Research On Mechanism And Characteristics Of Elastic Wave Control Of Acoustic Topological Insulators

Engineering equipment is often accompanied by vibration and noise problems.Excessive vibration and niose seriously affects the efficiency and life of engineering equipment and the physical and mental health of operators.Therefore,vibration and noise control are important components of engineering equipment development.Vibration in structures is usually transmitted in the form of elastic waves.The essence of vibration control is to suppress,guide and regulate the elastic waves in structures and materials.Traditional vibration control technology has limitations in the precise and efficient guidance and regulation of elastic waves.In recent years,the concept of acoustic topological insulators proposed by analogous topological phase changes in the electromagnetic and optical fields and the theory of topological insulators has provided a new solution and theoretical methods to the regulation of elastic waves.Compared with traditional defected waveguides,waveguides based on acoustic topological insulators have unique backscatter suppression and defect immunity unidirectional propagation characteristics,which can achieve accurate and efficient guidance and regulation of elastic waves.This thesis focuses on the mechanism and design issues of acoustic topological insulators guided and regulated by elastic waves in engineering beams and plate structures.The main research contents and innovations are as follows:1.A one-dimensional acoustic topological insulator based on a variable-section periodic beam structure is designed.The periodic structure theory and transfer matrix method were used to study the longitudinal and bending wave band structure and band topological characteristics of the periodic structure,respectively.By changing the cell structure parameters,it is found that the band gap formed by the second and third order energy bands has an opening-closing-opening process.With this process,the cell vibration mode is reversed,and its topological characteristics also undergo a topological phase change.By hybridizing cells with different topological characteristics to construct a one-dimensional acoustic topological insulator structure,the phenomenon of energy concentration at the topological boundary and the conditions for the existence of the topological boundary were studied.2.Aiming at two-dimensional acoustic topological insulators,combined with the theory of periodic plate elastic wave propagation and point group symmetry,a hexagonal lattice cell with triangular holes was designed.The finite element method was used to calculate the band structure and finite structure vibration propagation characteristics.Simple angular rotation can cause degeneracy and inversion of the energy band,resulting in a topological phase change.Furthermore,by studying the vibration modes corresponding to different energy bands and analogizing the one-dimensional acoustic topological insulator construction method,cells with different topological characteristics are hybridized to construct a two-dimensional acoustic topological insulator with a topological boundary state.3.According to the designed one-dimensional and two-dimensional acoustic topological insulator structure,principle samples were prepared,and the topological boundary state phenomenon of longitudinal and bending waves in the structure was verified by experiments.For the two-dimensional acoustic topological insulator structure,the vibration propagation path in the test plate is used to verify the guiding and regulating characteristics of elastic waves on the topological boundary.In this paper,aiming at the precise regulation of elastic wave,the structural mechanism and influencing factors of acoustic topological insulator are systematically analyzed.The elastic wave propagation characteristics and vibration characteristics are expounded.The key points and methods of its structure are fully understood.This paper fully reflects the cross-fusion of physics,acoustics and mechanics and can provides new ideas and methods for vibration and noise reduction of equipment.