Study On Low-frequency Bandgap Characteristics And Acoustic Confinement And Waveguides Of Defect States For A Two-dimensional Cross-like Phononic Crystal

Phononic crystal is a kind of synthetic periodic composite structure,which is generally represented by a periodic array formed by the addition of two or more material components.This periodic arrangement structure can suppress and modulate elastic waves at certain wavelengths.This physical phenomenon is called the bandgap of phononic crystals.Bandgap characteristics show that phononic crystals have potential applications in manufacturing(precision manufacturing,etc.)and acoustic equipment(vibration isolators,filters,etc.).Focusing on the broad application prospect of the bandgap characteristics of phononic crystals,a cross-like phononic crystal structure with hollow scatterers is proposed in this thesis,and its bandgap and defect state characteristics are studied.In this thesis,firstly,a two-dimensional cross-like phononic crystal plate with hollow scatterers is designed,and its low-frequency bandgap characteristics are studied by finite element method.The results show that there are several wide low-frequency complete band gaps in the energy band structure.Compared with the three evolution models of cross scatterers stacked on a complete quadrilateral matrix,cross scatterers stacked on a cross matrix and embedded in a cross-like matrix,the newly designed embedded cross-like hollow scatterer model can obtain a wider low-frequency bandgap.In the range of 1000 Hz,the total bandgap width is increased by nearly 10 times,the first complete bandgap is increased by nearly 20 times,and the starting frequency is lower.By observing and analyzing the intrinsic vibration modes of the bandgap edges,the generation and broadening mechanism of the bandgaps are clarified.In addition,the effects of geometric parameters,translations,and rotations of the structure on the energy band structure are also discussed.The results show that the low-frequency band in the energy band structure is not greatly affected by translations and rotations,but the translations and rotations have a specific sensitivity to the high-frequency bands.The main reason is that these changes lead to significant changes in the high-frequency local modes.Considering the influence of the structural parameters of the phononic crystal on the band structure,another significant factor affecting the bandgap of the phononic crystal is the construction material used.Therefore,the acoustic confinement and waveguides in the phononic crystals of two-dimensional cross-like hollow scatterers with material defects are studied theoretically.The material defect states are established by replacing a single scatterer or a row of scatterers in a perfect phononic crystal with scatterers of different materials.The energy band structure of phononic crystals is studied by finite element method combined with supercell technique.After the material defects are introduced into the perfect phononic crystals,the defect states and defect bands appear,and the elastic waves with specific frequencies propagate locally at the point defects or along the line,respectively.The intrinsic vibration modes at the defects are calculated,and the acoustic constraints and waveguides in the material defect phononic crystals are intuitively explained.On this basis,the effects of material parameters on the point defect states and waveguides are further discussed.The numerical results show that the material parameters of defects can effectively adjust the position and number of defect states.In order to realize the active control of the band structure of phononic crystal,the piezoelectric material is introduced into the newly designed periodic structure to form a new intelligent phononic crystal model,and its band structure characteristics are studied.The results show that the tunability of the bandgap can be realized by the piezoelectric effect and the closed-circuit boundary condition.By calculating the intrinsic vibration mode at the tunable frequency band,it is found that the vibration mode shows a compression expansion mode,which is a typical piezoelectric adjustable mode.On this basis,a tunable point defect mode based on the piezoelectric phononic crystal is proposed.a passband based on local resonance is generated in the whole bandgap by modulating the closed-circuit boundary conditions.the vibration modes at the passband are represented by two coupled compression resonance modes,which can be used to realize waveguides.Therefore,the two-dimensional phononic crystal waveguides composed of closed-circuit electrical boundary defects are studied.the results show that the electrical boundary defects can lead to multiple defect bands in the complete bandgap,and by adjusting the external closed-circuit conditions and spatial distribution,the working frequency and shape of the waveguide can be adjusted at the same time.The cross-like hollow scatterer phononic crystal model designed in this thesis has a strong low-frequency bandgap and light self-mass while having a wide low-frequency bandgap.This excellent model property can not only save the cost but also benefit the application in the engineering field.The position and width of the defect bands can be controlled by introducing material defects,which can provide a theoretical basis for the manufacture and research of filter elements and acoustic waveguide equipment.The piezoelectric defect model has good tunability and can provide direction for the design of tunable elastic wave sensors and frequency filter structures.