Research On Bandgap Characteristics Of Local Resonant Phononic Crystal Double-layer Beam Structure

With the urgent need for vibration and noise reduction in industrial products,phononic crystals have attracted wide attention of scholars at home and abroad with the existence of band gaps,which can attenuate elastic waves.The discovery of local resonant phononic crystals makes it possible to suppress low-frequency vibration.And double-layer beam structure has a better performance than the single-vibrator beam structure.Therefore,it is necessary to study the band gap characteristics of the local resonant phononic crystal double-layer beam structure.Based on the simplified models of Euler beam and Timoshenko beam,the effectiveness of plane wave expansion(PWE)method in calculating the bandgap of phononic crystal Euler beam is verified,and the rationality of Euler beam replacing Timoshenko beam model at low frequency is pointed out.The similarities and differences of band structure between multi-vibrator Euler beam and single-vibrator beam are compared,the band gap formation mechanism of multi-vibrator beam is revealed,and the formulas for calculating the initial and cut-off frequencies are obtained.Based on the analysis of the bandgap characteristics of single-vibrator beam,a simplified model of double-layer Euler beam is established,and the eigen equation of the bending vibration motion is deduced.The bandgap formation mechanism of double-layer phononic crystal is revealed according to the structure diagram of bending vibration band and the natural mode of the unit cell obtained by finite element simulation.The regulation law of the bandgap is revealed,and formulas for calculating initial and cut-off frequencies of the double-layer beam bandgap are obtained.The comparison indicates the advantages of doublelayer beam in vibration reduction performance over single-layer beam structures.Finally,based on COMSOL Multiphysics software,the band gap characteristics of attached phononic crystal doublelayer beams are studied,and the corresponding natural vibration modes of each frequency band are studied.It is pointed out that the initial and cut-off frequencies of band gap are determined by the antisymmetric bending vibration mode and the symmetric bending vibration mode respectively.The influences of structural parameters,geometric parameters and material parameters on the band structure are also studied,and theoretical explanation of the influence law are also given based on the springmass model.