A phase-space asymptotic approach to wave propagation in homogeneous dispersive and dissipative media is discussed which has several advantages by comparison to conventional techniques, such as the stationary phase method, ordinary ray tracing, etc. This approach, which is based on the wave-kinetic theory [1,2], is used to examine in detail three types of one-dimensional canonic dispersive and dissipative media: cubic dispersive and quadratic dissipative, cubic dispersive and quartic dissipative, quintic dispersive and quartic dissipative. Purely dissipative media are also investigated. The analysis is also carried out using standard Fourier techniques for comparison purposes. For an arbitrary medium, exact solutions are impossible. Approximations must be made which give rise to new basic functions defined in integral form. The method of steepest descents [3], the WKB method [4], the method of dominant balance [4] and the FORMAC73 language [5] are utilized to find asymptotic series for these functions. / M.S.

The characteristics of carbon fiber composites have enabled these materials to be accepted as replacements for metal parts in industry. However, due to their unsymmetrical material properties, carbon fiber composites are susceptible to damage, such as a delamination, which can cause premature failure in the structure. This has resulted in the need for nondestructive testing methods that can provide quick, reliable results so that these parts can be tested while in service. In this study, an approach was examined that involved a pencil lead break to excite multiple wave modes in a composite plate in an effort to identify key characteristics based on the wavespeed and frequency. These characteristics were then compared to models based on boundary conditions to generate dispersion curves using the transfer matrix method for whole composite plates that were either undamaged or damaged. To first test this approach, experiments were performed on multilayer isotropic plates and then on a composite plate. The results for all cases showed that modes could be excited by the pencil lead break in the undamaged region of the plates that were not theoretical possible in a delaminated region. Also modes that were specific to the delaminated region were excited and this allowed for a clear comparison between the two regions. This approach could be placed into practice to provide routine testing to detect delamination for in-service, carbon fiber composite parts. / Master of Science / The physical properties of high strength and low weight and the economic benefits of carbon fiber composites has resulted in these materials replacing metals in several industries. It is important, however, to be aware that the change in materials used impacts the different types of damage composites experience compared to conventional metals. One type of damage that could cause a composite part to fail is a delamination or a separation of layers. In order to identify if this damage has occurred, it is beneficial to have an inspection technique that will not damage the part. In this study, a technique was tested that involved breaking a piece of pencil lead on a plate in order to generate multiple wave modes that would propagate in the plate. Based on boundary conditions caused by the damage in the plate, the speed of the wave and frequency content could be compared to an undamaged plate to identify a delamination. A model was created to compare experimental results and demonstrated that using wavespeed and frequency could identify a delamination. The experimental results compared well with the model dispersion curves for a plate with and without a delamination suggesting this approach could be placed into practice to provide routine testing to detect delamination for in-service, carbon fiber composite parts.

No description available.

The analysis of wave propagation in solids with complex microstructures, and local heterogeneities finds extensive applications in areas such as material characterization, structural health monitoring (SHM), and metamaterial design. Within continuum mechanics, sources of heterogeneities are typically associated to localized defects in structural components, or to periodic microstructures in phononic crystals and acoustic metamaterials. Numerical analysis often requires computational meshes which are refined enough to resolve the wavelengths of deformation and to properly capture the fine geometrical features of the heterogeneities. It is common for the size of the microstructure to be small compared to the dimensions of the structural component under investigation, which suggests multiscale analysis as an effective approach to minimize computational costs while retaining predictive accuracy. This research proposes a multiscale framework for the efficient analysis of the dynamic behavior of heterogeneous solids. The developed methodology, called Geometric Multiscale Finite Element Method (GMsFEM), is based on the formulation of multi-node elements with numerically computed shape functions. Such shape functions are capable to explicitly model the geometry of heterogeneities at sub-elemental length scales, and are computed to automatically satisfy compatibility of the solution across the boundaries of adjacent elements. Numerical examples illustrate the approach and validate it through comparison with available analytical and numerical solutions. The developed methodology is then applied to the analysis of periodic media, structural lattices, and phononic crystal structures. Finally, GMsFEM is exploited to study the interaction of guided elastic waves and defects in plate structures.

Wave induced electron precipitation (WIEP) can modify the ionosphere above a sub-ionospherically propagating VLF signal in such a way as to perturb the amplitude and phase of the signal: The "Trimpi Event". In this thesis trimpi events are used in a study of WIEP events and in the responsible mechanism: The gyroresonant interaction. Trimpi activity at middle latitudes (SANAE, Antarctica, L = 4.02) and low latitudes (Durban, RSA , L = 1.69) together with the corresponding theory for the gyroresonant interaction is examined and compared. A newly developed computerised system for the detection and analysis of trimpi events has been developed in Durban. This system has been used to analyse tape data recorded at SANAE. Trimpi events were found on various transmitter paths to SANAE and a complete study of 1982 data has led to the establishment of trimpi characteristics as seen at SANAE: an absence of positive events and causative whistlers, a preference for short duration events (t < 25s), the occurrence of some very large events (up to 90% signal attenuation) , two minima in occurrence near 0015 and 0400 h Local Time, low occurrence and occurrence rate of events and evidence that interactions with non-ducted whistlers are of importance. The computerised sytem was then extended to collect data at Durban simultaneously from up to 20 transmitters worldwide. Examination of data from this survey showed very low occurrence rates of trimpis but yielded some daytime events for which the effectiveness of the gyroresonance interaction, which successfully explains the trimpi event at middle and low latitudes, had to be questioned. Thus a fully relativisic test particle simulation of the gyroresonant interaction was used to examine the effectiveness of gyroresonance at low L for producing trimpi events. This simulation was run for a wide range of interaction parameters and yielded the following constraints for effective pitch angle scattering (and hence precipitation) of electrons at low L: wave intensities in excess of 150 nT, wave frequencies in excess of 10 kHz and background electron densities at least one order of magnitude higher than normal. First data from the OMSKI project, a sophisticated VLF receiver operated at Durban as part of an international project, shows further evidence of low-latitude trirmpi activity. A survey of one month's continuous data is presented. In face of the evidence that trimpi events that occur at low L have the same signature as those at middle L but that the standard gyroresonance interaction is insufficient to cause them, alternate scenarios that could enhance the interaction were sought. In particular distortions in the ambient magnetic field (eg. PC-5 pulsations) were modelled using a new dipole-like background field model. This simulation showed that distortions which tend to reduce magnetic field curvature along field lines can significantly enhance the gyroresonant conditions and hence the interaction. A new set of conditions for effective gyroresonance at low L is thus established and contrasted with the more lenient conditions at middle L. A study of "frequency tracking" as a means to prolong resonance showed that natural whistlers do not posess the required frequency /time characteristics for this mechanism, and that artificial waves in a narrow range around the equatorial resonance frequency would ~ well suited for this purpose. An overview of the status of worldwide Trimpi detection networks together with the S.P.R.I. 's role in this regard is presented. / Thesis (Ph.D.)-University of Natal, Durban, 1991.

This study extends a recently-developed [1] cellular automata (CA) elastodynamic modeling approach to arbitrary two-dimensional geometries through development of a rule set appropriate for triangular cells. The approach is fully object-oriented (OO) and exploits OO conventions to produce compact, general, and easily-extended CA classes. Meshes composed of triangular cells allow the elastodynamic response of arbitrary two-dimensional geometries to be computed accurately and efficiently. As in the previous rectangular CA method, each cell represents a state machine which updates in a stepped-manner using a local "bottom-up" rule set and state input from neighboring cells. The approach avoids the need to develop partial differential equations and the complexity therein. Several advantages result from the method's discrete, local and object-oriented nature, including the ability to compute on a massively-parallel basis and to easily add or subtract cells in a multi-resolution manner. The extended approach is used to generate the elastodynamic responses of a variety of general geometries and loading cases (Dirichlet and Nuemann), which are compared to previous results and/or comparison results generated using the commercial finite element code, COMSOL. These include harmonic interior domain loading, uniform boundary traction, and ramped boundary displacement. Favorable results are reported in all cases, with the CA approach requiring fewer degrees of freedom to achieve similar or better accuracy, and considerably less code development.

Thesis (M. Phil.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 148-154).

The ionosphere is an important factor in high frequency (HF) radio propagation providing an opportunity to study ionospheric variability as well as the space weather conditions under which HF communication can take place. This thesis presents the validation of HF propagation conditions for the Ionospheric Communication Enhanced Profile Analysis and Circuit (ICEPAC) and Advanced Stand Alone Prediction System (ASAPS) models over Africa by comparing predictions with the measured data obtained from the International Beacon Project (IBP). Since these models were not developed using information on the African region, a more accurate HF propagation prediction tool is required. Two IBP transmitter stations are considered, Ruaraka, Kenya (1.24°S, 36.88°E) and Pretoria, South Africa (25.45°S, 28.10°E) with one beacon receiver station located in Hermanus, South Africa (34.27°S, 19.l2°E). The potential of these models in terms of HF propagation conditions is illustrated. An attempt to draw conclusions for future improvement of the models is also presented. Results show a low prediction accuracy for both ICEPAC and ASAPS models, although ICEPAC provided more accurate predictions for daily HF propagation conditions. This thesis suggests that the development of a new HF propagation prediction tool for the African region or the modification of one of the existing models to accommodate the African region, taking into account the importance of the African ionospheric region, should be considered as an option to ensure more accurate HF Propagation predictions over this region.

This thesis has two parts: In the first part, we study the dispersion characteristics of structural-acoustic waveguides by obtaining closed-form solutions for the coupled wave numbers. Two representative systems are considered for the above study: an infinite two-dimensional rectangular waveguide and an infinite fluid- filled orthotropic circular cylindrical shell. In the second part, these asymptotic expressions are used to study the nonlinear wave propagation in the same two systems. The first part involves obtaining asymptotic expansions for the fluid-structure coupled wave numbers in both the systems. Certain expansions are already available in the literature. Hence, the gaps in the literature are filled. Thus, for cylindrical shells even in vacuo wavenumbers are obtained as part of the objective. Here, singular and regular perturbation methods are used by taking the thickness parameter as the asymptotic parameter. Valid wavenumber expressions are obtained at all the frequencies. A transition in the behavior of the flexural wavenumbers occurs in the neighborhood of the ring frequency. This frequency of transition is identified for the orthotropic shells also. The closed-form expressions for the orthotropic shells are obtained in the limit of slight orthotropy for the circumferential orders n > 0 at all the frequency ranges. Following this, we derive the coupled wavenumber expressions for the two systems for an arbitrary fluid loading. Here, the two-dimensional rectangular waveguide is considered first. This rectangular waveguide has a one-dimensional plate and a rigid surface as its lateral boundaries. The effects due to the structural boundary are studied by analyzing the phase change due to the structure on an incident plane wave. The complications due to the cross-sectional modes are eliminated by ignoring the presence of the other rigid boundary. Dispersion characteristics are predicted at various regions of the dispersion diagram based on the phase change. Moreover, the also identified. Next, the rigid boundary is considered and the coupled dispersion relation for the waveguide is solved for the wavenumber expressions. The coupled wavenumbers are obtained as the coupled rigid-duct, the coupled structural and the coupled pressure-release wavenumbers. Next, based on the above asymptotic analysis on a two-dimensional rectangular waveguide, the asymptotic expansions are obtained for the coupled wavenumbers in isotropic and orthotropic fluid- filled cylindrical shells. The asymptotic expansions of the wavenumbers are obtained without any restriction on the fluid loading. They are compared with the numerical solutions and a good match is obtained. In the second part or the nonlinear section of the thesis, the coupled wavenumber expressions are used to study the propagation of small but a finite amplitude acoustic potential in the above structural-acoustic waveguides. It must be mentioned here that for the rst time in the literature, for a structural-acoustic system having a contained fluid, both the structure and the acoustic fluid are nonlinear. Standard nonlinear equations are used. The focus is restricted to non-planar modes. The study of the cylindrical shell parallels that of the 2-D rectangular waveguide, except in that the former is more practical and complicated due to the curvature. Thus, with regard to both systems, a narrow-band wavepacket of the acoustic potential centered around a frequency is considered. The approximate solution of the acoustic velocity potential is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that the amplitude modulation is governed by the Nonlinear Schr•odinger equation (NLSE). The nonlinear term in the NLSE is analyzed, since the sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. This sign change is predicted using the coupled wavenumber expressions. Secondly, at specific frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonic. This happens when the phase speeds of the waves match. The frequencies of such interactions are identified, again using the coupled wavenumber expressions. The novelty of this work lies firstly in considering nonlinear acoustic wave prop-agation in nonlinear structural waveguides. Secondly, in deriving the asymptotic expansions for the coupled wavenumbers for both the two-dimensional rectangular waveguide and the fluid- filled circular cylindrical shell. Then in using the same to study the behavior of the nonlinear term in NLSE. And lastly in identifying the frequencies of nonlinear interactions in the respective waveguides.

We study noise from wind turbines while taking irregular terrain and non-constant atmosphere into consideration. We will show that simulating the distribution of 3D acoustic waves can be done by using only low frequencies, thus reducing the computational complexity significantly.