Calculations And Analysis Of Band Gap Properties Of Phononic Crystal Plates In Low Frequencies

The phononic crystal is a new type of functional material which is formed by periodic distributions of elastic constants or densities. Band gap characteristics can be found in phononic crystals. This means that elastic waves within a certain frequency range can not spread but other waves in other frequency ranges can get through. The frequency range which prevents the wave propagation is called as phononic crystal band gap. The band gap characteristics of phononic crystals lead to the potential applications of PC (phononic crystal) in the fields of vibration reductions and noise controls.In this paper, locally resonant single side column plate phononic crystals are firstly studied. Based on the finite element method, the material properties of the scatterer and the effect of the plate shape on the band gap characteristics of the locally resonant single side column plate phononic crystals are calculated and analyzed by use of the multi-physics software COMSOL, and the physical mechanism of the changes of band gap characteristics of phononic crystals is explained by calculating and comparing the single cell displacement modes of phononic crystals. Based on the analysis on the effects of the density, the elastic modulus, the poisson ratio and the shape of the scatterer, it is shown that the density, the elastic modulus and the shape of the scatterer can obviously affect the band gaps of phononic crystals by changing the locally resonant states of them. For further investigations on the vibration reductions of the designed phononic crystals in low frequencies, four cases with different low frequency vibration characteristics are established. From the comparison, the best case can be obtained.The holes in the materials can lead to the improvement of band gap properties in some cases. So the band gaps of the locally resonant single side column plate phononic crystals with holes are further designed and studied. Two cases of low band gap characteristics are computed in current work—the one kind of locally resonant single side column plate phononic crystals with holes in the scatterers and the other kind with holes in the matrix. The results show that only the locally resonant single side column plate phononic crystals have larger holes in scatterers can holes have obviously negative impacts on band gap characteristics. Then displacement modes of single cells of the locally resonant single side column plate phononic crystals with holes are computed and discussed. Based on the simple spring model, the physical mechanism of effects of holes on band gaps are given.In this article, the study of low frequency band gap properties of different configurations of photonic crystal plates will provide a reference for the applications of precision structure vibration reductions and noise controls in practical engineering.