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.

Models, modelling and control design play important parts in automatic control. The contributions in this thesis concern topics in all three of these concepts. The poles are of fundamental importance when analyzing the behaviour of a system, and pole placement is an intuitive and natural approach for control design. A novel parameterization for state feedback gains for pole placement in the linear multiple input case is presented and analyzed. It is shown that when the open and closed loop poles are disjunct, every state feedback gain can be parameterized. Other properties are also investigated. Hammerstein models have a static non-linearity on the input. A method for exact compensation of such non-linearities, combined with introduction of integral action, is presented. Instead of inversion of the non-linearity the method utilizes differentiation, which in many cases is simpler. A partial differential equation (PDE) can be regarded as an infinite order model. Many model based control design techniques, like linear quadratic Gaussian control (LQG), require finite order models. Active damping of vibrations in a viscoelastic beam, modelled as a PDE, is considered. The beam is actuated by piezoelectric elements and its movements are measured by strain gauges. LQG design is used, for which different finite order models, approximating the PDE model, are constructed. The so obtained controllers are evaluated on the original PDE model. Minimization of the measured strain yields a satisfactory performance, but minimization of transversal deflection does not. The effect of the model accuracy of the finite order model approximations is also investigated. It turns out that a model with higher accuracy in a specified frequency interval gives controllers with better performance. The wave equation is another PDE. A PDE model, with one spatial dimension, is established. It describes wave propagation in a tube perforated with helical slots. The model describes waves of both extensional and torsional type, as well as the coupling between the two wave types. Experimental data are used for estimation of model parameters, and for assessment of the proposed model in two different cases. The model is found adequate when certain geometrical assumptions are valid.

The primary objective of this thesis was to gain a deeper understanding of acoustic wave propagation in phononic crystals, particularly those that include materials whose properties can be varied periodically in time. This research was accomplished in three ways. First, a 2D phononic crystal was designed, created, and characterized. Its properties closely matched those determined through simulation. The crystal demonstrated band gaps, dispersion, and negative refraction. It served as a means of elucidating the practicalities of phononic crystal design and construction and as a physical verification of their more interesting properties. Next, the transmission matrix method for analyzing 1D phononic crystals was extended to include the effects of time-varying material parameters. The method was then used to provide a closed-form solution for the case of periodically time-varying material parameters. Some intriguing results from the use of the extended method include dramatically altered transmission properties and parametric amplification. New insights can be gained from the governing equations and have helped to identify the conditions that lead to parametric amplification in these structures. Finally, 2D multiple scattering theory was modified to analyze scatterers with time-varying material parameters. It is shown to be highly compatible with existing multiple scattering theories. It allows the total scattered field from a 2D time-varying phononic crystal to be determined. It was shown that time-varying material parameters significantly affect the phononic crystal transmission spectrum, and this was used to switch an incident monochromatic wave. Parametric amplification can occur under certain circumstances, and this effect was investigated using the closed-form solutions provided by the new 1D method. The complexity of the extended methods grows logarithmically as opposed linearly with existing methods, resulting in superior computational complexity for large numbers of scatterers. Also, since both extended methods provide analytic solutions, they may give further insights into the factors that govern the behaviour of time-varying phononic crystals. These extended methods may now be used to design an active phononic crystal that could demonstrate new or enhanced properties.

The primary objective of this thesis was to gain a deeper understanding of acoustic wave propagation in phononic crystals, particularly those that include materials whose properties can be varied periodically in time. This research was accomplished in three ways. First, a 2D phononic crystal was designed, created, and characterized. Its properties closely matched those determined through simulation. The crystal demonstrated band gaps, dispersion, and negative refraction. It served as a means of elucidating the practicalities of phononic crystal design and construction and as a physical verification of their more interesting properties. Next, the transmission matrix method for analyzing 1D phononic crystals was extended to include the effects of time-varying material parameters. The method was then used to provide a closed-form solution for the case of periodically time-varying material parameters. Some intriguing results from the use of the extended method include dramatically altered transmission properties and parametric amplification. New insights can be gained from the governing equations and have helped to identify the conditions that lead to parametric amplification in these structures. Finally, 2D multiple scattering theory was modified to analyze scatterers with time-varying material parameters. It is shown to be highly compatible with existing multiple scattering theories. It allows the total scattered field from a 2D time-varying phononic crystal to be determined. It was shown that time-varying material parameters significantly affect the phononic crystal transmission spectrum, and this was used to switch an incident monochromatic wave. Parametric amplification can occur under certain circumstances, and this effect was investigated using the closed-form solutions provided by the new 1D method. The complexity of the extended methods grows logarithmically as opposed linearly with existing methods, resulting in superior computational complexity for large numbers of scatterers. Also, since both extended methods provide analytic solutions, they may give further insights into the factors that govern the behaviour of time-varying phononic crystals. These extended methods may now be used to design an active phononic crystal that could demonstrate new or enhanced properties.