dc.description.abstract | In this thesis, we discuss the acoustic behaviors of the bubble-in-water sonic crystal in water. Due to the large impedance mismatch between water and bubbles, bubbles are very efficient acoustic scatterers and have strong resonances at low frequencies. In our model, a bubble under the influence of low frequency incident acoustic wave vibrates radially as a driven oscillator as well as a monopole acoustic source. In addition to the expansion and contraction motion in the radial direction, there is also damping force acting on the bubble. We use this simple model of bubbles in water to analyze the effective dynamic bulk modulus and scattering function at low concentration. It can be found that in a wide range of frequency, the bubble-in-water medium has an effective negative elastic modulus, while the effective density of the medium is still positive. This frequency range corresponds to the bandgap of the bubble-in-water sonic crystal, thus why the acoustic waves cannot propagate in this medium. In addition, we also calculate the transmittance of the acoustic waves through the layered structure composed of bubbles and found that under the coupling effect of resonance and Bragg scattering mechanism, the dispersion relationship of the bubble phonon crystal is the same as that of the phonon-polariton in the ion crystal. In addition to explaining the long-wavelength behavior of the bubble sonic crystal, our theory can also be used for studying the transmission response in frequency to a point source inside or outside the bubble screen (a slab or a shell) of randomly distributed bubbles. Our numerical simulations are implemented by using the transfer matrix method. Since wave propagation in disorder media has always been one of the most important topics in wave theory, and our bubble scattering model provides simple ways to analyze the low-frequency isotropic scattering (the bubbles play the roles of impurities in water), so it is very helpful for us to understand the mechanism of acoustic localization. Our model can help to study marine acoustics. For example, using our model to analyze the scattering of the sound waves by ocean bubbles, we may develop efficient method to detect the ocean. Moreover, we can even generalize our model and apply it to other types of sound wave systems. | en_US |