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

Elastic Wave propagation in structures with irregular boundaries is studied by transforming the plates with irregular surfaces to sinusoidal wave-guides. Guided elastic wave in a two-dimensional periodically corrugated plate is studied analytically. The plate material is considered as homogeneous, isotropic and linearly elastic. In a periodically corrugated wave-guide, all possible spectral orders of wave numbers are considered. The dispersion equation is obtained by applying the traction free boundary conditions at the two surfaces. The analysis is carried out in the wave-number domain for both symmetric and anti-symmetric modes. Non-propagating 'stop bands' and propagating 'pass bands' are investigated. Experimental analyses with two different pairs of transducers are also performed and compared with the results from the mathematical analysis. Newly developed semi-analytical DPSM technique has been also adopted in this dissertation to model the ultrasonic field in sinusoidally corrugated plate. Distributed Point Source Method (DPSM) is gradually gaining popularity in the field of Non-Destructive Evaluation (NDE). DPSM can be used to calculate the ultrasonic field (pressure, velocity and displacement in a fluid or stress and displacement in a solid) generated by ultrasonic transducers. So far the technique has been used to model ultrasonic field in homogeneous or multilayered fluid structures. In this dissertation the method is extended to model the ultrasonic field generated in both fluid and solid media. The Prime objective of using DPSM technique in this dissertation is to model the ultrasonic field generated in the corrugated wave guide. This method has never been used to model ultrasonic field in solids. Development of stress and displacement Green's functions in solids are presented. In addition to the wave propagation problem in the sinusoidal wave guide, a few unsolved problems such as ultrasonic field generated by bounded acoustic beams in multilayered fluid structures, near a fluid-solid interface and in flat solid isotropic plates are also presented in this dissertation.

Several previous studies, including one using early Sanae radar data, have found examples of high speed ionospheric plasma flows on the nightside, mapping to the magnetospheric tail, during periods which were magnetically quiet. These high speed flows were interpreted to be associated with the release of energy from a rapid reconfiguration of tail magnetic field lines due to reconnection. Such events are now known as ‘TRINNIs’ or ‘tail reconnection during IMF northward, non-substorm intervals’. The purpose of this study was to identify further TRINNI events, using SuperDARN data from both hemispheres. In situations where the y-component of the Interplanetary Magnetic Field dominates over the z-component, the directions of both the high speed flows and the underlying convection pattern depend on the direction of the y-component. Some examples of likely TRINNI events for cases where the y-component was positive and negative are presented and discussed. The assumption of a non-substorm interval is justified by magnetometer and GOES satellite data, and the observations are discussed in relation to magnetic reconnection in the magnetotail. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2010.

The performance of astronomical interferometer arrays operating at (sub) millimeter wave-lengths is seriously compromised by rapid variations of atmospheric water vapour content that distort the phase coherence of incoming celestial signals. Unless corrected, these phase distortions, which vary rapidly with time and from antenna to antenna, seriously compromise the sensitivity and image quality of these arrays. Building on the success of a prototype infrared radiometer for millimeter astronomy (IRMA I), which was ued to measure atmospheric water vapour column abundance, this thesis presents results from a second generation radiometer (IRMA II) operating at the James Clerk Maxwell Telescope (JCMT) on Mauna Kea, Hawaii from December, 2000 to March, 2001. These results include comparisons with other measures of water vapour abundance available on the summit of Mauna Kea and a comparison with a theorteical curve-of-growth calculated from a new radiative transfer model, ULTRAM, developed specifically for the purpose. Plans for a third generation radiometer (IRMA III) are also be discussed. / xii, 143 leaves : ill. ; 28 cm.

Honeycomb core sandwich panels are widely used in the aeronautic industry due to their excellent flexural stiffness to weight ratio. Generally, classical homogenized model is used to model honeycomb core sandwiches in order to have an efficient but not expensive numerical modeling. However, previous works have shown that, while the homogenized models could correctly represent the membrane waves' behavior of sandwiches in a large frequency range, they could not give satisfying simulation results for the flexural waves' behavior in the high frequency range (HF). In fact, the honeycomb core layer plays an important role in the propagation of the flexural waves, so that when the involved wavelengths become close to the characteristic lengths of honeycomb cells, the cellular microstructure starts interacting strongly with the waves and its effect should no longer be neglected, which is unfortunately not the case of the homogenized models. In the present work, we are interested in improving the theoretical and numerical analysis of HF elastic waves' propagation in honeycomb core sandwich panels by a numerical approach based on the Bloch wave theorem, which allows taking into account the periodic characteristics of the honeycomb core. In fact, by decomposing non-periodic wave solutions into their periodic Bloch wave basis modes, numerical models are defined on a basic cell and solved in a efficient way, and provide a better description and so a better understanding of the interaction between HF wave propagation phenomena and the periodic structures. Our numerical approach is developed and validated in the cases of one-dimensional periodic beam structures, of two-dimensional periodic hexagonal and rectangular beam structures and of honeycomb core sandwich plates. By solving the eigenvalue problem of the Bloch wave modes in one primitive cell of the periodic structure for all the wave vectors located in the corresponding first Brillouin zone in the phase space, the dispersion relation between the wave vector and the eigenvalue is calculated. The analysis of the dispersion relation provides important results such as: the frequency bandgaps and the anisotropic and dispersive characteristics of periodic structures, the comparison between the first Bloch wave modes to those of the classical equivalent homogenized models and the existence of the retro-propagating Bloch wave modes with a negative group velocity.

The main objective of the research is to study the potential application of carbon nanotubes and graphene sheets as nano-resonator sensors in the detection of atoms/molecules with vibration and wave propagation analyses. It is also aimed to develop and examine new methods in the design of nano-resonator sensors for differentiating distinct gas atoms and different macromolecules, such as DNA molecules. The hypothesis in the detection techniques is that atoms or molecules attached on the surface of the nano-resonator sensors would induce a recognizable shift in the resonant frequency of or wave velocity in the sensors. With this regard, a sensitivity index based on the shift in resonant frequency of the sensors in the vibration analysis and/or a shift in wave velocity in the sensors in the wave propagation analysis is defined and examined. In order to achieve the objective, the vibration characteristics of carbon nanotubes and graphenes are studied using molecular dynamics simulations to first propose nano-resonator sensors, which are able to differentiate distinct gas atoms with high enough resolutions even at low concentration. It is also indicated that the nano-resonator sensors are effective devices to identify different genes even with the same number of nucleobases in the structure of single-strand DNA macromolecules. The effect of various parameters such as size and restrained boundary conditions of the sensors, the position of attached atoms/molecules being detected, and environment temperature on the sensitivity of the sensors is investigated in detail. Following the studies on vibration-based sensors, the wave propagation analysis in carbon nanotubes and graphene sheets is first investigated by using molecular dynamics simulations to design nano-resonator sensors. Moreover, a nonlocal finite element model is presented and calibrated for the first time to model propagation of mechanical waves in graphene sensors attached with atoms through a verification process with atomistic results. The simulation results reveal that the nano-resonator sensors are able to successfully detect distinct types of noble gases with the same mass density or at the same environmental condition of temperature and pressure.

The majority of commercially available ultrasonic transducers used to excite and measure wave propagation in structures can be coupled only to a free surface. While convenient, this method is likely to excite multiple structural modes, making data interpretation difficult. Furthermore, the many modes excited make predicting the structure’s response a computationally intensive task. Here the dynamic radial displacement induced by a transient radial point load is calculated at more than 230,000 points on the outer surface of a virgin steel pipe to simulate a typical experiment. The radial component of the displacement field is calculated by convolving the Green’s functions of the pipe with the transient load. These functions are calculated on personal computers (in a distributed arrangement) by employing modal summation. The mode shapes are obtained from a Semi-Analytical Finite Element formulation used in conjunction with a separation of variables. The results are presented in a four dimensional animation, providing easier interpretations and insight into how to best select observation points for the detection of defects. The accuracy of the calculated displacements is verified experimentally. Agreement is good when magnitude and phase corrections are incorporated from the frequency response curves of the transducers used.

The present work focuses on the numerical resolution of the acoustic or elastic wave equation in a piece-wise homogeneous medium, splitted by interfaces. We are interested in a high-frequency setting, introduced by strongly oscillating initial conditions, for which one computes the distribution of the energy density by a so-called kinetic approach (based on the use of a Wigner transform). This problem then reduces to a Liouville-type transport equation in a piece-wise homogeneous medium, supplemented by reflection and transmission laws at the interfaces. Several numerical techniques and ranges of application are also reviewed. The transport equation which describes the evolution of the energy density in the phase space positions _ wave vectors is numerically solved by finite differences. This technique raises several difficulties related to the conservation of the total energy in the medium and at the interfaces. They may be alleviated by dedicated numerical schemes allowing to reduce the numerical dissipation by either a global or a local approach. The improvements presented in this thesis concern the interpolation of the energy densities obtained by transmission on the grid of discrete wave vectors, and the correction of the difference of variation scales of the wave celerity on each side of the interfaces. The interest of the foregoing developments is to obtain conservative schemes that also satisfy the usual convergence properties of finite difference methods. The construction of such schemes and their effective implementation constitute the main achievement of the thesis. The relevance of the proposed methods is illustrated by several numerical simulations, that also emphasize their efficiency for rather coarse meshes.