The Optimization Of Band Gaps In Two-dimension Phononic Crystals

In recent years, more and more works have been devoted to the study of the phononic crystals, especially for the phononic band gaps. It is not only because the phononic crystals are expected to be used as sound insulation, sound filter and waveguide materials, but also there are many physical contents to reveal, just as the existence of the band gaps is significant for us to better understand the Anderson localization of sound and vibrations in composite media. All the above properties and applications of the phononic crystals are based on the characteristics of the phononic band gaps. Therefore, how to optimizing the gap is one of the important problems in the field of phononic crystals.In this dissertation, using the plane wave method we have numerically calculated the band structures of a two-dimensional phononic crystal with elliptic-cylinder or cylinder scatters squarely and rectangularly arranged in the matrix, respectively. The case of the elliptic-cylinder scatters has been investigated scarcely. Comparing with the band structures of the phononic crystal with the cylinder, we find that larger band gaps can be obtained by taking elliptic cylinders as scatters. Moreover, for the phononic crystal consisting of the elliptic-cylinder scatters, the band gap of the rectangular arrangement is much wider than that of the square arrangement under the given volume filling ratio. Because the largest band-gap can be obtain when the structure symmetry of the scatters is consistent with the symmetry of the crystal lattice.Then, we have proposed a model of a one-dimension phononic crystal with quasi-periodical structure, the layer thickness of which can be changed gradually. The transmission coefficients of the elastic waves through the quasi-periodical phononic crystal have been numerically calculated with the eigen-mode match theory method, and compared with the transmission coefficients of the periodical structure. The results show that for the quasi-periodical systems the frequency position of the band-gaps will be moving, and the shapes of the transmission spectra will be different. The localized resonant modes present in the band gap of the quasi-periodical systems. It is because the effect of the quasi-periodical structure is just like that of the defect in crystals. The numerical results also show that the width and the frequency position of the band gap can be adjusted by utilizing the special structure of the quasi-periodical arrangement. This study is benefit to the fabrication of the acoustic or elastic wave filters.At last, we have also designed a step-type phononic crystal, and computed the reflection coefficients of the elastic waves on the surface to the phononic crystal. Then elastic wave pass this phononic crystal cause to diffraction. The reflection spectra behave as the periodic-like oscillation,and the more larger reflection coefficient can be attained. The study of these properties can be used to fabricate a reflector of elastic waves.