School of Engineering, The University of Queensland
Abstract
The acoustic properties of an inhomogeneous bubbly medium are complex owing to the absorption and re-emission of acoustic energy by the bubbles. This phenomena can be approximated by a globally coupled system of linear oscillators. In previous studies, it has been shown that this simple model can produce results that are in qualitative agreement with experimental data. In order to achieve better quantitative agreement with experimental data, time-delays need to be introduced into the mathematical model. In the present study, the resulting delayed differential equations were solved numerically using a 4th order Runge-Kutta method. The numerical methodology was validated by comparing simplified cases with the solution using analytical methods. The effects of time-delay were assessed by comparing non-timedelayed and time-delayed versions of the mathematical model. Results from numerical simulations were then compared to assess the effects and importance of the inclusion of time-delay in the mathematical model. This study shows that the inclusion of time-delay has a noticeable effect on the lower frequency modes of the model. This effect propagates to the higher frequency modes as the magnitude of the time-delay increases. The results also shows that the time-delay shifts the dominant modes from the lower frequency modes to the higher frequency mode
