Two-dimensional Phononic Crystal Design And Its Characteristics Investegation

The study on the sonic wave transmitting in the periodic compound materials has been paid more attention recently. Since 1992, when M. M. Sigalas and E. N. Economou testified theoretically that the sonic prohibiting band existed in the compound materials composed by Au(Pb) balls based on Al(Si), M. S. Kushwaha etc gave definitely the idea of the phononic crystal. For decades, by the special distribution and design of the material elastic constant, most researches on the 1-D,2-D and 3-D phononic crystal have been done. That the sonic wave with a special frequency can be prohibit to transmit and the sonic wave with a frequency can be made to transmit in a certain direction or located in a certain region was achieved gradually in the frequent range of sonic wave, while the researches how to control the sonic wave transmitting to make a sonic waveguide by the defect structure of phononic structure have been done theoretically and experimentally. Novel ideas and methods to control effectively noise and vibration have been given by such properties of the phononic crystal, such as designing high effective filter and novel sonic transducer. At the same time it is very useful for the theoretical research on the phononic Anderson location, defect states and interface states characteristics in the waveguide structures.Focus on the gap forming mechanism and the waveguide local characteristics of the 2-D phononic crystal, the researches have been done by the plane-wave expansion method and the plane-wave expansion method with the super cell. the main research items in this dissertation are as follows:1. The method and calculation of the plan-wave expansion have been studied detailedly by lattice periodic function Fourier expansion and Bloch law of solid method, based on elastic wave equations of perfect elastic material, and deduced the eigen equations. The eigenvalue of the equations was gained with Matlab programs. The gap structure characteristics of 2-D phononic crystal were studied and the effect on the gaps by various materials and structure parameters was analyzed.2. The coupling characteristics between defect states and point defects of 2-D phononic crystals were studied by the plane-wave expansion method composed with super cells. The point defect can seize the phonon at the defect position to make it not transmit out, just as a micro cave. But the line defect can make the sonic wave in the range of stop band to transmit along the channel just as a wave guide. For the coupling of point defects, the coupling of two point defects can make the defect mode apart in the direction of (1 0) or (0 1) and the width of the apart frequency decreased with the increasing of the distance between the two point defects while the mode field distribution near the defects will change. In the direction of (1 1), the coupling strength between local phonons is very weak for the sonic evanescent field of the local phonon decays rapidly although the distance between defects is very small.3. Based on the study of two basic defects, the dislocation is introduced into the study on the phononic crystal. The dislocation defect and homogeneity defect junction are defined. The interface transmitting modes of homogeneity dislocation defect and heterogeneity dislocation defect were studied respectively in the two cases of transverse dislocation junction and longitudinal dislocation junction. The results showed that the transverse location made the sonic wave in the range of stop band to transmit along the channel and formed a wave guide as the line defect and the longitudinal dislocation could make local mode as the point defect while the nearest three 'atoms' at both sides of the dislocation interface formed a cave.4. The gap characteristics of heterostructure in the 2-D phononic crystal have been studied. Three types of heterostructure have been constructed: heterogeneity line defect, sandwich heterostructure and RRTC( or SCTC) heterostructure. For the former heterostructures, the transmitting mode can come into being and the number and the position of the transmitting mode in the gap will change with the rotation of the scatters at the defect. When the size of the heterogeneity scatter is too small, the rotation and shape of the scatter has no effect on the sonic waveguide in the gap. For RRTC (SCTC) heterostructure, he interface transmitting mode can come into being in the case of no lattice moving because there are different types of Broff lattice at the different sides of the interface in the phononic, which enlarges the aberrance at the interface.'The investigation results mentioned above may provide the tools of theoretical analysis and numerical simulation for simulating the energy band structure of phononic crystal and designing sonic devices. It also can provide valuable method and reference for the real engineering design and application to find more potential application.