Micah R. Shepherd

Bicoherence analysis of model-scale jet noise

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.

Identification of Nonlinear and Near-field Effects in Jet Noise Using Nonlinearity Indicators

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.

Evolution of statistical properties for a nonlinearly propagating sinusoid.

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.

Nonlinearity analysis of model-scale jet noise

This paper describes the use of a spectrally-based “nonlinearity indicator” to complement ordinary spectral analysis of jet noise propagation data. The indicator, which involves the cross spectrum between the temporal acoustic pressure and the square of the acoustic pressure, stems directly from ensemble averaging the generalized Burgers equation. The indicator is applied to unheated model-scale jet noise from subsonic and supersonic nozzles. The results demonstrate how the indicator can be used to interpret the evolution of power spectra in the transition from the geometric near to far field. Geometric near-field and nonlinear effects can be distinguished from one another, thus lending additional physical insight into the propagation.

Short-range shock formation and coalescence in numerical simulation of broadband noise propagation.

The number of jet and rocket noise studies has increased in recent years as researchers have sought to better understand aeroacoustic source and radiation characteristics. Although jet and rocket noise is finite-amplitude in nature, little is known about the existence of shock formation and coalescence close to the source. A numerical experiment is performed to propagate finite-amplitude noise and determine the extent of the nonlinearity over short distances with spherical spreading. The noise is filtered to have a haystack shape in the frequency domain, as is typical of such sources. The effect of the nonlinearity is compared in both the temporal and frequency domains as a function of distance. Additionally, the number of zero-crossings and overall sound pressure level is compared at several distances. The results indicate that the center frequency plays a particularly important role in the amount of coalescence and spectral redistribution that occurs. The general applicability of these results to actual near-field finite-amplitude jet and rocket noise experiments is also presented.

Simulations and Measurements of the Vibroacoustic Effects of Replacing Rolling Element Bearings With Journal Bearings in a Simple Gearbox

The effects of replacing rolling element bearings with journal bearings on the noise and vibration of a simple gearbox are computationally and experimentally evaluated. A modified component mode synthesis (CMS) approach is used, where the component modes of the shafting and gearbox housing are modeled using finite element analysis (FEA). Instead of using component modes with free boundary conditions, which is typical of CMS, the shafting and gearbox are coupled using nominal impedances computed for the different bearing types, improving convergence of the solution. Methods for computing the actual bearing impedances, including the high damping coefficients in journal bearings, are summarized. The sound radiated by the gearbox is computed using a boundary element (BE) model. The modeling results are validated against measurements made at the NASA Glenn Research Center. Both simulations and measurements reveal that the journal bearings, although highly damped, do not necessarily lead to strong reductions in gearbox vibration and noise.

Comment on plate modal wavenumber transforms in Sound and Structural Vibration [Academic Press (1987, 2007)] (L)

The wavenumber transform for rectangular, simply supported, isotropic thin plates has been rederived to correct a technical error found in the text Sound and Structural Vibration (Academic Press, 1985/2007) by Fahy/Fahy and Gardonio. The text states that the modal wavenumber corresponds to the peak of the wavenumber spectrum. While this is approximately true for higher-order modes, it does not hold for lower-order modes due to coupling between positive and negative wavenumber energy. The modal wavenumber is shown to be related to the zeros in the wavenumber spectrum by an integer multiple of 2π normalized by the plate length.

Minimizing the acoustic power radiated by a fluid-loaded curved panel excited by turbulent boundary layer flow

In order to address noise control problems in the design stage, structural-acoustic optimization procedures can be used to find the optimal design for reduced noise or vibration. However, most structural-acoustic optimization procedures are not general enough to include both heavy fluid loading and complex forcing functions. Additionally, it can be difficult to determine and assess trade-offs between weight and sound radiation. A structural-acoustic optimization approach is presented for minimizing the radiated power of structures with heavy fluid loading excited by complex forcing functions. The procedure is demonstrated on a curved underwater panel excited by a point drive and by turbulent boundary layer flow. To facilitate more efficient analysis, an uncorrelated pressure assumption is made for the turbulent boundary layer forcing function. The thicknesses of groups of elements were used as the design variables with an adaptive covariance matrix evolutionary strategy as the search algorithm. The objective function was a weighted sum of total sound power and panel mass and the Pareto front was computed to show the optimum trade-off between the two objectives. The optimal designs are presented which illustrate the best methods for reducing radiated sound and mass simultaneously.

An Approach for Structural-Acoustic Optimization of Ribbed Panels Using Component Mode Synthesis

Component mode synthesis (CMS) is an approach used to couple dynamics of complex structures using modes of individual components. A CMS approach is developed to determine the response of a ribbed panel based on the individual rib and plate modes. The CMS method allows for rapid evaluation of noise-control designs as component modes need to be solved only once. Since efficient evaluation is required for global design optimization procedures, the CMS approach can be well suited in optimization problems. A simple structural-acoustic optimization problem was created to demonstrate the utility of the formulation by finding the optimal rib location and material to reduce sound radiation for a point-driven plate. Several parameters of the optimization algorithm are varied to test convergence speed and accuracy.Copyright

Higher‐order statistical analysis of nonlinearly propagated broadband noise.

Nonlinearity indicators have recently been used to identify and characterize nonlinear effects present in high‐amplitude noise propagation. Although frequency‐domain approaches have many benefits, a time‐domain approach may be a more natural fit for the time‐domain phenomenon of wave form steepening and shock formation. Standard skewness and kurtosis metrics are computed for propagated Gaussian noise at both low and high amplitudes. The same higher‐order statistics are also computed for the first time derivative of the propagated noise in order to accentuate non‐Gaussian variation in the wave form. The results appear to reveal an asymptotic behavior of the statistical quantities as the time wave form becomes more shock dominated.