Research On Topological Coener State Of Two-Dimensional Acoustic Metamaterials Based On Parametric Orthogonal Control

In the 1880s,the quantum Hall effect was discovered in electronic systems,marking the beginning of the phase of matter topology.Recently,high-order topological insulators have appeared in people’s field of vision with new body-edge correspondences,and have new topological invariants,such as body polarization,Berry phase,and so on.The appearance of highorder topological insulators has broadened our understanding of the topological stage of matter in the field of condensed matter physics.Compared with traditional insulators(first-order),higher-order topological insulators are topologically protected at the lower dimensional boundary of the system.This paper constructs a two-dimensional square acoustic metamaterial structure topologically characterized by winding number.The number of windings refers to the number of times the spiral or vortex formed in the metamaterial structure such as air or water flows around a certain point.In this article,the value of the number of windings is related to the geometric structure of the metamaterial.By adjusting the configuration of the number of windings,a two-dimensional acoustic metamaterial with two types of topological corner states was designed,and the relationship between the two types of topological angle states and the number of windings was explored in detail,and the relationship between the two types of corner states was realized.Predictability.The research work in this paper provides a good idea for the subsequent expansion to three-dimensional high-order topological states,and provides new methods for energy recovery,acoustic information transmission,and acoustic sensor design.The research content of this article mainly includes the following aspects:(1)In this paper,a two-dimensional acoustic metamaterial structure that can realize two types of topological corner states is designed.The configuration of the number of windings is changed by adjusting the diameter of the transverse connecting pipes in the metamaterial cell,so as to design Atype(winding number is v1=v2=v3=v4=1),B-type(winding number is v1=0;v2=v3=v4=1),and C-type(winding number is v1=v3=0;v2=v4=1)The structure of an acoustic metamaterial.Calculate the characteristic frequencies and characteristic modes of the three-dimensional complete acoustic metamaterials of A-type,B-type,and C-type.It can be concluded that there are four first-class topological corner states observed in the A-type acoustic metamaterial,which are located on the four corners of the A-type acoustic metamaterial structure;two first-class corner states are observed in the Btype acoustic metamaterial;a first-class topological corner state and a second-class topological angular state are observed in the C-type acoustic metamaterial.(2)This article discusses the relationship between two types of topological corner states and different winding number configurations is discussed.On the basis of the second chapter,the thickness of the 8 connecting pipes was orthogonally designed,and an orthogonal table was developed.According to the orthogonal table,the configuration of the corresponding winding number is changed,and a total of 16 combinations are obtained.The characteristic frequencies and sound pressure field distribution of all 16 acoustic metamaterials are calculated and analyzed.Among them,a class of topological corner states is observed in 3 acoustic metamaterials(No.3,No.4,and No.10 acoustic metamaterials).The configuration relationship between the two types of topological corner states and the number of windings in the six acoustic metamaterials(A-type,B-type,C-type,No.3,No.4,and No.10)is analyzed in detail.Among them,the first type of topological corner state only needs a pair of adjacent winding numbers equal to 1,while the second type of topological corner state requires a pair of adjacent winding numbers equal to 1,and the other pair is equal to 0.(3)In this paper,the transmission characteristics of two two-dimensional acoustic metamaterials,A-type C-type,are simulated and verified by experiments.Use 3D printing technology to make experimental models,simulate and verify the transmission efficiency of the first-order edge states and the first-class topological corner states in the A-type coustic metamaterials,and verify the first-order and second-class corner states in the C-type coustic metamaterials The transmission efficiency of the topological corner state is simulated and verified by experiments.The results show that the transmission efficiency of the first-order edge states,the first-class topological corner states and the second-class topological corner states all maintain a high level,and they have good robustness to certain defects.The work in this paper uses a relatively simple metamaterial structure to realize two types of topological corner states in the acoustic field for the first time.A new mechanism,winding number measurement,can be used to predict the corner state in the field of acoustics,which has rich theoretical significance for exploring new high-order topological insulators and broadening the road.It provides more possibilities for the realization of acoustic energy recovery,acoustic sensor measurement and other applications.