This dissertation is a continuation of the work by Zabolotskaya (Sov. Phys. Acoust. 32, 296-299 (1986)) and Wochner et al. (J. Acoust. Soc. Am. 125, 2488-2495 (2008)) on the nonlinear propagation of shear wave beams in an isotropic solid. In those works, a coupled pair of nonlinear parabolic equations was derived for the transverse components of the particle motion in a collimated shear wave beam, accounting consistently for the effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to the nonlinearity present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The purpose of this work is to investigate the quadratic nonlinear term by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. Since shear wave beams with translational polarizations (linear, elliptical, and circular) do not exhibit any second-order nonlinear effects, we broaden the class of source polarizations considered by including higher-order polarizations that account for stretching, shearing and rotation of the transverse plane. We find that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic. Additionally, we consider the focusing of shear wave beams with this broader class of source polarizations, and find that a tightly-focused, radially-polarized shear wave beam contains a highly-localized region of longitudinal motion at the focal spot. When the focal distance of the beam becomes sufficiently short, the amplitude of the longitudinal motion becomes equal to the amplitude of the transverse motion. This phenomenon has a direct analogy in the focusing properties of radially-polarized optical beams, which was investigated experimentally by Dorn et al. (Phys. Rev. Lett. 91, 233901 (2003)). / text

Thesis (M.S.)--School of Mechanical Engineering, Georgia Institute of Technology, 2005. Directed by David Trivett. / Trivett, David, Committee Chair ; Berthelot, Yves, Committee Member ; Rogers, Peter, Committee Member. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (leaves 119-132).

No description available.

To help resolve certain practical issues with acoustical methods for landmine detection, experiments were performed using a pulsed, standoff source consisting of sixteen speakers mounted on a circular arc. This source, as well as a pair of 18-inch subwoofers, were used separately for acoustical excitation of the buried mine, and the response of the target site was examined as a function of source frequency, sound pressure level, and excitation signal type, with a particular focus on multitone signals. In addition, modeling was undertaken to investigate the effects of nonlinearity, including bimodular nonlinearity, on frequency generation. A numerical, time-domain solution based on a lumped-element model proposed by Donskoy et al. [J. Acoust. Soc. Am. 117, 690 (2005)] was developed and used to simulate pulsed excitation and the effects of bimodular nonlinearity, which allowed experimentally observed spectra to be compared with modeled results. / text

A scaling model based on an effective Gol'dberg number is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jets. Two acoustic length scales, the shock formation distance and the absorption length are expressed in terms of jet exit parameters. This approach allows one to compute the degree of cumulative nonlinear distortion in a full-scale scenario, from laboratory-scale observations, or vice versa. Surveys of the acoustic pressure waveforms emitted by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support the findings of the model. These acoustic waveforms are acquired on a planar grid in an acoustically treated and range-restricted environment. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes skewness, kurtosis, the number of zero crossings in the waveform, a wave steepening factor, the Morfey-Howell nonlinearity indicator and an application of the generalized Burgers equation. It is advocated that in order for the Morfey-Howell indicator to be used as an investigative tool for the presence of cumulative nonlinear waveform distortion, that it be applied as a multi-point indicator. Based on findings of the model and the spatial topography of the metrics, it is concluded that cumulative nonlinear steepening effects are absent in the current data set. This implies that acoustic shock-structures in the waveforms are generated by local mechanisms in, or in close vicinity to, the jet's hydrodynamic region. Furthermore, these shock-structures induce the crackle noise component. The research aims to quantify crackle in a temporal and spectral fashion, and is motivated by the fact that (1) it is perceived as the most annoying component of jet noise, (2) no unique measures of crackle exist, and (3) significant reductions in jet noise will be achieved when crackle can be controlled. A unique detection algorithm is introduced which isolates the shock-structures in the temporal waveform that are responsible for crackle. Ensemble-averages of the identified waveform sections are employed to gain an in-depth understanding of the crackling structures. Moreover, PDF's of the temporal intermittence of these shocks reveal modal trends and show evidence that crackling shock-structures are present in groups of multiple shocks. A spectral measure of crackle is considered by using wavelet-based time-frequency analyses. The increase in sound energy is computed by considering the global pressure spectra of the waveforms and the ones that represent the spectral behavior during instances of crackle. This energy-based metric is postulated to be an appropriate metric for the level of crackle. / text

Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2011.

Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: G. Tong Zhou; Committee Co-Chair: Xiaoli Ma; Committee Member: David V. Anderson; Committee Member: James Stevenson Kenney; Committee Member: Liang Peng; Committee Member: William D. Hunt. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Dissertation (D.M.A.)--The University of North Carolina at Greensboro, 2009. / Directed by Kelly Burke; submitted to the School of Music. Title from PDF t.p. (viewed May 11, 2010). Includes bibliographical references (p. 148-159).

In order to facilitate the acquisition and accurate interpretation of intensity and energy density data in high-amplitude pressure fields, the expressions for intensity and energy density are examined to ascertain the impact of nonlinear processes on the standard expressions. Measurement techniques for estimating acoustic particle velocity are presented. The finite-difference method is developed in an alternate manner and presented along with bias and confidence estimates. Additionally, two new methods for estimating the local particle velocity are presented. These methods appears to eliminate the errors and bias associated with the finite-difference technique for certain cases.