Tunable Band Gaps And Topological Edge States For Bulk Waves In Solid Phononic Crystals

With the increasing demand for high precision parts and protection of workers,the problem of vibration and noise in modern industrial manufacturing is becoming more and more prominent.The band gaps characteristic of phononic crystal has good control effects on elastic waves in specific frequency band and has great application prospect in industry and life.In addition,topological concepts have been widely used in artificial periodic composites in recent years,topological phononic crystal have shown their unprecedented edge states and other new characteristics,opening up a new research direction of phonon crystals and their potential application value in quantum communication and other aspects.However,the band structure of phononic crystal is often fixed by the determination of the model structure and the constituent materials.To achieve the tunability of frequency range,it is usually necessary to design complex periodic models with variable structure or replaceable materials.This leads to the limitation of phononic crystals in practical applications.In order to enhance the functionality and facilitation of elastic waves control in engineering application,the band tunability of phononic crystals is discussed in this paper.Firstly,the effects of scatterer materials,filling rate and lattice constant on the forbidden band frequency range are discussed.The effects of temperature and magnetic field on band regulation is also discussed.Finally,the active tunability of temperature on the frequency of bandgaps and topological edge states of topological phononic crystals is discussed.The main content of this paper is as follows:(1)The two-component ideal phononic crystal model is established,and the band structures of P-waves and SH-waves in 1D phononic crystal with different scatterer materials and filling rates are simulated.Meanwhile,the band structures of in-plane waves and out-plane waves in 2D phononic crystals with different lattice constants are also calculated.The effects of scatterer materials,filling rates and lattice constant on the tunability of band gap frequency are discussed.(2)Based on the change of the elastic modulus of the materials,the active tunability of temperature to the corresponding elastic bandgap in the same model is discussed.In addition,the adjustment of band structures by external static magnetic field is discussed when ferromagnet is used as an element material.(3)A 2D two-component phononic crystal model of triangular lattice is established,and the quadruple band degeneracy is obtained at the high symmetry point of irreducible Brillouin zone by band folding method.Topological band gaps are obtained by adjusting the relative position of the scatterers to break the lattice symmetry.The active regulation of temperature to the topological band-gaps frequency is realized by using the thermal sensitivity of materials.(4)The supercell model of phononic crystal was established,and the topological edge states of phononic crystal were obtained.The active frequency tunability of the topologically protected edge states for bulk waves is realized by applying a thermal field.Finally,a model with arbitrary preset path is constructed,in which the robust propagation of bulk waves is demonstrated within different frequency bands.