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Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Although wind turbine bearings are designed to operate 18-20 years, in the recent years premature failure among these bearings has caused this life to reduce to as low as a few months to a year. One of the leading causes of premature failure called white structure flaking is a mechanism that was first cited in literature decades ago but not much is understood about it even today. The cause of this mode of failure results from the initiation of white etched cracks (WECs). In this report, different failure mechanisms, especially premature failure mechanisms that were tested and analyzed are demonstrated as a pathway to understanding this phenomenon. Through the use of various tribometers, samples were tested in diverse and extreme conditions in order to study the effect of these different operational conditions on the specimen. Analysis of the tested samples allowed for a comparison of the microstructure alterations in the tested samples to the field bearings affected by WSF.
ContributorsSharma, Aman (Author) / Foy, Joseph (Thesis director) / Adams, James (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2015-05
Description
A model has been developed to modify Euler-Bernoulli beam theory for wooden beams, using visible properties of wood knot-defects. Treating knots in a beam as a system of two ellipses that change the local bending stiffness has been shown to improve the fit of a theoretical beam displacement function to edge-line deflection data extracted from digital imagery of experimentally loaded beams. In addition, an Ellipse Logistic Model (ELM) has been proposed, using L1-regularized logistic regression, to predict the impact of a knot on the displacement of a beam. By classifying a knot as severely positive or negative, vs. mildly positive or negative, ELM can classify knots that lead to large changes to beam deflection, while not over-emphasizing knots that may not be a problem. Using ELM with a regression-fit Young's Modulus on three-point bending of Douglass Fir, it is possible estimate the effects a knot will have on the shape of the resulting displacement curve.
ContributorsSexton, Thurston Bryant (Author) / Takahashi, Timothy (Thesis director) / Jones, Donald (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2015-05
Description
The following is a report that will evaluate the microstructure of the nickel-based superalloy Hastelloy X and its relationship to mechanical properties in different load conditions. Hastelloy X is of interest to the company AORA because its strength and oxidation resistance at high temperatures is directly applicable to their needs in a hybrid concentrated solar module. The literature review shows that the microstructure will produce different carbides at various temperatures, which can be beneficial to the strength of the alloy. These precipitates are found along the grain boundaries and act as pins that limit dislocation flow, as well as grain boundary sliding, and improve the rupture strength of the material. Over time, harmful precipitates form which counteract the strengthening effect of the carbides and reduce rupture strength, leading to failure. A combination of indentation and microstructure mapping was used in an effort to link local mechanical behavior to microstructure variability. Electron backscatter diffraction (EBSD) and energy dispersive spectroscopy (EDS) were initially used as a means to characterize the microstructure prior to testing. Then, a series of room temperature Vickers hardness tests at 50 and 500 gram-force were used to evaluate the variation in the local response as a function of indentation size. The room temperature study concluded that both the hardness and standard deviation increased at lower loads, which is consistent with the grain size distribution seen in the microstructure scan. The material was then subjected to high temperature spherical indentation. Load-displacement curves were essential in evaluating the decrease in strength of the material with increasing temperature. Through linear regression of the unloading portion of the curve, the plastic deformation was determined and compared at different temperatures as a qualitative method to evaluate local strength.
ContributorsCelaya, Andrew Jose (Author) / Peralta, Pedro (Thesis director) / Solanki, Kiran (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2015-05
Description
Widespread knowledge of fracture mechanics is mostly based on previous models that generalize crack growth in materials over several loading cycles. The objective of this project is to characterize crack growth that occurs in titanium alloys, specifically Grade 5 Ti-6Al-4V, at the sub-cycle scale, or within a single loading cycle. Using scanning electron microscopy (SEM), imaging analysis is performed to observe crack behavior at ten loading steps throughout the loading and unloading paths. Analysis involves measuring the incremental crack growth and crack tip opening displacement (CTOD) of specimens at loading ratios of 0.1, 0.3, and 0.5. This report defines the relationship between crack growth and the stress intensity factor, K, of the specimens, as well as the relationship between the R-ratio and stress opening level. The crack closure phenomena and effect of microcracks are discussed as they influence the crack growth behavior. This method has previously been used to characterize crack growth in Al 7075-T6. The results for Ti-6Al-4V are compared to these previous findings in order to strengthen conclusions about crack growth behavior.
ContributorsNazareno, Alyssa Noelle (Author) / Liu, Yongming (Thesis director) / Jiao, Yang (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.
ContributorsMcleod, Kristyn Noelle (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor)
Created2014-05
Description
The study of the mechanical behavior of nanocrystalline metals using microelectromechanical systems (MEMS) devices lies at the intersection of nanotechnology, mechanical engineering and material science. The extremely small grains that make up nanocrystalline metals lead to higher strength but lower ductility as compared to bulk metals. Effects of strain-rate dependence on the mechanical behavior of nanocrystalline metals are explored. Knowing the strain rate dependence of mechanical properties would enable optimization of material selection for different applications and lead to lighter structural components and enhanced sustainability.
ContributorsHall, Andrea Paulette (Author) / Rajagopalan, Jagannathan (Thesis director) / Liao, Yabin (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2014-05
Description
Monatomic gases are ideal working mediums for Brayton cycle systems due to their favorable thermodynamic properties. Closed Brayton cycle systems make use of these monatomic gases to increase system performance and thermal efficiency. Open Brayton cycles, on the other hand, operate with primarily diatomic and polyatomic gases from air and combustion products, which have less favorable properties. The focus of this study is to determine if monatomic gases can be utilized in an open Brayton cycle system, in a way that increases the overall performance, but is still cost effective.
Two variations on open cycle Brayton systems were analyzed, consisting of an “airborne” thrust producing propulsion system, and a “ground-based” power generation system. Both of these systems have some mole fraction of He, Ne, or Ar injected into the flow path at the inlet, and some fraction of monatomic gas recuperated and at the nozzle exit to be re-circulated through the system. This creates a working medium of an air-monatomic gas mixture before the combustor, and a combustion products-monatomic gas mixture after combustor. The system’s specific compressor work, specific turbine work, specific net power output, and thermal efficiency were analyzed for each case. The most dominant metric for performance is the thermal efficiency (η_sys), which showed a significant increase as the mole fraction of monatomic gas increased for all three gas types. With a mole fraction of 0.15, there was a 2-2.5% increase in the airborne system, and a 1.75% increase of the ground-based system. This confirms that “spiking” any open Brayton system with monatomic gas will lead to an increase in performance. Additionally, both systems showed an increase in compressor and turbine work for a set temperature difference with He and Ne, which can additionally lead to longer component lifecycles with less frequent maintenance checks.
The cost analysis essentially compares the operating cost of a standard system with the operating cost of the monatomic gas “spiked” system, while keeping the internal mass flow rate and total power output the same. This savings is denoted as a percent of the standard system with %NCS. This metric lumps the cost ratio of the monatomic gas and fuel (MGC/FC) with the fraction of recuperated monatomic gas (RF) into an effective cost ratio that represents the cost per second of monatomic gas injected into the system. Without recuperation, the results showed there is no mole fraction of any monatomic gas type that yields a positive %NCS for a reasonable range of current MGC/FC values. Integrating recuperation machinery in an airborne system is hugely impractical, effectively meaning that the use of monatomic gas in this case is not feasible. For a ground-based system on the other hand, recuperation is much more practical. The ground-based system showed that a RF value of at least 50% for He, 89% for Ne, and 94% for Ar is needed for positive savings. This shows that monatomic gas could theoretically be used cost effectively in a ground-based, power-generating open Brayton system. With an injected monatomic gas mole fraction of 0.15, and full 100% recuperation, there is a net cost savings of about 3.75% in this ground-based system.
Two variations on open cycle Brayton systems were analyzed, consisting of an “airborne” thrust producing propulsion system, and a “ground-based” power generation system. Both of these systems have some mole fraction of He, Ne, or Ar injected into the flow path at the inlet, and some fraction of monatomic gas recuperated and at the nozzle exit to be re-circulated through the system. This creates a working medium of an air-monatomic gas mixture before the combustor, and a combustion products-monatomic gas mixture after combustor. The system’s specific compressor work, specific turbine work, specific net power output, and thermal efficiency were analyzed for each case. The most dominant metric for performance is the thermal efficiency (η_sys), which showed a significant increase as the mole fraction of monatomic gas increased for all three gas types. With a mole fraction of 0.15, there was a 2-2.5% increase in the airborne system, and a 1.75% increase of the ground-based system. This confirms that “spiking” any open Brayton system with monatomic gas will lead to an increase in performance. Additionally, both systems showed an increase in compressor and turbine work for a set temperature difference with He and Ne, which can additionally lead to longer component lifecycles with less frequent maintenance checks.
The cost analysis essentially compares the operating cost of a standard system with the operating cost of the monatomic gas “spiked” system, while keeping the internal mass flow rate and total power output the same. This savings is denoted as a percent of the standard system with %NCS. This metric lumps the cost ratio of the monatomic gas and fuel (MGC/FC) with the fraction of recuperated monatomic gas (RF) into an effective cost ratio that represents the cost per second of monatomic gas injected into the system. Without recuperation, the results showed there is no mole fraction of any monatomic gas type that yields a positive %NCS for a reasonable range of current MGC/FC values. Integrating recuperation machinery in an airborne system is hugely impractical, effectively meaning that the use of monatomic gas in this case is not feasible. For a ground-based system on the other hand, recuperation is much more practical. The ground-based system showed that a RF value of at least 50% for He, 89% for Ne, and 94% for Ar is needed for positive savings. This shows that monatomic gas could theoretically be used cost effectively in a ground-based, power-generating open Brayton system. With an injected monatomic gas mole fraction of 0.15, and full 100% recuperation, there is a net cost savings of about 3.75% in this ground-based system.
ContributorsBernaud, Ryan Clark (Author) / Dahm, Werner (Thesis director) / Wells, Valana (Committee member) / Mechanical and Aerospace Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.
ContributorsWhitehurst, Ryan David (Author) / Kostelich, Eric (Thesis director) / Jones, Donald (Committee member) / Armbruster, Dieter (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-05
Description
The goal of this research is to compare the mechanical properties of CP-Ti and Ti-O and to understand the relationship between a material's microstructure and its response to fatigue. Titanium has been selected due to its desirable properties and applicability in several engineering fields. Both samples are polished and etched in order to visualize and characterize the microstructure and its features. The samples then undergo strain-controlled fatigue tests for several thousand cycles. Throughout testing, images of the samples are taken at zero and maximum load for DIC analysis. The DIC results can be used to study the local strains of the samples. The DIC analysis performed on the CP-Ti sample and presented in this study will be used to understand how the addition of oxygen in the Ti-O impacts fatigue response. The outcome of this research can be used to develop long-lasting, high strength materials.
ContributorsRiley, Erin Ashland (Author) / Solanki, Kiran (Thesis director) / Oswald, Jay (Committee member) / School of Art (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05