Research On Vibration Properties Of 2D Generalized Phononic Crystals In Cylindrical Coordinate

As a type of periodic structure of material or geometry parameters, phononic crystals show a great application prospect in the control of elastic wave and acoustic wave for its unique characteristics of negative refraction,sound focusing,and band gaps. It has been attracting a lot of scholars to engage in this young field. Recently, the concept of phononic crystals has been extended to a various of special periodic structures from traditional ones of which the generalized phononic crystals (GPCs) is an important part.Based on the concept of GPCs, a two-dimensional circular plate and a composite cylindrical shell of this kind of structure are proposed and analyzed in this thesis. By using the finite element theory and energy method, three types of elastic waves propagating radially in the two-dimensional circular plate of GPCs are investigated and the properties of band gaps are discussed in details. Besides, the acoustic characteristics of the cylindrical shell of GPCs are also analyzed for the excitation of central line acoustic source. The main contents are as follows:1.The damping boundary is used to construct the power flow path, and the energy transmission ratio is introduced to evaluate the band gap of the GPC plate. On this basis, the band gap characteristic of flexural wave, torsional wave, and radial wave are analyzed.Furthermore, the mechanisms of the band gaps are revealed and the effect of factors on the band gaps is presented.2. The structure intensity and its visualization are introduced to study the energy flow of the GPC plate. Detailed features of the band structure are analyzed in terms of energy through the relationship between the energy transmission ratio and the structure intensity. In addition, the phenomena of the stress localization under the specific frequency are discussed.3. The radial wave band gaps of the GPC shell are obtained by the energy transmission ratio.Based on the simulation of acoustic-structural coupling field, the sound isolation characteristics and directive property of the shell are investigated, which meet with the results of the structural field analysis.The study shows that the two-dimensional GPC plate has significant band gaps, whose start and center frequencies are determined by the Bragg mechanism due to the periodic property in the radial direction. Within these band gaps, the resonance peaks are caused by the local resonance or energy path of the scatters. Similarly, the band gaps can also be obtained in the GPC shell structure. Within the band gap, the shell exhibits strong sound-insulated capability.Furthermore, this thesis indicates also that the finite theory combined with the energy method is an effective way for the research of two dimensional GPCs, providing an workable approach for this type of special periodic structure.