Study On Multi-degree-of-freedom Control Of Topological States Of Phononic Crystals

In recent years,phononic crystals and acoustic topological states have been the research hotspots in acoustics field.In phononic crystals,the topological properties of the energy band are closely related to the geometric structure.Commonly,once the geometric structure of a phononic crystal is determined in the manufacturing process,it cannot be easily changed when it is applied,which limits the actual application of acoustic topological state.Generally,it is desirable that phononic crystals have rich and controllable structural parameters for obtaining rich topological properties,in order to meet different application scenarios.Therefore,two methods to increase the adjustable parameters of phononic crystal are proposed in this work,and two phononic crystals with corresponding structures are studied.With the help of the finite element analysis software COMSOL,the acoustic topological states of phononic crystals are detailedly studied.The main contents and conclusions are as follows:(1)A kind of two-dimensional phononic crystal composed of core-shell cylinder is proposed.The scatterer of this phononic crystal is composed of an outer rubber cylinder and a steel core cylinder,and the host is water.Two independent degrees of freedom are introduced by adjusting the offset distance and offset angle of the center of the steel cylinder in the unit cell.Through numerical calculation,the vertical relation between the wave vector direction of the degenerate point of the Dirac cone and the symmetry axis of the unit cell in this system is found.This law has guiding significance for exploring Dirac cones in low symmetric systems.(2)A kind of two-dimensional phononic crystal composed of double layers of rod is proposed.The scatterer of this phononic crystal is composed of upper and lower rigid rods,and separated by a rigid plate in the middle,the host is air.Four independent degrees of freedom are introduced by adjusting the radius of the upper and lower cylinders in the unit cell.Through numerical calculation,the eightfold degenerate Dirac cone is found.And the degeneracy of Dirac cones can be partially or completely relieved under different parameters.Therefore,the introduction of the bilayer structure has practical significance for increasing the controllable parameters of the system and controlling the acoustic topological states.(3)For the above two structures,the topological properties of the energy bands of the unit cells and the dispersion curves of the topological edge states are studied.Different forms of acoustic interfaces are established,and the propagations of acoustic waves of edge states are studied.The results consistently show that the transmission energy of acoustic waves mainly concentrate on the propagation path,the acoustic waves can bypass defects and maintain unidirectional propagation.This suggests that the acoustic waves in the frequency range of edge states are topologically protected and have strong robustness and have ability to suppress the backscattering.