Doctoral defense
Theoretical studies of acoustic waves with consideration of nonlinearity, dispersion, dissipation and diffraction
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| Defendant |
Main Advisor |
Extra Advisor |
Date |
| Henrik Sandqvist |
Bengt Enflo |
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2003-06-13 |
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| Opponent |
| Oleg Rudenko, Moscow
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| Evaluation committee |
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AbstractAcoustic waves propagating according to nonlinear as well as linear theory have been studied. In the nonlinear case, the propagation and decay of shock waves in dispersive and dissipative media are considered. Waves in e.g. a bubbly fluid can be described by Korteweg-de Vries-Burgers` equation (KdVB). The focus of this investigation was to find analytical solutions to Korteweg-de Vries` equation (KdV) by using the inverse scattering transform (IST). To be able to use IST, the initial waveform must be localized. Therefore, we used an N-wave as a shock wave model. IST transforms the nonlinear KdV into the linear Marchenko`s integral equation. Attempting an iteration solution, it was shown that already the zeroth order solution of the integral equation (i.e. letting the integrand be zero) corresponds to a solution to KdV which reconstructs the initial waveform. This holds for moderate values of the dispersion coefficient and not too far away from the wave front. The initial behaviour around the two discontinuities of the N-wave are similar. The shock front slows down and leaves an oscillating tail behind. However, the oscillating tail of the leading shock soon disrupts the structure of the tailing shock and only a single wave front with an oscillating tail is seen. Asymptotic solutions for Burgers` equation and KdV, for small values of the dissipation and dispersion coefficient respectively are also given. For KdVB the case, which has contributions from dispersion and dissipation of the same order of magnitude, is analysed. In the linear case, diffraction of sound at noise barriers with straight and non-straight edge profiles is considered. The problem with the straight edge normally used is that it acts as a secondary source and thus reduces the shielding effect. For some areas behind the barrier, the sound is even louder than without a screen. A way to reduce this problem is to use edge profiles with varying height. The focus of the investigation is to examine how the efficiency of periodic varying height edge profiles depends on the frequency of the source and the structure of the edge profile. This in order to construct optimal varying height profiles as linear combinations of periodic edge profiles. The sound field around a barrier is calculated by a Green`s function method. Thereafter the efficiency of the screen is determined by comparing the total energy transferred to the area behind the screen. Results for square, rectangular and stair profiles are presented. The diffraction of broadband sources and sawtooth sources are also analysed.
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