Analyses of Nonlinearity Measures in High-Amplitude Sound Propagation

• Main Author: Muhlestein, Michael B.
• Format: Others
• Published: BYU ScholarsArchive 2013
• Subjects: jet; nonlinear; shock; skewness; wave steepening factor; Astrophysics and Astronomy; Physics
• Online Access: https://scholarsarchive.byu.edu/etd/3994; https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4993&context=etd

Military aircraft generate high-amplitude noise which can cause injury to attending personnel. Efforts to mitigate the effects of this noise require a detailed understanding of the propagation of the noise, which was shown previously to be nonlinear. This thesis presents an analysis of high-amplitude noise propagation, emphasizing measures used to quantify the importance of considering nonlinearity. Two measures of the importance of nonlinearity are compared. These measures are the wave steepening factor and a skewness estimate. The wave steepening factor is a measure of how much nonlinear waveform steepening has occurred in a waveform. The skewness estimate is the skewness of the first time-derivatives of the pressure amplitudes, and can be considered a measure of the shock content in a waveform. These two measures are analyzed analytically in terms of the Earnshaw, Fubini, Fay, and Khokhlov solutions to the Burgers equation. In addition, an analysis of how discrete sampling affects the estimation of these quantities is also presented. It is determined that the wave steepening factor is robust with respect to low sampling rates, but the skewness of the first time-derivatives of the pressure amplitudes is not robust, and requires very large sampling rates to be adequately estimated. Using numerical and experimental techniques, the two nonlinearity measures are applied to more complicated waveforms, such as Gaussian noise and noise with jet noise-like statistics. It is found that the evolution of the two nonlinearity measures discussed above for noise signals is distinctive in various ways. In particular, the skewness of the first time derivative of the pressure amplitudes suggest that noise waveforms experience nonlinear phenomena faster than initially sinusoidal signals, while the wave steepening factor suggests that they occur at approximately the same rate. The measures are then applied to full-scale military aircraft. By comparing these nonlinearity metrics with the results of the analytical, numerical, and experimental results found in this thesis, it is determined that nonlinearity is likely to be significant in the near field of a military aircraft at military and afterburner engine conditions.