a periodic structure is designed to realize high-order topological central bound states.The influence of structural disorder on the topological central bound state is explored systematically over the deformation ranges r=0.2mm,0.8mm,and 1.2mm.The topological protected central bound state is found to persist strongly under a wide range of lattice deformations.Finally,we design a faulty two-dimensional elastic phononic plate by omitting the magnet.Under the influence of the vacancy disturbance,it is discovered that the elastic wave energy is highly concentrated in the central corner.