Bicoherence analysis has been used to characterize nonlinear effects in the propagation of noise from a model-scale, Mach-2.0, unheated jet. Nonlinear propagation effects are predominantly limited to regions near the peak directivity angle for this jet source and propagation range. The analysis also examines the practice of identifying nonlinear propagation by comparing spectra measured at two different distances and assuming far-field, linear propagation between them. This spectral comparison method can lead to erroneous conclusions regarding the role of nonlinearity when the observations are made in the geometric near field of an extended, directional radiator, such as a jet.

The nonlinear propagation of a pure sinusoid is considered using time domain statistics. The probability density function, standard deviation, skewness, kurtosis, and crest factor are computed for both the amplitude and amplitude time derivatives as a function of distance. The amplitude statistics vary only in the postshock realm, while the amplitude derivative statistics vary rapidly in the preshock realm. The statistical analysis also suggests that the sawtooth onset distance can be considered to be earlier than previously realized.

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In the collection and analysis of high-amplitude jet noise data for nonlinear acoustic propagation, both model-scale and full-scale measurements have limitations. Model-scale measurements performed in anechoic facilities are usually limited by transducer and data acquisition system bandwidths and maximum propagation distance. The accuracy of fullscale measurements performed outdoors is reduced by ground reflections and atmospheric effects. This paper describes the use of two nonlinearity indicators as complementary to ordinary spectral analysis of jet noise propagation data. The first indicator is based on an ensemble-averaged version of the generalized Burgers equation. The second indicator is the bicoherence, which is a normalized version of the bispectral density. These indicators are applied to Mach-0.85 and Mach-2.0 unheated jet noise data collected at the National Center for Physical Acoustics. Specifically, the indicators are used to separate geometric near-field effects from nonlinear propagation effects for the Mach-2.0 data, which cannot be done conclusively using comparisons of power spectral densities alone.

Structures with power law tapers exhibit the acoustic black hole (ABH) effect and can be used for vibration reduction. However, the design of ABHs for vibration reduction requires consideration of the underlying theory and its regions of validity. To address the competing nature of the best ABH design for vibration reduction and the underlying theoretical assumptions, a multi-objective approach is used to find the lowest frequency where both criteria are sufficiently met. The Pareto optimality curve is estimated for a range of ABH design parameters. The optimal set could then be used to implement an ABH vibration absorber.