Study Of Vibration Attenuation Properties And Optimal Design Of Phononic Crystals

Phononic structures consist of phononic crystal cells with periodic spatial arrangement. Phononic crystals feature band gap characteristic. Elastic waves with the frequencies in some certain frequency regime cannot propagate through phononic crystals, while those with the frequencies out of the frequency regime can propagate. The frequency regime is called the band gap of phononic crystal. Due to the band gap characteristic, phononic crystals is promising in vibration reduction.Firstly, some improvement designs are proposed to some cylinder-shaped pipe and sandwich panel structures to achieve band gap characteristic in this dissertation. The results show that the pipe-shaped locally resonant phononic crystals open up relatively wide and low3D polarization band gaps. Elasticity modulus of the middle layer material and material density of the scatterer are of the greatest importance to the band gap characteristic of crystal cells. Band gap cannot be generated with too small or big elasticity modulus of the middle layer material, or with too small material density of the scatterer. The relative band gap increases and then decreases with the rising elasticity modulus of the middle layer material under a big enough material density of the scatterer. For sandwich plate structures, wrapped layers on the web members and the metal masses inside the quadrilateral honeycomb cores becomes the scatterer changing the transmission pattern of elastic waves, thus helping to generate band gap characteristic.Secondly, band gap characteristic of stacking composite material like nacre is also studied and the material is turned out to boast relatively wide and low band gap. The wide elastic wave attenuation region derives from the material’s affluent band gap structure, in which several flat bands emerge in high orders of the dispersion curves, resulting in some continuous bands. Enlightened by this, a kind of phononic crystal with stacked square columns is designed with excellent band gap characteristic to make elastic waves with frequencies in the band gap regime attenuated to a large extent and achieve wonderful vibration reduction effect. The main design parameters influencing band gap characteristic of the phononic crystal are material density of the out layer and elasticity modulus of the middle layer material. The phononic structure with only one period of phononic cell can achieve good vibration reduction effect which can be better pursued by more periods. Finally, topology optimization and design of2D phononic crystal cell is studied, with the method of moving asymptotes (MMA), genetic algorithm (GA) and the combination of both of them respectively. The combination method can avoid the problem of initial solution choosing and improve computational efficiency. The key factors for the generation of band gap are the material filling rate, the concentration degree of the filling material and the symmetry of the topology configuration. Relatively large band gaps of optimal topology configurations are achieved by large relative elasticity modulus and density, while low central frequencies of band gaps are achieved by small relative elasticity modulus and big relative density. The optimal topology configurations are affected by material parameters as well.The design and optimization of phononic crystals in this dissertation may provide reference for novel design of vibration reduction structures in low frequencies to some extent.The dissertation was supported by National Natural Science Foundation of China (11172057,11232003) and National Basic Research Program of China (2011CB013401).