الفهرس 
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Abstract
During this thesis, the propagation of elastic and acoustic waves has been investigated in several structures of PnCs and under the effect of many physical parameters. Our findings are summarized in the following points: First, we have theoretically investigated the propagation of acoustic waves through 1D and 2D mass spring structures. The band gaps can be adjusted by calculating the band gap width as a function of mass value. Additionally, by modeling the structures from host materials with very low elastic properties, we obtained low frequency band gaps at small dimensions compared with the conventional structures. Such systems could be used to transmit acoustic waves at very narrow pass bands inside a broad gap. Moreover, we have studied waveguiding properties of acoustic waves in 2D mass spring systems. This device permits the transmission of NPB of frequencies corresponding to the elastic properties of the material. Additionally, by appropriately designing an active guiding device, we can impose transmission at more than one NPB frequencies. Therefore, we have discussed the model of a multiplexer and DE multiplexer based on the X-shaped waveguide. These systems can be utilized for separating or merging narrow transmission bands with different frequencies. Next, the dispersion relation and reflection coefficient were derived for evaluating the frequency band structure of SH-waves and plane waves in perfect and defect PnCs layered structures. The effects of periodicity type (filling fraction ratio) and angle of incidence on phononic band gap characteristics have been thoroughly investigated. Our results exposed the essential features of the frequency band structure under the variation of the filling ratio and provided a quantitative description of the dependence of the relative band gap size (of the first band gap) upon the various filling fraction ratio of each material. A comparison between a single and double defect in PnC structure was also carried out. It is important to note that the type of material filled defect layer must be taken into account to understand extraordinary acoustic transmission phenomenon and its relevance to material property determination of the liquid type. As a consequence, by this technique, we obtained an optimization to sensing different liquids dependent on the intensity and number of resonant frequencies. Therefore, the respective resonant frequency can be used as an indicator for the type and properties of a liquid. The transmitted resonant frequencies inside PnC related to the defect layer technique needs to be further optimized for sensor purposes especially the number and shape of the transmitted peaks for various types of other liquids. Also, we considered two PnCs structures namely, (Bi-2223/Nylon)N and (Terfenol-D/Nylon)N and we call them PnCs1 and PnCs2, respectively. We have studied the effects of the temperature and the magnetic field on the phononic gaps of these PnCs. The presented results show that the local resonance property is achieved in PnCs1 very clearly, where very narrow sharp resonance modes are generated within the band gaps. The number of these modes and intensity of the modes increase with increasing temperature while the band gap width decreases. Moreover, the band structure of PnCs1 become as a complete band gap over a wide range of frequencies. We note that the magnetic field can tune the phononic gap width of the PnCs1 due to its effect on the velocity of the sound waves. For PnCs2, the phononic band gaps are greatly enhanced by the magnetic field due to its effect on the dimension of the magnetostrictive material. Based on these observations, phononic crystals can be used to detect and measure the magnetic field intensity depending on the constituent magnetostrictive materials. Finally, we have studied the interactions of PnCs with radioactive nuclei. We have proposed new models can detect and measure the incident ionizing radiation based on the novel properties of PnCs. In the study, we found that the energy transferred via nuclear scattering of helium-4 ions across PnCs imparts some energy to phonons. The energies lost to phonons have a maximum value for a 1 keV helium-4 ion. The transmittance versus phonon frequency was examined for normal incident longitudinal and transverse waves on 1D PnCs consisting of four and two layers made from PMMA and PE, respectively. There is a correlation between the total phonon energies and the transmittance of PnC structures. The maximum transmission of phonons due to the passage of helium-4 ions was found in the case of making polyethylene the first layer in a PnC structure. Thus, the sensitivity of the PnC structure to helium-4 ion effects was increased. Meanwhile, ion detection based on PnC structure is achievable. To the best of our knowledge, this work is the first design of this type of novel radiation detectors.