The Lamb And Surface Waves In Phononic Crystal

In recent years, there is an increasing interest in the studies of acoustic or elastic waves propagating in the periodic elastic artificial composite materials which is called phononic crystal (PC). Due to the existence of the frequency band gaps, acoustic or elastic waves in the phononic crystal show some special properties, implying a great potential application. In the present thesis, we have studied the behavior of Lamb and Surface waves in the finite two- or three-dimensional phononic crystal.(1). Based on the Plane Waves Expansion theory (PWE) and the symmetric properties of the Lamb modes in PC plate, we present a revised PWE method, by which the symmetric and anti-symmetric Lamb modes can be calculated respectively. Using the revised PWE method, we investigated a phononic crystal system consisted by two symmetric void holes embedded in a uniform plate. The numerical results show that the opening of the folded points at the center/edge of Brillouin zone (BZ) is strongly dependent on the distance between these holes. We found that this phenomenon can be understood by the distribution of potential energy of the Lamb mode.(2). Using the finite element method (FEM), we studied the acoustic property of a novel phononic crystal structure constructed by periodically depositing the single-layer or two-layer stubs on the surface of thin uniform plate. We obtained the band structure of these systems with different radius and thickness of resonance stubs. The displacement field distribution of the oscillating mode is given to explain why the resonance modes selectively coupled with the modes in plates. The physics behind the opening of the LRBG in our phononic structures can be understood by a simple "spring-mass" model.(3). By comparing the Bulk modes with the Lamb modes in multi-layers plate, we studied the surface modes in phononic crystal. We also investigated the feature of surface modes in the system constructed by depositing a uniform layer or periodical non-uniform layer on the surface of phononic crystal. We found that this can be an efficient way to control the dispersion relation of the surface waves. By which, some special acoustic properties can be expected for the surface waves, because many novel phenomena in the bulk phononic crystal, such as acoustic focusing, acoustic localization, etc., are based on its adjustable band structure.