Study On Tunable Complete Bandgaps In A Novel Two-dimensional Three-component Piezoelectric Phononic Crystal Slab

Phononic crystal is the periodic elastic medium with band gaps.It can act as a filter,vibration or sound isolation,waveguide and so on.Introducing piezoelectric materials into the pure elastic phononic crystals and taking the mechanical-electrical coupling into account,the piezoelectric phononic crystals with superior behaviors are obtained.Because of their new physical properties and many potential applications,the study on piezoelectric phononic crystals has received increasing attention.This dissertation has designed a new type of two-dimensional three-component phononic crystal slab possessing a low frequency range of complete band gap.The band structures,transmission loss spectrum and displacement field are studied using the finite element method in conjunction with the Bloch theorem.The low frequencies band gap characteristics of the two-dimensional phononic crystal slab consisting of pure elastic materials are studied.In addition,in order to overcome the deficiencies of passive structure vibration reduction technology,the piezoelectric materials are introduced into the designed periodic structures to form an intelligent phononic crystal slab,and the active control of band gap and acoustic waveguides are further studied.The dissertation firstly theoretically designed a novel two-dimensional phononic crystal slab composed of lead cylindrical stub with rubber coatings connected by epoxy thin bars,and studied the low band gap characteristics of the structure.The results show: in contrast to the traditional locally resonant phononic crystal slab without connection-bars structure,the present structures can obtain wider complete band gap in a extremely low frequency range and an increased quantity of complete band gaps at higher frequencies.The first complete band gap has fewer influencing factors,the boundary frequency of band gap is just influenced by the corresponding vibrator mass and spring equivalent stiffness.There is no vibration coupling between the lead stub and the connecting bars at the boundary frequency of the first band gap.The research shows that the coexistence of the Bragg band gap and locally resonant band gap in the band structure,the locally resonant band gap appears in the low frequency range,the Bragg band gap appears in the high frequency range.The advantages of the low-frequency local resonance band gap and the high-frequency Bragg scattering band gap are combined,which could endow the phononic crystal with a wider band gap.Furthermore,the studies show that by adjusting the geometric parameters of the phononic crystal slab,such as the radius and heights of the lead stub,the position and width of the band gap can be effectively regulated.The controlling of the BGs can be explained by the introduced effective mass of the PCs and the strain energy.The research results can provide the basis for the research of phononic crystals with low frequency wide band gaps.To investigate the active control of the band gap,the paper next introduces thepiezoelectric material into the newly designed periodic structure to form a new type of intelligent phononic crystal slab.Numerical results show that the frequency of the first complete band gap of the new designed phononic crystal slab is lower and the band width was enlarged by a factor of 5 compared to the traditional binary phononic crystal.With different electrical boundary conditions imposed on the upper and lower surfaces of the piezoelectric inclusions,a series of complete band gaps can be controlled actively.The geometric parameters of the piezoelectric scatterer have a great influence on the band structure.By adjusting the radius and height of the scatterer,the gap width of the first complete band gap can be enlarged.Piezoelectric effect on the band structure has a great impact,a comparative analysis is implemented and we can find that the piezoelectric effects benefit the expansion and generation of the complete band gaps.Furthermore,according to the tunability of the bandgaps,the switchable piezoelectric phononic crystal slab waveguides are analyzed.The study shows that the elastic waves energy flows can be limited by changing the applied electrical boundary conditions.In summary,the contents of this dissertation can provide a reliable basis for the study of phononic crystals with wide band gaps,and this study can provide a model reference for designing phononic crystal structures of active controlled transmission,guiding,switching,and emission for slab waves.