Study On Band Gap And Defect State Of Two - Dimensional Liquid Phononic Crystals

In recent years, there has been growing interest in propagation of acoustic orelastic wave in periodic elastic composite materials, known as phononic crystals. Atpresent, the scatterer is mostly solid on research of phononic crystals. In this paper,we choose the hollow cylinder as scatter, and use an improved plane expansionmethod combine with the supercell technique to calculate the band gaps. In thisdissertation, theoretical investigation of (1) band gaps in two dimensional liquidphononic crystal of hollow cylinder with square lattice,(2) one point defect states anddouble point defects states in two dimensional liquid phononic crystal,(3) lineardefect states in two dimensional liquid phononic crystals.Firstly, on the basis of the improved PWE method combined with the supercelltechnique, the band gaps of the two dimensional phononic crystals of mercury andwater are calculated. This paper deals with both hollow mercury cylinder as scattererand hollow water cylinder as scatterer，which are arranged in a square lattice, thedependence of the band gaps on filling fraction were discussed in detail, and comparewith structure of solid scatter. The results show, when solid water cylinder transformsinto hollow cylinder, the band gaps reduce gradually with filling fraction reduce, andthe new band gaps appear. It is thus clear that the solid scatterer produce absoluteband gap of low frequency easier than hollow scatterer, and the hollow scatterproduce absolute bang gap of high frequency easier than solid scatterer forwater-mercury system, and the same phenomenon has been observed inmercury-water system.Secondly, this paper researches the cavity point defect consist of mercury andwater. The results show that the defect states almost do not change with filing fraction.And this dissertation calculates some point defect pressure to analyze the degree oflocation of defect frequency. We study couplings of double-cavity in two dimensionalphononic crystals, we notice that the double-cavities of the different kinds and thedistance of the two cavities in one supercell is same have the identical band structure, this is exactly the reflection of the latticeperiodicity. This paper also calculates thepressure field of different double-cavities modes to analyze the degree of localization.Finely, the linear defect states in two dimensional phononic crystals consist ofmercury and water have been researched, for some shapes of those linear defect states,similar surface wave has been found while some defect frequencies propagate in thisstructure.