Study On The Effect Of Oblique Incidence On The Band Gap Of Two - Dimensional 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 scatter is mostly solid on research of phononic crystals. In this paper, wechose two kinds of materials as scatters, and use an improved plane expansion methodto calculate the band gaps. In this dissertation, theoretical investigation of (1) bandgaps in two dimensional liquid phononic crystals of solid square column and cylinderwith square lattice,(2) in-of-plane propagation of elastic waves in three-componenttwo-dimensional phononic band-gaps materials,(3) out-of-plane propagation ofelastic waves in three-component two-dimensional phononic band-gaps materials.First, based on the improved PWE method, the band gaps of two dimensionalphononic crystals of solid water or tetrachloromethane embedded in a mercury hostare calculated. In this paper, we deal with both water cylinder as scatters andtetrachloromethane cylinder as scatters, which are arranged in a square lattice. Theresults show that the bad gaps reduce gradually with the filling fraction increasing,and new band gaps appear. It is thus clear that the lowest band gap gradually reducewith the normalized-wave-vector zincrease. At the same time, the width of thelow-frequency band gap is seen to increase quasimonotonically from zero with zincreasing.Secondly, in this paper we research the in-of-plane propagation of elastic wavesin three-component two-dimensional phononic band-gaps materials, which composedas tetrachloromethaneco coated water or water coated tetrachloromethane embeddedin a mercury host. And we calculate the influence of filling fraction and the shape ofscatters on band gaps. In water-tetrachloromethaneco/mercury system, no matter thescattering cross section is circular or square, large width of band gaps are easy toobtain with the same filling fraction, which is due to the higher symmetry degree ofcylinder, the more intensely Bragg scattering of sound waves. However, the first gapis always stable, etrachloromethaneco-water/mercury system is the same as water-tetrachloromethaneco/mercury system. The difference between those systems is therelative width of band gaps greatly influenced by insert material filling fraction, andappears saddle points.Finally, out-of-plane propagation of elastic waves in three-component two-dimensional phononic band-gaps materials has been studied， also under therotation operation for square column. An interesting feature of phononic bandstructure is that scattering cross section is both circular and square, the frequencies ofthe lower and upper limits of those gaps shift to higher values as zincreases. Also,it is easier to obtain lager band gap width for square and to influence by zforcircular. At certain oblique incidence, the relative width of the lowest complete bandgaps for square section is higher than ones for circular. And the width of thelow-frequency band gap is seen to increase quasimonotonically from zero with zincreasing.In a word, for the same materials, when the way of combination and the shapeare not same, obtained position, width and distribution of band gaps will be largedifference. By changing the size, form of combination，the shape of scatters androtation angle for the square column can control the frequency of the band gaps.Those behaviors provide controlling the band gap with the size, form of combinationand the shape of scatters. Consequently, the frequency filtering characteristics oftwo-dimensional phononic structures can be modified by varying z. This propertycan be useful for technological applications of periodic structures, but also impliesthat accurate alignment of the wave vector of the elastic waves is required.