الفهرس 
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Abstract
In this thesis, we will introduce a comprehensive study of the stop-band/pass-band dispersive behavior of 1D phononic crystal structures. We theoretically study the interactions between the elastic waves and different multilayer periodic phononic crystal structures such as binary, ternary and defect structures. Based on the transfer matrix method (TMM) and Bloch theory, the interactions of elastic waves will be studied for plane waves (longitudinal and transverse) incident normally on phononic crystals, and for the general case of wave oblique incidence( anti-plane shear waves ).
The main idea within this thesis is concentrated on explaining the dispersion relations and reflection coefficients that represent the band structure of phononic crystals. Dispersion relations are calculated and plotted for the binary and ternary structures. The reflection coefficient is another tool used for representing the band structure of phononic crystals especially in the case of plane waves propagation. Numerical simulations are performed to investigate the effects of materials thickness, unit cell ratio and state of polarization on the band gap properties and band gap width.
Additionally, different materials in the constituents are taken to examine their possible effects on the phononic band gaps. The effects of these parameters will greatly appear on the response of the phononic band gaps and increase their potential applications.
Finally, we will treat the propagation and localization of (P and S)/ (SH) waves in perfect/defect phononic crystals. For this purpose, we will study the effects of defect mode properties and temperature on phononic band gap materials for these two waves. The roles played by the related parameters such as type and thickness of defect layer and their effects on wave localization will be discussed and illustrated. In the same manner, different temperatures will be considered to investigate phononic crystals response to temperature and the ability to use these materials in technology such as temperature sensors.