Optimal Design Of Phononic Crystal Microstructure Considering Defects

Phononic crystal is a kind of artificial periodic structure material with phononic band gap.The acoustic waves with frequencies in the band gap cannot propagate inside the phononic crystal.This kind of function which can attenuate the acoustic waves has a wide application prospect in the engineering fields of vibration reduction,noise reduction,sound insulation and so on.When the periodic structure of the phononic crystal is destroyed and defects are introduced,the propagation direction and range of sound wave can be controlled artificially.Therefore,the width of band gap and the position of defect band can be adjusted by designing the defect structure.This opens up a new way for sound wave to filter,collect and conduct.This thesis use the finite element method based on Abaqus to calculate the energy band structure of the phononic crystal,and optimizes and designs the structure of the phononic crystal,so as to regulate the band gap and defect state.The main work includes:1.By establishing two phononic crystal unit cell models with the same grid of real and imaginary parts,we can solve the problem that complex periodic boundary conditions cannot be applied to the unit cell in Abaqus.Use Python language to call Abaqus finite element software to perform parametric modeling of the band structure calculation of phononic crystals,and verify the accuracy of the calculation results of the program in this thesis through comparison.2.By appropriately distributing the material of the phononic crystal unit cell,then using a superellipse to fit the shape of the scatterer,and then combined with the Isight optimization platform,the maximum band gaps of two-dimensional solid-solid phononic crystals of different orders can be opened and optimized.3.Use supercell technology to introduce point defects in phononic crystals with the largest band gap of different orders,and optimize the defect structure parameters to adjust and control the position of the defect band frequency in the band gap,then discuss the modal distribution of the structure corresponding to the frequency of the defect zone and the efficiency and state of acoustic wave transmission respectively.The results show that the point defect phononic crystal obtained by the optimized design has acoustic local effect at the desired defect band frequency.4.Discuss the change law of the band structure under the change of the inner radius when the scatterers of phononic crystals are tubulars of different shapes.The results show that this phononic crystal has a certain range of passband frequencies in the band gap.Take the tubular phononic crystal as the line defect,combined with the perfect phononic crystal,discuss the influence of changing the inner radius of the line defect on the energy band structure.The results show that the band gap of the combined phononic crystal is controlled by the band gap of the perfect phononic crystal,and there are different ranges of waveguide states in the band structure.Establish a finite element model of sound wave propagation for the investigated structure,and we can obtain a waveguide structure in which acoustic waves of different frequency ranges propagate along line defects.