Surface Acoustic Wave Bandgaps In A Two-dimensional Piezoelectric Honeycomb Phononic Crystal

Phononic crystal is a kind of elastic medium with periodic structure,which has the characteristic of suppressing elastic wave in band gap frequency range.Piezoelectric materials are widely used in intelligent structures,such as sensors,filters and so forth,owing to their mutual conversion of electrical energy and mechanical energy.When piezoelectric materials are introduced into the phononic crystal,there will be special acoustic and elastic wave band gap,which creates a new idea for improving the design of elastic wave filtering,guided wave and acoustic functional devices.The dispersion curves,transmission characteristics and vibration displacement fields of two kinds of surface acoustic wave(SAW)phononic crystals with different scatterers under Bloch's theorem are simulated and calculated by finite element method.A brief introduction to the basic theory of phononic crystals,including inverted lattice,Brillouin zone and so on.In terms of lithium niobate piezoelectric material,the theoretical formula for simulating the band structure of SAW phononic crystal by finite element method is provided,and the detailed process and steps of calculating the band structures of a case by finite element Comsol software are introduced.The theory,model and steps for simulating the transmission loss are introduced in order to verify the correctness of the SAW band gap in the band structure.Then,a part of the scatterer is embedded in a piezoelectric substrate to construct a two-dimensional embedded SAW phononic crystal and its band gap characteristics are studied.The results reveal that compared with direct-deposited structure,embedded structure has lower and more SAW band gap and more geometric freedom to manipulate the band gap.Meanwhile,it is analyzed that both local resonance band gap and Bragg band gap exist in embedded structure.Besides,several factors affecting the band gap of SAW are explored,and it is found that the band gap characteristics,such as height and diameter,can be adjusted by changing the geometric parameters of the scatterer.The piezoelectric effect has barely effect on the band gap of SAW,but the band gap gradually decreases until it disappears as the unit cell lattice constant increases.The density and elastic modulus of the scatterer materials are the main factors influencing the band gap of the SAW.Finally,a composite phononic crystal is formed by adding an epoxy with a smaller elastic modulus to the bottom of the pure elastic material scatterer in order to more effectively regulate the band gap characteristics of SAWs.It is found that composite phononic crystal,compared with pure scatterer phononic crystal,can effectively reduce the complete band gap of SAW and generate multiple directional band gaps,but the transmission rate of SAW in band gap will be weakened according to the transmission characteristics.Besides,theformation mechanism of the band gap is discussed by analyzing the eigen displacement field of the band gap edge frequency.Furthermore,the adjustment of the geometry size of the scatterer to the complete and directional band gap of SAW is researched,and there is a wide directional band gap.The influence of lattice form on the band gap of SAW is analyzed,and it is concluded that it has no influence on the local resonance band gap in lower frequency,but has great influence on Bragg band gap in higher frequency band.The research content provides a reference for regulating the band gap characteristics of micron-scale SAW phononic crystals and a new idea for the design of micro-phononic crystals.