Research On Wave Manipulation Mechanism And Design Of The Elastic Topological Insulator

In large engineering equipment,vibration problems are common and propagate in the structure in the form of elastic waves.The research on the mechanism and method of elastic wave manipulation is widely used in equipment operation state perception,dynamic characteristic design,vibration and noise control,and so on.The design of high stability,high sensitivity,and low loss elastic waveguide materials and devices to realize the accurate control of structural vibration propagation is an important issue in the current engineering and academic fields.In recent years,the continuous in-depth cross integration of acoustics,mechanics,condensed matter physics,quantum physics,and other disciplines has greatly enriched the research of wave propagation manipulation and provided a new theoretical basis and implementation means for realizing accurate wave regulation.The relevant research has shown unprecedented vitality.Among them,the elastic topological insulator proposed by analogy with the topological insulator in condensed matter physics is a specially designed artificial periodic structure or material,which can produce topological edge states or corner states with high stable wave manipulation ability in the elastic wave bandgap.Compared with the classical wave control method,the topological states have the extraordinary characteristics of nonreciprocal unidirectional transmission,backscattering suppression,and defect immunity.It can accurately manipulate the spatial distribution of wave energy and shows excellent application prospects.For the demand of low-frequency elastic wave manipulation in engineering,the elastic topological insulators are designed based on locally resonant acoustic metamaterials in this paper.Focusing on the formation mechanism of topological states of one-dimensional and two-dimensional elastic topological insulators,the law of wave regulation,and the key theoretical or technical problems to be solved in optimal design,systematic research is carried out through the combination of theoretical analysis,modeling simulation and experimental verification.The main research contents and conclusions include:1.Based on classical theoretical models in the electronic system,the elastic topological structures with local resonators are designed,and the propagation characteristics of elastic wave in these structures are studied by the plane wave expansion method and finite element method.Through the cross fusion of quantum physics theory,the formation mechanism of topological states is deeply revealed,and the feasibility of subwavelength elastic wave manipulation using the locally resonant system is verified,which provides theoretical guidance for the research of elastic topological states.2.For the locally resonant topological insulators,the topological phase transitions of the unit cells are systematically analyzed based on the band inversion phenomenon,and the topological characteristics of the edge states and corner states,as well as the effects of material parameters and structural parameters on the topological state,are explored.These studies deeply analyze the internal wave behaviors of Bloch modes of the nontrivial system,reveal the wave manipulation mechanism of elastic topological insulators in the subwavelength regime,and show the extraordinary wave control ability of the locally resonant system.3.Aiming at the on-demand inversion design problem of topological structure,a mathematical model is established based on finite element analysis theory and solved by genetic algorithm,to obtain the elastic high-order topological insulator with specified operating frequency.This method provides an effective technical means for the rapid reverse design of high-order topological insulator unit cell configuration.In short,through the method of interdisciplinary integration,this paper deeply studies and analyzes the basic theory,topological characteristics,wave manipulation mechanism,and design method of a low-frequency topological insulator,which provides new technical support for realizing low-frequency and wide-band elastic wave regulation by using small-size structure,which has important reference significance for realizing stable and sensitive structural vibration control.