Characteristics Of The Waveguide And Localization In A Two-dimensional Phononic Crystal

In recent years, the researching of phononic crystals made great progress. There areapplication values in many ways because of its superiority. For example, reducing noise,controlling frequency, new devices, and negative refraction et al. Now, national experts andscholars are tackling the studies of theoretical and experimental, and it provides strongprotection to service mankind at an early date.Focus on the waveguide local characteristics of the2-D phononic crystal, main resultsare as follows:1. We explored the researching method of a2-D phononic crystal, and introduced thebasic knowledge of square lattice. We got the band gap structure by Matlab, studied andanalyzed it. It showed that the band gap structure changed with filling fraction, and it wasnonlinear. At last, we studied two basic defect states: point defect and linear defect. Theresults showed that there was a localized mode in the band gap of the point defect, it related tothe length of “atom” and filling fraction. We can control the frequency of the localized modeby changing the length of “atom” and filling fraction. We analyzed the band gap structure oflinear defect, there was a guided mode in the band gap, and the frequency variation range ofthe guided mode was (0.3467—0.3858)(2C0/a).2. Based on the study of two basic defects, two-dimensional three-component phononiccrystals with point defects and linear defects have been constructed. We get the results whichcompared with two-component，it shows that: For the point defect, a localized mode appearedin the first band gap, but the ideal point defect appeared in the second band gap, and thefrequency of the localized mode was significantly reduced. For the linear defect，thefrequency of the guided mode changed with the rotational angle and filling fraction.Compared with two-component, the frequency variation range of the guided mode increasedsignificantly. When-45°<<45°,the frequency range of the guide is symmetric to thedirection (01). The sonic waveguide characteristics of the PC were not changed with theorientation and the type of cross-section of the defect cylinders when the filling fraction isvery small. In addition, we also discuss the different density and propagation velocity of theimpact on the frequency of the band gap, which provides a theoretical basis for thedevelopment of new materials. 3. Three heterostructure models were constructed. They are square and triangular latticeround scattering column heterostructure,2-D three-component square lattice round scatteringcolumn heterostructure and2-D three-component square lattice round and square scatteringcolumn heterostructure. The results showed that: The guide modes can exist in these threeprototype heterostructures, and the number and position of guide modes were influenced bythe relative sideslipping. For square scattering column heterostructure, the number andposition of guide modes were influenced by rotation angle.