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.

<p>Mechanical oscillators form the primary structure of a wide variety of devices including energy harvesters and vibration absorbers, and also have parallel systems in electrical fields for signal processing. In the area of wave propagation, recent study in periodic chains have focused on active tuning methods to control bandgap regions, bands in the frequency response in which no propagating wave modes exist. In energy harvesting, several coupled systems have been proposed to enhance the peak power or bandwidth of a single harvester through arrays or dynamic magnification. Though there are applications in several fields, the work in this dissertation can all fit into the category of coupled non-linear oscillators. In each sub-field, this study demonstrates means to advance state of the art techniques by adding nonlinearity to a coupled system of linear oscillators, or by adding a coupled device to a nonlinear oscillator.</p><p>The first part of this dissertation develops the analytical methods for studying wave propagation in nonlinear systems. A framework for studying rotational systems is presented and used to design an testbed for wave propagation experiments using a chain of axially aligned pendulums. Standard analytical methods are also adapted to allow uncertainty analysis techniques to provide insight into the relative impact of variations in design parameters. Most analytical insight in these systems is derived from a linearlized model and assumes low amplitude oscillations. Additional study on the nonlinear system is performed to analyze the types of deviations from this behavior that would be expected as amplitudes increase and nonlinear effects become more prominent.</p><p>The second part of this dissertation describes and demonstrates the first means of passive control of bandgap regions in a periodic structure. By imposing an asymmetrical bistability to an oscillator in each unit cell, it is analytically shown that each potential well has different wave propagation behaviors. Experimental demonstrations are also provided to confirm the simulated results.</p><p>The final section performs analytical and numerical analysis of a new system design to improve the performance of a nonlinear energy harvester by adding an excited dynamic magnifier. It is shown that this addition results in higher peak power and wider bandwidth than the uncoupled harvester. Unlike standard dynamic magnifiers, this performance does not come at the expense of power efficiency, and unlike harvester arrays, does not require the added cost of multiple energy harvesters.</p> / Dissertation

Recently, there is emerging interests in deploying wireless sensor networks in forests for applications such as forest fire detection, environmental monitoring and remote surveillance. One challenge in the design of such networks is to ensure reliable communication between sensors located near the ground and over short distances. However, the propagation mechanisms in this type of scenario are complex and not well understood. Furthermore, the design of antennas that can exploit the resulting propagation mechanisms for optimal power transfer remains an open question. The objective of this dissertation is to understand wave propagation and antenna radiation in forested environments in the HF/VHF frequency range. To achieve this objective, several forest scaled models are introduced. The first scaled forest model is a periodic metal cut-wire array. The transmission data inside the cut-wire array are simulated and measured. The propagation mechanisms inside the array are extracted. Several interesting propagation phenomena associated with surface waves and leaky waves are observed and explained. Next, a dielectric rod array consisting of water-filled straws is investigated as a more realistic forest model. Water is chosen since its dielectric constant in the microwave range is close to that of tree trunks in the HF/VHF frequencies. The propagation mechanisms in the water rod array are investigated through scaled model measurements in the laboratory, numerical simulations and an effective medium theory. Randomization effects due to rod spacing and rod height on the propagation mechanisms are also studied. Finally, the transmission data in a real forest are collected in the HF/VHF frequency range to corroborate the findings from the models. The measurement site is located at Bastrop, Texas. For comparison, the transmission data are also measured in an open field. The transmission data are processed and the resulting propagation mechanisms are extracted and compared with the model predictions. As an extension of the propagation study, the potential to achieve directive antenna radiations in a forest is explored. A simple metal cut-wire array environment is considered for ease in modeling. For the case when both the transmit antenna and the receive antenna are embedded inside the array, two design ideas are presented. The first design tries to couple the antenna radiation into the dominant propagation mechanism through phase matching and the second design uses a closely spaced Yagi array to decouple the antenna from its surrounding medium. For the case when the transmit antenna is embedded inside the array and the receive antenna is located outside the array, the leaky wave mechanism is explored to achieve directive radiation. These designs are verified through theoretical predictions, numerical simulations and prototype measurements. / text