Band Gap Coupling And Waveguide Tunability Of Two-dimensional Phononic Crystals

The tunable acoustic transmission has always been a holt topic in the field of acoustic.It may provide many more flexible acoustic wave manipulation technologies for acoustic engineering,communication engineering,national defense engineering and other fields.As a kind of artificial acoustic metamaterials,phononic crystal has excellent control characteristics for the propagation of acoustic waves due to its periodically arranged artificial atomic structure.It has broad potential application prospects in acoustic isolation,acoustic waveguide,acoustic filtering,acoustic signal sensing,etc.Among them,the acoustic waves with low-frequency is difficult to modulate due to its long wavelength.Realizing high-efficiency control of lowfrequency acoustic waves through a reasonably designed phononic crystal structure has become a hot issue in the field of acoustics in recent years.In this thesis,a two-dimensional spherical phononic crystal plate structure and a twodimensional spherical composite cylindrical surface wave phononic crystal structure with low frequency complete band gaps are designed for the optimization of the low frequency band gap and its formation mechanism.The dispersion relation,transmission loss spectrum and displacement vector field of the designed structures are calculated by finite element method combined with Bloch theorem.The formation mechanism of the ultra-wide low band gap of the two phononic crystal models is analyzed by investigating the displacement vector field.On this basis,the pressure,pre-strain and temperature are introduced as the applied load conditions to explore the adjustable characteristics of the band gap.In addition,the acoustic waveguide characteristics of the waveguide structures are explored via introducing linear defects into the supercell structure to form a composite waveguide.The main research contents are as follows:Based on the study of the band gap characteristics of plate wave,a two-dimensional coated spherical phononic crystal model is designed in this thesis,which consists of a lead sphere coated with silicone rubber embedded in an epoxy spherical shell with four silicone rubber short connecting plates.The results of finite element method show that there are multiple band gaps in the middle and low frequency range,and exist the degenerate-like states between the first and second band gaps.The separation of the degenerate-like modes of the torsional resonance,via reducing the structural symmetry,can open newly band gap.Specially,a torsional resonance equivalent spring mass model is built and the prediction formula of the torsional resonance frequency is proposed,based on the analysis of the torsional resonance mode,and the correctness of the proposed equivalent model and formula is verified.According to the coupling theory of band gap,the first band gap and second band gap are merged into a new wider band gap by replacing the silicon rubber coating with an aluminum coating.Based on this,the tungsten sphere is used to replace the coated sphere,which formed a coupled phonon crystal model.The analysis shows that this coupled model has an ultra-wide band gap covering the low and medium frequency range,and the multiple resonance units are the direct cause of the existence of multiple pass bands.In addition,the influence of external high pressure and prestrain on the band structure is considered,the linear defects are introduced by applying axial pre-strain on some of the element base plates in the supercell structure.The real-time adjustment of the waveguide path is realized based on the real-time adjustment characteristics of the band gap which caused by the tensile pre-strain along the z-axis.Based on the study of band gap characteristics of surface waves,a surface wave phononic crystal structure consisted of a composite column deposited on lithium niobate substrate is designed,which column composed of a nickel ball and an epoxy resin cushion.The results show that compared with the existing inverted conical surface wave phonon crystal structure with the same lattice constant,the designed structure can open a wider complete band gap of surface acoustic wave at a lower frequency range.With the increase of the radius of composite column,a confined cavity mode is formed between the hard boundaries of the nickel sphere and piezoelectric substrate,and there is energy coupling and vibration mode inheritance between adjacent high-order band gaps.In addition,the active control of band gap can be realized by introducing the temperature field,and the band gap frequency range moves to low frequency with the increase of temperature.Via increasing the number of layers of the composite cylinder,the multi-vibrator structure and traveling wave generate multipole resonance coupling,and the complete band gap can be opened between high-order energy bands.Finally,a bipartite defect state structure is introduced into the surface wave phononic crystal supercell to explore its waveguide characteristics,the results prove that the waveguide structure can effectively guide the acoustic waves of the defect structure passband frequency.The research results of this thesis are able to provide a reliable theoretical basis for the design and optimization of a two-dimensional phononic crystal plate with a low-frequency wide band gap,and can provide support for the design of low-frequency noise and vibration isolators and active tunable filters.It can also provide a reference for the design of micron-level surface wave phononic crystal structure that realizes active acoustic signal transmission,acquisition and real-time guidance in the frequency range below 100 MHz.