Characteristics Of Two-Dimensional Phononic Crystals Based On The Similarly Of Photonic Crystals

In recent years there has been growing interest in the propagation of acoustic (AC) or elastic (EL) waves in periodic elastic composite materials known as phononic crystals, which have phononic band gaps. Of particular interest is the existence of band gaps in which sound and vibration are all forbidden. The motivation for these studies is to better understand the Anderson localization of sound and vibrations in composite media, as well as their numerous engineering applications such as elastic/acoustic filters, vibrationless environments for high-precision mechanical systems or the design of new transducers and sonar.In this dissertation, the plane-wave expansion method (PWM) is developed for the 2D phononic crystals' modeling and simulation. The theory and algorithm of PWM are studied in detail and implemented by Matlab in a unique and efficient approach. PWM is used to obtain the gap information of 2D phononic crystals. Several material and structural parameters are shown to affect the band gap.Effects of defects in phononic crystals are studied in detail by using the plane-wave method combined with the supercell technique. Results show that point defects can pin the sound waves to the defect, then sound can not escape, and form resonator, whereas line defects can mold the flow of sound, which lie in the bandgap, along the channel and form the so called waveguides. Based on the studies on the two basic defects, we ulteriorly construct the homogeneity dislocation structures, and investigated transverse dislocation structures and longitudinal dislocation structures respectively. We found that transverse dislocation structures, acted as the line defect, can form waveguides too; while, longitudinal dislocation structures can form a cavitylike void surrounded by the three nearest cylinders around the interface, which acted just as the point defect.Finally, we studied the guide modes formed in two-dimensional phononic crystal heterostructures. We construct three different types of heterostructures: SCSC heterostructure, SCRC heterostructure and RRTC heterostructure. Results show that localized interface states are absent in the former two heterostructures, they can be created either by lateral lattice slipping or by increasing the interface separation; the absolute gap width and the position of guide modes strongly depend on the relatively transverse and longitudinal gliding displacement, so we can artificially control the guide modes by adjusting the relatively transverseand longitudinal gliding displacement of lattices in a heterostructure. But the RRTC heterostructure can produce guide modes in bandgap without any relative gliding or transverse displacement. This feature is quite different from other phononic crystal heterostructures. The reason can be ascribed to the prototype phononic crystals have different lattices, which augments the aberrance at the interface.