abstract: A control method based on the phase angle is used to control oscillating systems. The phase oscillator uses the sine and cosine of the phase angle to change key properties of a mass-spring-damper system, including amplitude, frequency, and equilibrium. An inverted pendulum is used to show a further application of the phase oscillator. Two methods of control based on the phase oscillator are used for swing-up and balancing of the pendulum. The first control method involves two separate stages. The scenarios where this control works are discussed. The second control method uses variable coefficients to result in a smooth transition between swing-up and balancing. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2015

A análise harmônica e o ramo da matemática que estuda a representação de funções ou sinais como a sobreposição de ondas base. Ela investiga e generaliza as noções das séries de Fourier e da transformação de Fourier. Neste trabalho, investigou-se um teorema de restrição da transformada de Fourier devido a Mitsis e Mockenhaupt (uma generalização do teorema de Stein-Tomas). Foram realizados estudos analíticos sobre o método para operadores integrais oscilatórios, baseado na fase estacionária. Os resultados permitem deduzir o teorema de restrição no plano (em seu caso geral) e o teorema de Carleson-Sjölin. / Harmonic analysis is the mathematical branch that studies the function or signals representation as a base wave overlay. It investigates and generalizes the notions of Fourier series and of the Fourier transform. In this work, was investigated a restriction theorem of the Fourier transform due to Mitsis and Mockenhaupt (a generalization of Stein-Tomas theorem) . Were performed analytic studies on the method for oscillating integral operators, based in the stationary phase. The results allow deducing the restriction theorem on the plane (in the general case) and the Carleson-Sjölin theorem.

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The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. / The numerical experiments, carried out through the use of a pressure-velocity coupled method to solve the Favre Averaged Navier-Stokes equations, on steady and sinusoidally oscillating flows at five different Keluegan-Carpenter numbers, and three periodicity levels are described. A second-order in time, second-order in space, second-level predictor-corrector finite difference scheme has been used. The solutions were solved by the CFD-ACE program from the CFD Research Corporation. The analysis has produced in-line force coefficients comparable to those obtained experimentally for sinusoidally-oscillating flows.

Passive and compact heat dissipation systems are and will remain vital for the successful operation of modern electronic systems. Oscillating heat pipes (OHPs) have been a part of this research area since their inception due to their ability to passively manage high heat fluxes. In the current investigation, different designs of tubular, flat plate, and multiple layer oscillating heat pipes are studied by using different operating parameters to investigate the operating limitations of each design. Furthermore, selective laser melting was demonstrated as a new OHP manufacturing technique and was used to create a compact multiple layer flat plate OHP. A 7-turn tubular oscillating heat pipe (T-OHP) was created and tested experimentally with three working fluids (water, acetone, and n-pentane) and different orientations (horizontal, vertical top heating, and vertical bottom heating). For vertical, T-OHP was tested with the condenser at 0°, 45° and 90° bend angle from the y-axis (achieved by bending the OHP in the adiabatic) in both bottom and top heating modes. The results show that T-OHP thermal performance depends on the bend angle, working fluid, and orientation. Another design of L-shape closed loop square microchannel (750 x 750 microns) copper heat pipe was fabricated from copper to create a thermal connector with thermal resistance < 0.09 ˚C/W for electronic boards. The TC-OHP was able to manage heat rates up to 250 W. A laser powder bed fusion (L-PBF) additive manufacturing (AM) method was employed for fabricating a multi-layered, Ti-6Al-4V oscillating heat pipe (ML-OHP). The 50.8 x 38.1 x 15.75 mm3 ML-OHP consisted of four inter-connected layers of circular mini-channels, as well an integrated, hermetic-grade fill port. A series of experiments were conducted to characterize the ML-OHP thermal performance by varying power input (up to 50 W), working fluid (water, acetone, NovecTM 7200, and n-pentane), and operating orientation (vertical bottom-heating, horizontal, and vertical top-heating). The ML-OHP was found to operate effectively for all working fluids and orientations investigated, demonstrating that the OHP can function in a multi-layered form, and further indicating that one can ‘stack’ multiple, interconnected OHPs within flat media for increased thermal management.

In this thesis, a stacked double-layer flat plate oscillating heat pipe charged with degassed DI water was designed, fabricated and characterized under different operating conditions (orientation, system or cooling water temperature and heat load). The oscillating heat pipe was designed to dissipate 500 W within a footprint of 170 x 100 mm2. The oscillating heat pipe had a total of 46 channels (23 channels per layer) with a nominal diameter of 2 mm. Tests were performed to characterize the performance of the oscillating heat pipe for (i) axial heat transfer and (ii) as a heat spreader. The stacked oscillating heat pipe showed a distinctive feature in that it overcame the absence of the gravity effect when operated in a horizontal orientation. The thermal performance was found to be greatly dependent on the operational parameters. The oscillating heat pipe was able to dissipate a heat load greater than 500 W without any indication of dry-out. An increase in the cooling water temperature enhanced the performance and was accompanied with an increase in the on/off oscillation ratio. The lowest thermal resistance of 0.06 K/W was achieved at 500 W with a 50℃ cooling water temperature, with a corresponding evaporator heat transfer coefficient of 0.78 W/cm2K. The oscillating heat pipe improved the heat spreading capability when locally heated at the middle and end locations. The thermal performance was enhanced by 27 percent and 21 percent, respectively, when compared to a plain heat spreader. / Thesis / Master of Applied Science (MASc)

Mathematical theory of partial differential equations (PDEs) is a pretty old classical area with wide range of applications to almost every branch of science and engineering. With the advanced development of functional analysis and operator theory in the last century, it became a topic of analysis. The theory of homogenization of partial differential equations is a relatively new area of research which helps to understand the multi-scale phenomena which has tremendous applications in a variety of physical and engineering models, like in composite materials, porous media, thin structures, rapidly oscillating boundaries and so on. Hence, it has emerged as one of the most interesting and useful subject to study for the last few decades both as a theoretical and applied topic. In this thesis, we study asymptotic analysis (homogenization) of second-order partial differential equations posed on an oscillating domain. We consider a two dimensional oscillating domain (comb shape type) consisting of a fixed bottom region and an oscillatory (rugose) upper region. We introduce optimal control problems for the Laplace equation. There are mainly two types of optimal control problems; namely distributed control and boundary control. For distributed control problems in the oscillating domain, one can apply control on the oscillating part or on the fixed part and similarly for boundary control problem (control on the oscillating boundary or on the fixed part the boundary). We consider all the four cases, namely distributed and boundary controls both on the oscillating part and away from the oscillating part. The present thesis consists of 8 chapters. In Chapter 1, a brief introduction to homogenization and optimal control is given with relevant references. In Chapter 2, we introduce the oscillatory domain and define the basic unfolding operators which will be used throughout the thesis. Summary of the thesis is given in Chapter 3 and future plan in Chapter 8. Our main contribution is contained in Chapters 4-7. In chapters 4 and 5, we study the asymptotic analysis of optimal control problems namely distributed and boundary controls, respectively, where the controls act away from the oscillating part of the domain. We consider both L2 cost functional as well as Dirichlet (gradient type) cost functional. We derive homogenized problem and introduce the limit optimal control problems with appropriate cost functional. Finally, we show convergence of the optimal solution, optimal state and associate adjoint solution. Also convergence of cost-functional. In Chapter 6, we consider the periodic controls on the oscillatory part together with Neumann condition on the oscillating boundary. One of the main contributions is the characterization of the optimal control using unfolding operator. This characterization is new and also will be used to study the limiting analysis of the optimality system. Chapter 7 deals with the boundary optimal control problem, where the control is applied through Neumann boundary condition on the oscillating boundary with a suitable scaling parameter. To characterize the optimal control, we introduce boundary unfolding operators which we consider as a novel approach. This characterization is used in the limiting analysis. In the limit, we obtain two limit problems according to the scaling parameters. In one of the limit optimal control problem, we observe that it contains three controls namely; a distributed control, a boundary control and an interface control.

Typescript (photocopy). / Digitized by Kansas Correctional Industries