Study On Bandgap Characteristics Of Two - Dimensional Plate Phononic Crystals

Phononic crystals, which are a composite medium composed of periodic arraysof two or more materials with different mass densities and elastic properties, areattracted broadly research interest in the last decade。Prohibited band appears aselastic waves propagate in it. therefore,Investigation of the energy band structure ofthe phononic crystal is of great importance for both theoretical studies andapplications。Thin plate structure is widely used in industrial fields such as civilengineering, chemical, shipbuilding, aviation and space, and it is one of the primarystudy objects in vibration control field for many years. Therefore, it can beconstructed the phononic crystals thin plate structure through brings the idea ofperiodicity to this thin plate structure. In this paper，the band gaps of two-dimensionalphononic crystal thin plate were studied by using the plane-wave expansion methodand supercell calculations. The main research items in this dissertation areas follows:(1) First we introduce the basic concepts on phononic crystals，characteristic andrecent research activities at home and abroad. Then we introduce the basic theory andmethod for the calculation of band structure, and deduced the eigenequation. At lastwe give matlab code detailed process and idea.(2) The band gap of2D perfect phononic crystal thin plate was investigated byplane-wave expansion (PWE), which is consist of copper embedded in the organicglass. Find that we can obtain larger band gap (56.482kHz). The energy distributionof propagation of acoustic wave with different frequencies are also obtained, thepropagation of vibration is forbidden when frequency in the band gaps, but vibrationwith frequency in the pass band can propagated in the whole-plane.(3) We discuss the effect of structural parameters, material parameters (the massdensity ratio,the Young’s modulus ratio,the sheer modulus ratio), thickness of thinplate on phononic crystal thin plate band gaps. Noted that it has a large impart on theband width of phononic crystal.(4) Study the transmission properties of2D phononic crystal thin plate pointdefect and linear defect. We calculate the defect mode change with radius of point defect. Than The band gap of straight linear defect, branching linear defect, andsymmetrical linear defect are calculated respectively，, the band gap width are alsocalculated As the filling fraction function.