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University of Macau / Faculty of Science and Technology / Department of Mathematics

This thesis presents a theoretical study of thermoelastic guided waves in cylinders in the context of Lord-Shulman generalized theory of thermoelasticity. Two different methods were formulated to study dispersion relations in infinite cylinders. One of them is a Semi Analytical Finite Element (SAFE) method and the other is an analytical method. In the SAFE method, the dispersion equation has been formulated as a generalized eigenvalue problem by treating radial displacement and temperature with a one dimensional finite element model through the thickness of the cylinder. In the analytical method, displacement potentials are introduced to obtain the dispersion relations of guided wave modes. This method is applicable to isotropic cylinders and has been developed primarily to cross check the SAFE formulation. Frequency spectra obtained by both methods for an isotropic cylinder have shown excellent agreement with each other. Since the SAFE method can be used for an anisotropic composite cylinder, guided wave modes for anisotropic and composite cylinders are presented. Transient analysis of ultrasonic guided waves generated by concentrated heating of the outer surface of an infinite anisotropic cylinder has also been studied. The SAFE method is employed to model the response of a cylinder due to a pulsed laser focused on its surface. Green’s functions were constructed numerically by superposition of guided wave modes in frequency and wave number domains. Time histories of the propagating modes are then calculated by applying an inverse Fourier transformation in the time domain. Transient radial displacements of longitudinal and flexural modes of a silicon nitride cylinder are presented. Propagation of thermoelastic waves in finite length circular cylinders have also been investigated. The SAFE method is used to simulate the guided wave modes in the cylinder. Frequency spectra obtained by the SAFE formulation, for a finite length transversely isotropic cylinder, are validated by comparing the numerical results with relevant publications. Frequency spectra for axisymmetric and asymmetric modes in a silicon nitride finite cylinder with both ends insulated and restrained by frictionless rigid walls are presented. The plain strain problem of circumferential guided waves is also studied and the results are validated for an isothermal case.

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This thesis presents a theoretical study of thermoelastic guided waves in cylinders in the context of Lord-Shulman generalized theory of thermoelasticity. Two different methods were formulated to study dispersion relations in infinite cylinders. One of them is a Semi Analytical Finite Element (SAFE) method and the other is an analytical method. In the SAFE method, the dispersion equation has been formulated as a generalized eigenvalue problem by treating radial displacement and temperature with a one dimensional finite element model through the thickness of the cylinder. In the analytical method, displacement potentials are introduced to obtain the dispersion relations of guided wave modes. This method is applicable to isotropic cylinders and has been developed primarily to cross check the SAFE formulation. Frequency spectra obtained by both methods for an isotropic cylinder have shown excellent agreement with each other. Since the SAFE method can be used for an anisotropic composite cylinder, guided wave modes for anisotropic and composite cylinders are presented. Transient analysis of ultrasonic guided waves generated by concentrated heating of the outer surface of an infinite anisotropic cylinder has also been studied. The SAFE method is employed to model the response of a cylinder due to a pulsed laser focused on its surface. Green’s functions were constructed numerically by superposition of guided wave modes in frequency and wave number domains. Time histories of the propagating modes are then calculated by applying an inverse Fourier transformation in the time domain. Transient radial displacements of longitudinal and flexural modes of a silicon nitride cylinder are presented. Propagation of thermoelastic waves in finite length circular cylinders have also been investigated. The SAFE method is used to simulate the guided wave modes in the cylinder. Frequency spectra obtained by the SAFE formulation, for a finite length transversely isotropic cylinder, are validated by comparing the numerical results with relevant publications. Frequency spectra for axisymmetric and asymmetric modes in a silicon nitride finite cylinder with both ends insulated and restrained by frictionless rigid walls are presented. The plain strain problem of circumferential guided waves is also studied and the results are validated for an isothermal case.

Wave models are an integral part of coastal engineering due to their ability to quantify information that is either unobtainable or unavailable. However, these models rely heavily on the input of a directional wave spectrum that describes the variation of energy with frequency and direction. This study investigated how five methods for computing the directional wave spectrum perform within the nearshore spectral wave model, STWAVE. The results of the five experimental runs showed that overall, the greatest differences between spectra were observed in the significant wave height parameter. The mean wave direction showed greater differences at the offshore model domain boundary and lesser differences as the wave enters the nearshore; and the peak period had fewer differences at the boundary, but at the nearshore the differences were dependent upon the presence of wind forcing. Winds had a significant impact on observed differences between the spectra in the domain by dominating the wave field variation.

Thesis (MSc.) -- University of Limpopo, 2018 / A Major concern in the past years was the traditional static spectrum allocation which gave rise to spectrum underutilization and scarcity in wireless networks. In an attempt to solve this problem, cognitive radios technology was proposed and this allows a spectrum to be accessed dynamically by Cognitive radio users or secondary users (SUs). Dynamic access can efficiently be achieved by making necessary adjustment to some MAC layer functionalities such as sensing and channel allocation. MAC protocols play a central role in scheduling sensing periods and channel allocation which ensure that the interference is reduced to a tolerable level. In order to improve the accuracy of sensing algorithm, necessary adjustments should be made at MAC layer. Sensing delays and errors are major challenges in the design of a more accurate spectrum sensing algorithm or MAC protocol. Proposed in this study, is a scheme (EXGPCSA) which incorporate sensing at the MAC layer and physical layer. Energy detector was used to detect the presence of primary users (SU). A choice of how long and how often to sense the spectrum was addressed at the MAC layer. The focal point of this study was on minimizing delays in finding available channels for transmission. EXGPCSA used channel grouping technique to reduce delays. Channels were divided into two groups and arranged in descending order of their idling probabilities. Channels with higher probabilities were selected for sensing. Three network scenarios were considered wherein a group of SUs participated in sensing and sharing their spectral observations. EXGPCSA was designed such that only SUs with higher SNR were allowed to share their observations with other neighbouring SUs. This rule greatly minimized errors in sensing. The efficiency of EXGPCSA was evaluated by comparing it to another scheme called generalized predictive CSA. A statistical t-test was used to test if there is significant difference between EXGPCSA and generalized predictive CSA in terms of average throughput. A test has shown that EXGPCSA significantly performed better than generalized predictive CSA. Both schemes were simulated using MATLAB R2015a in three different network scenarios.

Modern communication systems demand ever-increasing data rates. Meeting this increased demand is not easy due to regulation and fundamental physical constraints. The utilization of more than one antenna at both the transmitter and receiver produces a multiple-input multiple-output (MIMO) channel, thereby enabling (under certain channel conditions) increased data rates without the need for increased bandwidth or transmission power. Concurrent with this increase in bandwidth is an increase in the receiver's computational complexity which, for a brute-force detector, increases exponentially. For receivers that possess error correcting capabilities, the problem of constructing a detector with low computational complexity that allows for near-exact a posteriori detection is challenging for transmission schemes employing even a modest number of transmit antennas and modulation alphabet sizes. The focus of this dissertation is on the construction of MIMO detection algorithms with low and fixed computational complexity. Specifically, the detection algorithms in this dissertation generate a list of potential transmission vectors resulting in realizable communication receivers with low and fixed computational complexity combined with low error rate performance in both coded and uncoded systems. A key contribution in this dissertation is a breadth-first fixed-complexity algorithm known as the smart-ordered and candidate-adding algorithm that achieves a desirable performance-complexity tradeoff. This algorithm requires only a single pass of a search tree to find its list of transmission vectors. We then construct a framework within which we classify a large class of breadth-first detection algorithms. The design of receiver algorithms for MIMO systems employing space-time codes and error correction is an important area of study. In this dissertation we propose a low and fixed computational complexity algorithm for an increasingly significant algebraic space-time code known as the golden code. The notion of computational complexity is critical in the design of practical MIMO receivers. We provide an analysis of computational complexity in relation to list-based soft-output detection where, in some instances, bounds are placed on the computational complexity of MIMO detection. For this analysis we utilize a metric known as the number of branch metric computations. The value at which the log-likelihood ratio (LLR) of conditional probabilities for a transmitted bit being either a 1 or a 0 is 'clipped' has an impact on a system's error rate performance. We propose a new approach for determining LLR clipping levels that, in contrast to prior approaches which clip to a predetermined fixed LLR clipping level, exploits channel state information to improve the error rate performance of suboptimal detection algorithms. Orthogonal frequency-division (OFDM) multiplexing is an effective technique for combating frequency-selective wideband communication channels. It is common practice for MIMO-OFDM detectors to implement the same detector at each subcarrier, in which case the overall performance is dominated by the weakest subcarrier. We propose a hard-output list detection receiver strategy for MIMO-OFDM channels called nonuniform computational complexity allocation, whereby the receiver adapts the computational resources of the MIMO detector at each subcarrier to match a metric of the corresponding channel quality. The proposed nonuniform algorithm improves performance over uniform allocation.

The study of wave production and propagation is a common phenomenon seen within a variety of math and physics problems. This thesis in particular will investigate the production and propagation of sound waves through musical instruments. Although this field of work has been examined since the late 1800s, approaching these types of problems can be very difficult. With the exception of the last fifty years, we have only been able to approach such problems by linearizing the necessary equations of gas dynamics. Without the use of a computer, one can only get so far in studying nonlinear acoustic problems. In addition, the numerical theory for nonlinear problems is incomplete. Proving stability is challenging and there are a variety of open problems within this field. This thesis will be examining the propagation of sound waves specifically through brass instruments. However, we will not be able to fully examine this problem in a master’s thesis because of the complexity. Instead, the objective is to provide a foundation and global picture of this problem by merge the fields of nonlinear acoustics as well as computational and analytical gas dynamics. To study the general behaviour of nonlinear wave propagation (and to verify previous findings), experiments have been carried on a trumpet. The purpose of these experiments is take measurements of the sound pressure waves at various locations along the instrument in order to understand the evolution of the wave propagation. In particular, we want to establish if the nonlinear distortion is strong enough to have musical consequences; and if there are such outcomes, what prerequisites are required for the observable behaviour. Additionally, by using the discontinuous Galerkin numerical method, a model of the system will be presented in this thesis. It will then be compared with the experimental data to verify how well we were able to describe the nonlinear wave motion within a trumpet.

Thesis (M.E.-Res.)--University of Wollongong, 2008. / Typescript. Includes bibliographical references: p. 164-179.