The position-dependent effective mass (PDEM) problem is of enormous importance to the realization of the extended Wentzel-Kramers-Brillouin (WKB) approximation in bound state calculations for semiconductor heterostructures. By studying some model problems, we show that the extended WKB method provides good approximations for the bound states with the high eigenenergies. In addition, the effect of the smoothness of the effective mass distribution functions and potential barrier in the PDEM problems is discussed in our work. We found the precision can be affected by the effective mass and potential barrier in the PDEM.

In the field of aeronautics (Aircraft, helicopters, space launchers...), as in the field of the automobile, reducing the harmful effects of acoustics constitutes a major concern at the international level and justifies the call for further research. With these challenges in mind, the manufacturers have expressed the need for simple models immediately available as early as the stage of preliminary drafts. This Master's Thesis presents the study and the validation of three different approaches to meet this industrial need. The first approach is based on the propagation of waves in the structure; the second approach uses the technique of SEA by calculating the equivalent damping; and the last approach uses the modal technique.In the three approaches, the transfer matrix method has been used to study the succession of layers. Applying these approaches to some aircraft structures confirm their relevance in relation to more exact and costly methods, such as the finite elements method.

Control design for flexible robots is a challenging problem. Part of the difficulty comes from a lack of controls-focused modeling tools. Practical flexible robots have several aspects that make them difficult to model: continuous elements, complicated actuators, multiple feedback loops, non-collocated sensors and actuators, and the ability to take on arbitrary three-dimensional poses. Even if existing techniques for modeling flexible structures could model the closed-loop response of a hydraulically-actuated flexible robot with a vibration suppression controller, how would such a model be used for control design? This work presents the development of a modeling approach that meets the needs of a controls engineer. The approach is based on the transfer matrix method (TMM). The TMM has been expanded in several ways to enable it to accurately model practical flexible robots. Quantitative agreement is shown between model and experiment for the interaction of a hydraulic actuator and a flexible structure as well as for the closed-loop response of a system with vibration suppression. Once the ability to model the closed-loop response of the system has been demonstrated, this work focuses on using the model for control design. Control design is facilitated by symbolic implementation of the TMM, which allows closed-form expressions for the closed-loop response of the system to be found without discretization. These closed-form expressions will be transcendental transfer functions for systems with continuous elements. These transfer functions can then be used in various optimization approaches for designing the closed-loop system response.

The McTronX Research Group at the North-West University is conducting research in the field of Active Magnetic Bearings (AMBs) with the aim of establishing a knowledge base for future industry consultation. AMBs are environmentally friendly and are a necessity in the pebble bed modular reactor (PBMR), a South-African initiated project, which is predicted to be the means of supplying Africa and many other countries with modular energy in the future. Aside from the PBMR, there are numerous other AMB industrial applications. The aim of this project is to develop a comprehensive AMB model that considers the effect that rotor dynamics has on an AMB system. This model is used to analyse a double radial AMB, capable of suspending a rigid- and flexible rotor, to explain previously noticed phenomena. Two modelling methods are focussed on namely the System Matrix Method and Transfer Matrix Method (TMM) both of which are implemented in MATLAB®. The rigid rotor model is firstly implemented as a point mass in state-space form followed by use of the TMM to analyse its bending modes. The stability and critical speeds of the system are analysed due to a change in the supports' properties along with rotor gyroscopy and its effect on the system. During analysis of the flexible rotor the TMM was used via a similar approach as was followed with the rigid rotor. The results indicate that the system is experiencing lower than expected damping due to the model that is used within the control loop. The previously assumed rotor model in the control loop is not sufficient to describe its complex behaviour. This causes the unexpected damping characteristics. This project suggests future work to be conducted in expanding the frequency domain model of the rotor within the control loop to account for its physical shape. / Thesis (M.Ing. (Computer and Electronical Engineering))--North-West University, Potchefstroom Campus, 2009.

The McTronX Research Group at the North-West University is conducting research in the field of Active Magnetic Bearings (AMBs) with the aim of establishing a knowledge base for future industry consultation. AMBs are environmentally friendly and are a necessity in the pebble bed modular reactor (PBMR), a South-African initiated project, which is predicted to be the means of supplying Africa and many other countries with modular energy in the future. Aside from the PBMR, there are numerous other AMB industrial applications. The aim of this project is to develop a comprehensive AMB model that considers the effect that rotor dynamics has on an AMB system. This model is used to analyse a double radial AMB, capable of suspending a rigid- and flexible rotor, to explain previously noticed phenomena. Two modelling methods are focussed on namely the System Matrix Method and Transfer Matrix Method (TMM) both of which are implemented in MATLAB®. The rigid rotor model is firstly implemented as a point mass in state-space form followed by use of the TMM to analyse its bending modes. The stability and critical speeds of the system are analysed due to a change in the supports' properties along with rotor gyroscopy and its effect on the system. During analysis of the flexible rotor the TMM was used via a similar approach as was followed with the rigid rotor. The results indicate that the system is experiencing lower than expected damping due to the model that is used within the control loop. The previously assumed rotor model in the control loop is not sufficient to describe its complex behaviour. This causes the unexpected damping characteristics. This project suggests future work to be conducted in expanding the frequency domain model of the rotor within the control loop to account for its physical shape. / Thesis (M.Ing. (Computer and Electronical Engineering))--North-West University, Potchefstroom Campus, 2009.

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Attenuation of low frequency turbofan engine noise has been a challenging task in an industry that requires low weight and tightly-packed solutions. Without innovative advancements, the technology currently used will not be able to keep up with the increasingly stringent requirements on aircraft noise reduction. A need exists for novel technologies that will pave the way for the future of quiet aircraft. This thesis investigates acoustic metamaterials and their ability to achieve superior transmission loss characteristics not found in traditional honeycomb liners. The acoustic metamaterials investigated are an array of Helmholtz resonators with and without coupled cavities periodically-spaced along a duct wall. Analytical, numerical, and experimental developments of these acoustic metamaterial systems are used herein to study the effects of this technology on the transmission loss. Particularly focusing on analytical modeling will aid in understanding the underlying physics that governs their interesting transmission loss behavior. A deeper understanding of the physics will be used to aid in future acoustic metamaterial liner design. A parameter study is performed to understand the effects of the geometry, spacing, and number of resonators, as well as resonator cavity coupling on performance. Increased broadband transmission loss, particularly in low frequencies, is achieved through intelligent manipulation of these parameters. Acoustic metamaterials are shown to have appealing noise cancellation characteristics that prove to be effective for aircraft engine liner applications. / Master of Science / Aircraft noise reduction is an ongoing challenge for the aerospace industry. Without innovative advancements, the next generation of aircraft will not be able to keep up with increasingly stringent noise regulations; novel acoustic technology is needed to pave the way for a future of quieter aircraft. This thesis investigates acoustic metamaterials and their ability to achieve superior noise reduction over traditional methods. Modeling techniques were developed, and experimental tests were conducted to quantitatively evaluate the effectiveness of a new acoustic metamaterial system. The acoustic metamaterial design explored herein was proven to reduce noise effectively and shows promise for a world of quieter aircraft.

When creating a muffler to be installed on a noise generating machine, the design parameters as well as the placements of sound attenuating elements has to be optimized in order to minimize the sound coming out of the equipage. This is exemplified in a small project task for students of a basic course in optimization at KTH. The task is however flawed, since both the way in which the optimization problem is formed is overly simplistic and the algorithm used to solve the problem, fmincon, does not cope well with the mathematical complexity of the model, meaning it gets stuck in a local optimum that is not a global optimum. This thesis is about investigating how to solve both of these problems. The model is modified to combine several frequencies and adjusting them to the sensitivity to different frequencies in the human ear. By doing this, the objective is changed from the previous way of maximizing Dynamic Insertion Loss Dilfor a specific frequency to minimize the total perceived sound level LA.  The model is based on the modular design of TMM from four-pole theory. This divides the muffler into separate parts, with the sound attenuating elements being mathematically defined only by what T matrix it has. The element types to choose from are the Expansion Chamber, the Quarter Wave Resonator and the Helmholtz Resonator. The global optimization methods to choose from are Global Search, MultiStart, Genetic Algorithm, Pattern Search and Simulated Annealing. By combining the different types of sound attenuating elements in every way and solving each case with every global optimization method, the best combination to implement to the model is chosen. The choice is two Quarter Wave Resonators being solved by MultiStart, which provides satisfactory results. Further analysis is done to ensure the robustness of chosen implementation, which does not reveal any significant flaws. The purpose of this thesis is fulfilled. / När man skapar en ljuddämpare som ska installeras på en ljud-genererande maskin bör designparametrarna samt placeringarna av ljuddämpande element optimeras för att minimera ljudet som kommer ut ur ekipaget. Detta exemplifieras i en liten projektuppgift för studenter till en grundkurs i optimering på KTH. Uppgiften är dock bristfällig, eftersom både det sätt som optimeringsproblemet är utformat är alltför förenklat och den algoritm som används för att lösa problemet, fmincon, inte klarar av modellens matematiska komplexitet bra, vilket menas med att den fastnar i ett lokalt optimum som inte är ett globalt optimum. Detta examensarbete handlar om att undersöka hur man kan lösa båda dessa problem. Modellen är modifierad för att kombinera flera frekvenser och anpassa dem till känsligheten för olika frekvenser i det mänskliga örat. Genom att göra detta är målet ändrat från det tidigare sättet att maximera den dynamiska insatsisoleringen DIL för en specifik frekvens till att minimera den totala upplevda ljudnivån LA. Modellen bygger på den modulära designen av TMM från 4-polsteori. Detta delar upp ljuddämparen i separata delar, med ljuddämpande element som matematiskt endast definieras av vilken T matris de har. De elementtyper att välja mellan är expansionskammare, kvartsvågsresonator och Helmholtzresonator. De globala optimeringsmetoder att välja mellan är Global Search, MultiStart, Genetic Algorithm, Pattern Search och Simulated Annealing. Genom att kombinera de olika typerna av ljuddämpande element på alla sätt och lösa varje fall med varje global optimeringsmetod, blir den bästa kombinationen vald och implementerad i modellen. Valet är två kvartsvågsresonatorer som löses genom MultiStart, vilket ger tillfredsställande resultat. Ytterligare analyser görs för att säkerställa robustheten av den valda implementationen, som inte avslöjar några väsentliga brister. Syftet med detta examensarbete är uppfyllt.

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