This thesis presents a multi-purpose sensor concept viable for the simultaneous measurement of pressure, temperature and thickness of plate structures. It also establishes the knowledge base necessary for future sensor design. Thermal-Acousto Photonic Non-Destructive Evaluation (TAP-NDE) is employed to remotely initiate and acquire interrogating ultrasonic waves. Parameters including pressure, temperature and plate thickness are determined through exploring the dispersion features of the interrogating waves. A theoretical study is performed, through which a modified wave propagation theory applicable to homogeneous, isotropic, linear elastic materials is formulated along with an associated numerical model. A numerical scheme for solving the model is also developed using FEMLAB, a finite element based PDE solver. Gabor Wavelet Transform (GWT) is employed to map numerical time waveforms into the joint time-frequency domain. Wave time-frequency information enables dispersion curves to be extracted and material pressure, temperature and thickness to be determined. A sensor configuration design integrating the wave generation and sensing components of the proven TAP-NDE technology is also developed. Conclusions of the research are drawn from wave dispersion obtained corresponding to the following ranges of parameters: 300-500kHz for frequency, 25-300oC for temperature, 1-3mm for plate thickness, and 6 10 1?? - 7 1 10 ?? N/m for pressure. Each of the three parameters considered in the study has a different level of impact on plate wave dispersion. Plate thickness is found to have the most impact on wave dispersion, followed by temperature of the plate. The effect attributable to pressure is the least prominent among the three parameters considered. Plate thickness and temperature can be readily measured while simultaneously resolved using dispersion curves. However, pressure variation can only be differentiated when the plate is smaller than 1mm in thickness. It is observed that the thicker the plate, the faster the frequency group velocity. Also, the group velocities of all frequency components considered are seen to increase with increasing temperature, but decrease with increasing pressure.

Understanding and modeling seismic wave propagation is important in regional and exploration seismology. Ray tracing is a powerful and popular method for this purpose. Wavefront construction (WFC) method handles wavefronts instead of individual rays, thereby controlling proper ray density on the wavefront. By adaptively controlling rays over a wavefront, it efficiently models wave propagation. Algorithms for a quasi-P wave wavefront construction method and a new coordinate system used to generate wavefront construction mesh are proposed and tested for numerical properties and modeling capabilities. Traveltimes, amplitudes, and other parameters, which can be used for seismic imaging such as migrations and synthetic seismograms, are computed from the wavefront construction method. Modeling with wavefront construction code is applied to anisotropic media as well as isotropic media. Synthetic seismograms are computed using the wavefront construction method as a new way of generating synthetics. To incorporate layered velocity models, the model based interpolation (MBI) ray tracing method, which is designed to take advantage of the wavefront construction method as well as conventional ray tracing methods, is proposed and experimental codes are developed for it. Many wavefront construction codes are limited to smoothed velocity models for handling complicated problems in layered velocity models and the conventional ray tracing methods suffer from the inability to control ray density during wave propagation. By interpolating the wavefront near model boundaries, it is possible to handle the layered velocity model as well as overcome ray density control problems in conventional methods. The test results revealed this new method can be an effective modeling tool for accurate and effective computing.

Predicting performance metrics for the next-generation of multi-mode and multi-antenna wireless communication systems demands site-specific knowledge of the wireless channel's underlying radio wave propagation mechanisms. This thesis describes the first measurement system capable of characterizing individual propagation mechanisms in situ. The measurement system merges a high-resolution spatio-temporal wireless channel sounder with a new field reconstruction technique to provide complete knowledge of the wireless channel's impulse response throughout a 2-dimensional region. This wealth of data may be combined with space-time filtering techniques to isolate and characterize individual propagation mechanisms. The utility of the spatio-temporal measurement system is demonstrated through a measurement-based investigation of diffraction around building corners. These measurements are combined with space-time filtering techniques and a new linear wedge diffraction model to extract the first semi-mpirical diffraction coefficient. Specific contributions of this thesis are: * The first ultra-wideband single-input multiple-output (SIMO) channel sounder based upon the sliding correlator architecture. * A quasi 2-dimensional field reconstruction technique based upon a conjoint cylindrical wave expansion of coherent perimeter measurements. * A wireless channel ``filming' technique that records the time-domain evolution of the wireless channel throughout a 2-dimensional region. * High-resolution measurements of the space-time wireless channel near a right-angled brick building corner. * The application of space-time filtering techniques to isolate the edge diffraction problem from the overall wireless channel. * An approximate uniform geometrical theory of diffraction (UTD)-style linear model describing diffraction by an impedance wedge. * The first-ever semi-empirical diffraction coefficient extracted from in situ measurement data. This thesis paves the way for several new avenues of research. The comprehensive measurement data provided by channel "filming" will enable researchers to develop and implement powerful space-time filtering techniques that facilitate measurement-based investigations of radio wave propagation. The measurement procedure described in this thesis may be adapted to extract realistic reflection and rough-surface scattering coefficients. Finally, exhaustive measurements of individual propagation mechanisms will enable the first semi-empirical propagation model that integrates empirical descriptions of propagation mechanisms into a UTD-style mechanistic framework.

Bloch analysis was originally developed by Felix Bloch to solve Schrödinger's equation for the electron wave function in a periodic potential field, such as that found in a pristine crystalline solid. His method has since been adapted to study elastic wave propagation in periodic structures. The absence of a rigorous mathematical analysis of the approach, as applied to periodic structures, has resulted in mistreatment of internal forces and misapplication to nonlinear media. In this thesis, we detail a mathematical basis for Bloch analysis and thereby shed important light on the proper application of the technique. We show conclusively that translational invariance is not a proper justification for invoking the existence of a "propagation constant," and that in nonlinear media this results in a flawed analysis. Next, we propose a general framework for applying Bloch analysis in damped systems and investigate the effect of damping on dispersion curves. In the context of Schrödinger's equation, damping is absent and energy is conserved. In the damped setting, application of Bloch analysis is not straight-forward and requires additional considerations in order to obtain valid results. Results are presented in which the approach is applied to example structures. These results reveal that damping may introduce wavenumber band gaps and bending of dispersion curves such that two or more temporal frequencies exist for each dispersion curve and wavenumber. We close the thesis by deriving conditions which predict the number of wavevectors at each frequency in a dispersion relation. This has important implications for the number of nearest neighbor interactions that must be included in a model in order to obtain dispersion predictions which match experiment.

Thesis (M.S.)--Brigham Young University. Dept. of Electrical and Computer Engineering, 2004. / Includes bibliographical references (p. 145-154).

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Dr. Michael Leamy; Committee Member: Dr. Karim Sabra; Committee Member: Dr. Aldo Ferri. Part of the SMARTech Electronic Thesis and Dissertation Collection.

The imaging of the interior of the Earth using ground motion data, or seismic tomography, has been a subject of great interest for over a century. The full elastic wave equations are not typically used in standard tomography codes. Instead, the elastic waves are idealized as rays and only phase velocity and travel times are considered as input data. This results in the inability to resolve features which are on the order of one wavelength in scale. To overcome this problem, models which use the full elastic wave equation and consider total seismograms as input data have recently been developed. Unfortunately, those methods are much more computationally expensive and are only in their infancy. While the finite element method is very popular in many applications in solid mechanics, it is still not the method of choice in many seismic applications due to high pollution error. The pollution effect creates an increasing ratio of discretization to best approximation error for problems with increasing wave numbers. It has been shown that standard finite element methods cannot overcome this issue. To compensate, the meshes for solving high wave number problems in seismology must be increasingly refined, and are computationally infeasible due to the large scale requirements. A new generalized least squares method was recently introduced. The main idea is to select test spaces such that the discrete problem inherits the stability of the continuous problem. In this dissertation, a discontinuous Petrov-Galerkin method with optimal test functions for 2D time-harmonic seismic tomography problems is developed. First, the abstract DPG framework and key results are reviewed. 2D DPG methods for both static and time-harmonic elasticity problems are then introduced and results indicating the low-pollution property are shown. Finally, a matrix-free inexact-Newton method for the seismic inverse problem is developed. To conclude, results obtained from both DPG and standard continuous Galerkin discretization schemes are compared and the potential effectiveness of DPG as a practical seismic inversion tool is discussed. / text

The research described in this dissertation undertakes a computational study of wave motion due to ground excitation in layered soil media. Adjustments of soil properties consistent with the level of deformation is applied using an equivalent linear approach. The finite element method provides the basis of the numerical procedure for soil-structure system response calculation in conjunction with a first-order perturbation scheme. Available experimental data are employed for shear-modulus and damping adjustments. The findings of the research are expected to lead to efficient calculation of structural response to earthquake ground motion. / text

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D. Tech. Mathematical Technology. / Investigates hyperbolic and pseudohyperbolic equations and the results are applied to higher-order rod approximations for the propagation of the longitudinal stress waves in elastic rods. The main objectives of this thesis are: 1. Provide a unified approach to the derivation of the families of one-dimensional hyperbolic differential equations simultaneously with the associated natural and essential boundary conditions describing longitudinal vibration of finite length rods. 2. Establish a new theoremto shorten the derivation of equations of motion and the corresponding boundary conditions, modelling longitudinal wave propagation in the rod. 3. Prove that, when deriving the higher-order rod equations, the lower-order are still included, thus increasing the number of deformations in the rod or the accuracy of the model. 4. Provide mathematical tools for the classification of the obtained equations. 5. Compare the accuracy of the above-mentioned vibration theories in elastic rods based on the investigation of their frequency spectrums which are not available in the literature. 6. Show how two of the above vibration theories, the Rayleigh-Bishop and Mindlin-Herrmann theories, can be applied to predict wave propagation in a piezoelectric circular cylinder and isotropic conical rod. In both cases a numerical example is given as a simulation of the solution.7. Find general methods for solving problems of longitudinal vibration of finite length rods for all of the above-mentioned theories.