Study On The Bandgaps Of One-dimensional Nearly Periodic Phononic Crystal Plates

Phononic crystal (PNC) generally refers to artificial periodic structures and functional material with acoustic band gaps. The essential property of the PNC is its band gaps which have numerous potential engineering applications such as acoustic filters, waveguides, noise suppression and transducers, etc. In fact, the actual periodic structures always have a certain deviation from the ideal ones, and we call these structures nearly periodic structures. In this paper, the nearly periodic structures we studied are one-dimensional PNCs with defects, quasi-periodic and random disordered PNCs. The importance of the propagation of elastic waves in the nearly periodic structures is self-evident. On the one hand, it is impossible to be strict periodicity due to the manufacturing errors. On the other hand, nearly periodic structure has more adjustable parameters than the periodic structure and the elastic wave propagation behavior and its band structures can be tuned more flexible.In addition, PNCs usually are not infinite in the practical applications which always have boundaries. So it is necessary to study the wave propagation in the finite PNCs, such as the propagation of lamb wave in the PNC plate. Lamb waves show great potential in nondestructive testing and became one of the powerful tools of the on-line detection. The PNC plate, naturally, received wide attention of scholars both at home and abroad. In this thesis, we study the following problems for lamb wave’s propagation in one-dimensional nearly PNC plates:1. Combined with the supercell method, the finite element software COMSOL Multiphysics is used to calculate the band structures of PNC plate with defects and random disorders. The defects we considered are point defects caused by the size or the material types of certain sub-layers. And disorders are three types which caused by thickness of each layer, material elastic modulus and density, respectively. The results show that random disorder will lead to the split phenomenon of the band gaps and has richer local modes than point defects. Random disorder generated by the sub-layer’ size can bring more local modes than material parameters does.2. Combined with the supercell method, the finite element software COMSOL Multiphysics is used to calculate the band structures and transmission of one-dimensional quasi-periodic PNC plates. The modal analysis of the lamb waves are studied combined with the modal distributions and displacement vector maps. The influences of the structure parameters (the volume ratio of component materials and the ratio of the thickness of the plate to the lattice constant) and material parameters (the ratio of elasticity modulus and the ratio of density) on the band structure are analyzed. The influences of the arrangement of the quasi-periodicity (Fibonacci, Cantor and Thue-Morse sequence) on the band structures are discussed. The results show that the width of the largest band gap and the position of the center frequency can be tuned by adjusting the structure and material parameters. In addition, we can control the number of the split band gap through the ratios of thickness to the lattice constant.3. The band gap properties of lamb waves in the one-dimensional periodic and quasi-periodic aluminum groove PNC plates are studied by experiment. At the same time the band structures and transmission spectrum are calculated by using the finite element method. The results of the above two methods are agree with each other which means that it is effective to study the lamb wave’s propagation in the one-dimensional periodic and quasi-periodic aluminum groove PNC plates by using this experiment system.