The Optimization Of Band Gaps In Phononic Crystals

The phononic crystals are the new research hotspots on the basis of traditional natural crystals and photonic crystals in the recent years. It extends and exceeds the concept of traditional natural crystals. A physical character of phononic crystals is the existence of phononic band gaps in which the sound and elastic waves are all forbidden. Base on this theory, the phononic crystals will have a broad foreground of engineering applications such as new sound insulation materials, elastic or acoustic filters, etc. Therefore, that the artificial design and optimization of the phononic band structure is meaningful for applications of phononic crystals.First, the basic theory and methods of phononic band structure are introduced in this paper. And the equations of plane-wave expansion (PWE) method are given in detail.Then, the influences of symmetry to phononic band gaps are investigated in two-dimensional systems. The lattice's and unit cell's symmetry and rotation effect are discussed in the paper, and the widest phononic band gaps are found for different symmetry compounding.Third, the popular genetic algorithm (GA) is introduced to optimization of phononic band gaps, and the combination of GA theory and the study of phononic crystals are discussed in the paper. Two examples reveal the GA's advantage in the design of band structures, and GA method is effective to find out excellent topology of unit cell with a widest absolute band gaps.Firth, we study the band gaps optimization in locally resonant phononic crystal. It is a three-component composite. We get the parameters of this kind of structure with maximum phononic band gaps.Finally, we study the defect states and defect modes. The defect modes of three-dimensional phononic crystal are studied. The localized defect modes of water waves over two-dimensional periodic bottoms with a point defect are investigated by supercell calculations and plane-wave expansion method. Two kinds of defects are introduced, one is a radius defect created by changing radius of cylinder, and another...