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Numerical Computations of Internal Combustion Engine related Transonic and Unsteady FlowsBodin, Olle January 2009 (has links)
Vehicles with internal combustion (IC) engines fueled by hydrocarbon compounds have been used for more than 100 years for ground transportation. During the years and in particular in the last decade, the environmental aspects of IC engines have become a major political and research topic. Following this interest, the emissions of pollutants such as NOx, CO2 and unburned hydrocarbons (UHC) from IC engines have been reduced considerably. Yet, there is still a clear need and possibility to improve engine efficiency while further reducing emissions of pollutants. The maximum efficiency of IC engines used in passenger cars is no more than $40\%$ and considerably less than that under part load conditions. One way to improve engine efficiency is to utilize the energy of the exhaust gases to turbocharge the engine. While turbocharging is by no means a new concept, its design and integration into the gas exchange system has been of low priority in the power train design process. One expects that the rapidly increasing interest in efficient passenger car engines would mean that the use of turbo technology will become more widespread. The flow in the IC-engine intake manifold determines the flow in the cylinder prior and during the combustion. Similarly, the flow in the exhaust manifold determines the flow into the turbine, and thereby the efficiency of the turbocharging system. In order to reduce NOx emissions, exhaust gas recirculation (EGR) is used. As this process transport exhaust gases into the cylinder, its efficiency is dependent on the gas exchange system in general. The losses in the gas exchange system are also an issue related to engine efficiency. These aspects have been addressed up to now rather superficially. One has been interested in global aspects (e.g. pressure drop, turbine efficiency) under steady state conditions.In this thesis, we focus on the flow in the exhaust port and close to the valve. Since the flow in the port can be transonic, we study first the numerical modeling of such a flow in a more simple geometry, namely a bump placed in a wind tunnel. Large-Eddy Simulations of internal transonic flow have been carried out. The results show that transonic flow in general is very sensitive to small disturbances in the boundary conditions. Flow in the wind tunnel case is always highly unsteady in the transonic flow regime with self excited shock oscillations and associated with that also unsteady boundary-layer separation. To investigate sensitivity to periodic disturbances the outlet pressure in the wind tunnel case was varied periodically at rather low amplitude. These low amplitude oscillations caused hysteretic behavior in the mean shock position and appearance of shocks of widely different patterns. The study of a model exhaust port shows that at realistic pressure ratios, the flow is transonic in the exhaust port. Furthermore, two pairs of vortex structures are created downstream of the valve plate by the wake behind the valve stem and by inertial forces and the pressure gradient in the port. These structures dissipate rather quickly. The impact of these structures and the choking effect caused by the shock on realistic IC engine performance remains to be studied in the future. / CICERO
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Vers un modèle de comportements de véhicules lourds en utilisant une méthode incrémentale basée sur la vérification et l'hystérésis : le modèle ArchiPL / Toward a model of heavy vehicle's behavior using an incremental method based on verification and hysteresys : the ArchiPL modelSix, Lancelot 05 November 2014 (has links)
Les phénomènes de congestion sont dangereux, et couteux économiquement. La compréhension de ces phénomènes est un sujet majeur ayant occupé la communauté scientifique depuis la moitié du vingtième siècle. L'approche microscopique, cherchant à reproduire les phénomènes macroscopiques grâce à la modélisation des comportements individuels, a proposé un grand nombre de modèles. Cependant, alors que la littérature a mis en avant l'impact négatif des véhicules lourds, peu se sont intéressés à savoir si les véhicules lourds ont un comportement similaire à celui des véhicules légers. Les principaux modèles considèrent que les comportements sont indifférenciés, à quelques paramètres près. Dans ces travaux, nous proposons de remettre en cause cette hypothèse. Nous proposons une démarche incrémentale, VIM4MAS, au cours de laquelle nous cherchons à identifier les principales différences entre les propriétés du comportement d'un véhicule lourd avec celle d'un véhicule léger. Cette démarche nous permet de construire un modèle de véhicules lourds en se fondant sur un modèle pré-existant de véhicules légers et en n'apportant que les modifications nécessaires. Dans le cadre de cette démarche, nous proposons également une méthode d'analyse des comportements longitudinaux fondée sur l'étude des boucles d'hystérésis. Cette méthode permet d'étudier les capacités d'anticipation des conducteurs, selon une approche boite noire. Le modèle de véhicules lourds produit, ArchiPL, montre d'une part des comportements de meilleure qualité du point de vue individuel, et d'autre part une cohérence avec la littérature existante. / Congestion phenomena are a major issue modern societies have to face. Understanding them, their creation, their evolution and their real impact are major questions addressed by the scientific community since the half of the twentieth century. A large number of simulation models have been developed to reproduce and study the traffic dynamics. Among them, microscopic model are designed to reproduce macroscopic phenomena such as congestion by reproducing individual vehicles' behavior. However, despite the negative influence of large vehicles on the flow, very few models took them into account. Those vehicles are usually dealt with as any other vehicle, except for a few parameters. In this thesis, we reconsider this hypothesis and try to identify how the behavior of large vehicles differs from other vehicles' behavior. We propose the VIM4MAS development methodology to help in this process. This method is used to improve a generic vehicle's behavior model and refine it until it can reproduce the most important aspects of the large vehicles' behaviors. To understand and identify key properties of longitudinal behaviors of vehicles, we have developed an analysis methodology based on the study of hysteresis phenomena. This analysis methodology allows to highlight key properties such as anticipation capabilities of drivers. The outcome of this work is the ArchiPL model for large vehicles' behaviors. This models shows an improvement of the behaviour quality at the microscopic level, while being consistent with the literature with respect to emergent phenomena.
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Analysis of Current-Voltage Hysteresis and Ageing Characteristics for CH3NH3PbI3-xClxBased Perovskite Thin Film Solar Cells / Analyse de l'hystérésis de courant-tension et des caractéristiques de vieillissement pour les cellules solaires à couche mince de perovskite à base de CH3NH3PbI3-xClxLee, Heejae 24 January 2018 (has links)
Les perovskites organiques-inorganiques en halogénures de plomb sont des matériaux très prometteurs pour la prochaine génération de cellules solaires avec des avantages intrinsèques tels que leur faible coût de fabrication (grande disponibilité des matériaux de base et leur mise en œuvre à basse température) et leur bon rendement de conversion photovoltaïque. Cependant, les cellules solaires pérovskites sont encore instables et montrent des effets d'hystérésis courant-tension délétères. Dans cette thèse, des résultats de l’analyse physique de couches minces de pérovskite à base de CH3NH3PbI3-xClx et de cellules solaires ont été présentés. Les caractéristiques de transport électrique et les processus de vieillissement ont été étudiés avec différentes approches.Dans une première étape, la synthèse du matériau pérovskite a été optimisée en contrôlant les conditions de dépôt des films en une seule étape telles que la vitesse de rotation (6000 rpm) de la tournette et la température de recuit des films (80 °C). Dans un second temps, des cellules solaires perovskites à base de CH3NH3PbI3-xClx ont été fabriquées en utilisant la structure planaire inversée et caractérisées optiquement et électriquement.Grace à l’utilisation de la spectroscopie optique à décharge luminescente (GDOES), un déplacement des ions halogénures a été observé expérimentalement et de façon directe sous l’application d’une tension électrique. Une longueur de diffusion ionique de 140 nm et un rapport de 65% d'ions mobiles ont été déduits. Il est montré que l'hystérésis courant-tension dans l'obscurité est fortement affectée par la migration des ions halogénures provoquant un écrantage substantiel du champ électrique appliqué. Nous avons donc trouvé sous obscurité un décalage de la tension à courant nul jusque 0,25 V et un courant de fuite jusque 0,1 mA / cm2 en fonction des conditions de mesure. Grâce aux courbes courant-tension en fonction de la température, nous avons déterminé la température de transition de la conductivité ions/électrons à 260K et analysé les résultats expérimentaux en utilisant l'équation de Nernst- Einstein donnant une énergie d'activation de 0.253 eV pour les ions mobiles.Enfin, le processus de vieillissement de la cellule solaire a été étudié avec des mesures optiques et électriques. Nous avons déduit que le processus de vieillissement apparaît d'abord à la surface des cristaux de pérovskite ainsi qu’aux joints de grains. Les mesures GDOES nous indiquent que les caractéristiques électriques des cellules pérovskites sont perdues par une corrosion progressive de l'électrode supérieure en argent causée par la diffusion des ions iodures. / Organic-inorganic lead halide perovskites are very promising materials for the next generation of solar cells with intrinsic advantages such as a low-cost material due to the availability of source materials and low-temperature solution processing as well as a high power conversion efficiency of the sunlight. However, perovskite solar cells are still unstable and show deleterious current-voltage hysteresis effects. Inthis thesis, analyses of CH3NH3PbI3-xClx based perovskite thin films and solar cells are presented. The electrical transport characteristics and the ageing processes are investigated using different approaches.The synthesis of the halide perovskite materials is optimized in a first step by controlling the deposition conditions such as annealing temperature (80°C) and spinning rate (6000 rpm) in the one step-spin-casted process. CH3NH3PbI3-xClx based perovskite solar cells are then fabricated in the inverted planar structure and characterized optically and electrically in a second step.Direct experimental evidence of the motion of the halide ions under an applied voltage has been observed using glow discharge optical emission spectroscopy (GDOES). Ionic diffusion length of 140 nm and ratio of mobile iodide ions of 65 % have been deduced. It is shown that the current-voltage hysteresis in the dark is strongly affected by the halide migration which causes a substantial screening of the applied electric field. Thus we have found a shift of voltage at zero current (< 0.25 V) and a leakage current (< 0.1 mA/cm2) in the dark versus measurement condition. Through the current-voltage curves as a function of temperature we have identified the freezing temperature of the mobile iodides at 260K. Using the Nernst-Einstein equation we have deduced a value of 0.253 eV for the activation energy of the mobile ions.Finally, the ageing process of the solar cell has been investigated with optical and electrical measurements. We deduced that the ageing process appear at first at the perovskite grain surface and boundaries. The electrical characteristics are degraded through a deterioration of the silver top-electrode due to the diffusion of iodides toward the silver as shown by GDOES analysis.
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Enhanced Coarse-Graining for Multiscale Modeling of ElastomersUddin, Md Salah 12 1900 (has links)
One of the major goal of the researchers is to reduce energy loss including nanoscale to the structural level. For instance, around 65% of fuel energy is lost during the propulsion of the automobiles, where 11% of the loss happens at tires due to rolling friction. Out of that tire loss, 90 to 95% loss happens due to hysteresis of tire materials. This dissertation focuses on multiscale modeling techniques in order to facilitate the discovery new rubber materials. Enhanced coarse-grained models of elastomers (thermoplastic polyurethane elastomer and natural rubber) are constructed from full-atomic models with reasonable repeat units/beads associated with pressure-correction for non-bonded interactions of the beads using inverse Boltzmann method (IBM). Equivalent continuum modeling is performed with volumetric/isochoric loading to predict macroscopic mechanical properties using molecular mechanics (MM) and molecular dynamics (MD). Glass-transition and rate-dependent mechanical properties along with hysteresis loss under uniaxial deformation is predicted with varying composition of the material. A statistical non-Gaussian treatment of a rubber chain is performed and linked with molecular dynamics in order predict hyperelastic material constants without fitting with any experimental data.
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Vývoj a přezkoušení nové metody pro měření tuhostních a tlumicích vlastností kloubů v paralelně kinematických strukturách / Development And Verification Of A New Method For Measuring The Stiffness And Damping Properties Of Joints In Parallel Kinematic StructuresKolouch, Martin January 2009 (has links)
In this dissertation is presented the development of a new measurement method for the stiffness and damping characteristics of a joint in a parallel kinematic machine tool. The main contribution of this method is specially for applications, that demand accurate information about stiffness and damping parameters from assembled parts of machines tool. Methods for compensation of deformations in machines tool, that are carried out by control, belong to these applications. Another contribution of this work is the technical implementation of the proposed principle of the new method. At this point the focus of the work was devoted to signal processing, that differs in a certain degree from other types of signal processing methods, that are used in other dynamic measurements, e.g. modal analysis. One of the main requirements was the possibility to consider the nonlinear behavior of the measured structure. In another chapter the modified signal processing method was used for measuring a joint in a test rig. The results were compared with results from other measurement methods. On account of this comparison the statement was made that the new method can be used for measuring the stiffness and damping parameters of machine parts. Finally the new method was applied to measure the properties of a joint, which was built in a machine tool. Moreover, the problems, that appeared during the measurement, were also described.
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STORMWATER MANAGEMENT PRACTICE MONITORING USING LONG-TERM TIME LAPSE ELECTRICAL RESISTIVITY TOMOGRAPHY AND SOIL SENSORS: IMPLICATIONS FOR DESIGN, MAINTENANCE, AND SOIL MOISTURE MONITORINGPope, Gina Ginevra January 2023 (has links)
Due to the large amount of impervious surface cover, urban areas are at high risk for flooding and, in cities with combined sewer systems, subject to sewer overflow during heavy storm events. The Pennsylvania Department of Transportation (PennDot) is currently reconstructing and expanding parts of Interstate 95 (I-95) through the city of Philadelphia. Due to both federal and local laws, PennDOT must account for the stormwater runoff and minimize outflow to the sewer system. To do so, PennDOT has plans to construct a series of stormwater management practices (SMPs) adjacent to I-95 to control the volumes of highway runoff. In partnership with Villanova University, Temple University has been tasked with monitoring these SMPs, known as bioswales, to provide insight and guidance as the project moves forward and to ensure mistakes aren’t reproduced in future construction. This research is contributing to the overall project goals by testing the application of geophysical monitoring to one of the bioswales known as SMP A. Unlike commonly used point measurements, geophysical surveys are non-invasive and provide extensive spatial coverage. Specifically, this research involves the use of electrical resistivity tomography (ERT), in which a series of cable-connected electrodes are placed in the ground and measure electric potential differences when an electric current is applied. Once processed, the results are a contoured subsurface image of the distribution of electrical resistivity (the inverse of electrical conductivity). If multiple surveys are taken over time, the data can be differenced, known as time lapse inversion, to quantify changes in electrical resistivity. ERT is a favorable for these SMPs as survey results are sensitive to changes in soil moisture and fluid conductivity, which are essential parameters when tracking infiltration and road salt influx at these SMPs. Additionally, the ERT data can be converted to soil moisture values using Archie’s law, which is important for determining soil moisture at points where no sensors are currently placed. We built and installed three ERT survey lines connected to an on-site monitoring station in April 2019 and collected quasi-daily measurements until monitoring seized in November 2021. One way to test SMPs is through a simulated runoff test, in which an SMP is flooded with water from an external source and the SMP’s response is recorded. During September 2020, Villanova University performed an SRT at SMP A, while we performed ERT surveys before, during, and after the SRT to track the infiltration and dry-out cycle. Knowing how long the soil at an SMP takes to recover to pre-storm soil moisture levels is essential in understanding an SMP’s performance and functionality. We were successfully able to capture the wet-up associated with the SRT and the corresponding dry-out period with the ERT data, which showed around a 20% decrease in resistivity when soil sensors indicated saturation. This resistivity change began to decrease and finally reached pre-SRT levels (0 – 5% change) after 68 hours, leading to our estimate of a three day recovery time for SMP A. Interestingly, inflow/outflow measurements at SMP A showed that only 24% of the input water exited the SMP via the overflow drain, meaning the rest of the water remained in the SMP. This discrepancy was solved with our ERT data, which showed that the decrease in resistivity, and therefore increase in soil moisture, was seen at depths beyond the 0.60 m layer of amended fill the SMP contained. Overall, the water was infiltrating past this layer and into the urban soil below. Initially it was thought that the native urban soil would impede infiltration, hence SMP A was designed around this assumption. However, our geophysical results indicate that the native urban soil underlying the SMP has an infiltration rate of 10 cm/hr and is contributing to the overall function of the SMP. This was unknown as previous monitoring was focused on the layer of amended fill material, not the underlying native soil.
The relationship between electrical resistivity and soil moisture, fluid conductivity, and porosity is known as Archie’s law, who derived an empirical formula that allows electrical resistivity data to be converted to soil moisture values. However, this equation requires quantifying two parameters, m (also known as the cementation factor) and n, the saturation exponent. Researchers commonly use pre-published values for m and n, or establish site-specific values by fitting Archie’s law to a set of soil moisture and conductivity data. However, as soil is heterogeneous, one set of m and n values may not be accurate across an entire site, especially with the presence of hysteresis, where one soil moisture value can correspond to multiple conductivity values depending on whether the soil is experiencing imbibition or drainage. Additionally, m and n can change over time as soil fabric changes, as well as soil conductivity changes due to the influx of road salt during winter months. In December 2019, we finished installing 16 TEROS12 soil sensors at SMP A, which recorded soil volumetric water content (VWC) and bulk electrical conductivity (bulk EC) every five minutes for nearly two years. These sensors were at six different locations within SMP A at depths of either 0.10 m, 0.30 m, or 0.60 m. We selected 13 storm events and fit Archie’s law to the soil VWC and bulk EC data to get values for m and n. While we were able to find m and n for all events, including events that exhibited hysteresis in soil VWC and bulk EC, each sensor had a different pair of m and n values. This discrepancy was surprising, given that the soil at SMP is a homogeneous, sandy-loam fill with no more than 10% clay. However, even sensors at the same depth show statistically significant differences. We also found that m and n were changing over time, notably m was increasing over time, possibly due to porosity changes. This result indicates that multiple sensors are needed to accurately calculate m and n, even at sites with relatively homogeneous soil. Most notably, the reason why we had success in fitting Archie’s law for every sensor was due to our accounting for changes in porewater conductivity. Most researchers assume a constant value for porewater (fluid) conductivity in Archie’s law. However, we found that not accounting for porewater conductivity changes lead to severe misestimation of soil VWC, even getting physically impossible values (VWC > 1.0 m3/m3) in some cases. Therefore, accounting for changes in porewater conductivity is essential when using Archie’s law.
Road salt transport in SMPs is a concern, especially in Philadelphia, which is subject to winter storms and freezing conditions. In some PennDOT SMPs, the presence of road salt in the soil during leaf-out has been suspected to be the cause of stunted plant growth and pre-mature plant mortality. Vegetation is an important aspect of the SMPs, as they provide evapotranspiration pathways, aesthetics, and soil erosion control. Thus, vegetation impairment affects SMP functionality, and plants often need to be replaced, increasing maintenance costs. To track and assess the spatial distribution of road salt, we performed ERT surveys along three lines, with two lines in the topographically lower portion of the SMP, or flood zone, and the other line on the elevated bank parallel to the other lines. All three of these lines had vegetation. In total, we collected 900 ERT surveys from October 2020 to September 2021, sufficiently covering the winter months and growing season. During February 2021, the soil sensors indicated significant increases in conductivity, with sensors ranging from 5.0 – 20.0 mS/cm, compared to pre-winter values of 0.1 – 0.6 mS/cm. The winter ERT surveys show the formation of a shallow conductive (< 10 Ω) layer in the top 0.25 m of soil, and an overall decrease in resistivity of up to 70%. This change decreased over the spring and summer months, indicating that dilute runoff was flushing the salt through the soil column. However, flood-zone ERT data still showed a 20% decrease in resistivity in June when compared to pre-winter data, indicating that road lingered in the soil during the spring and summer months. In May, we began taking bimonthly measurements of plant height, width, and leaf chlorophyll content (SPAD) on plants along the ERT lines, then in July took leaf tissue, root tissue, and root-zone soil samples and analyzed them for sodium content. We found that the plants along Lines 2 and 3 (flood-zone) had statistically significant stunted growth when compared to the plants along the elevated bank, as well as elevated sodium levels (> 400 mg/kg) in root tissue. No detectable sodium was found in leaf tissue samples. The stunted growth and elevated root sodium in the flood-zone plants indicate that early spring storms are not enough to flush out the road salt, and therefore artificial flooding may be required before leaf-out to ensure plant survival. We also suggest planting salt-tolerant plant species in areas of SMPs prone to flooding, such as the topographically lower portions. ERT can also be used to guide the placement of these plant species, as ERT can delineate areas of higher conductivity. / Geoscience
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EXPERIMENTAL INVESTIGATION OF THE THERMAL PERFORMANCE OF VERTICAL AND ELBOW THERMOSYPHONSHammouda, Mohamed January 2021 (has links)
The thermal performance of two thermosyphons with different geometries was experimentally investigated in this study. The first thermosyphon utilized a 310 mm long vertical evaporator and a 385 mm long condenser section that was inclined at 5 degrees from the vertical. The second was an elbow configuration with a 140 mm long vertical evaporator and a 190 mm long condenser oriented 8 degrees from the horizontal. Both thermosyphons were made of internally grooved copper tubing with an outer diameter of 15.87 mm, wall thickness of 0.5 mm and a nominal groove height of 0.3 mm. Tests were performed over a range of input heat fluxes where the condenser was cooled by flowing water around the condenser with inlet temperature of 10°C, 20°C, and 35°C. The effects of incrementally increasing and decreasing heat flux was investigated for the elbow thermosyphon. Temperature measurements along the thermosyphon were taken when incrementally changing the heat flux from 0.5 to 11 W/m2 for the first thermosyphon and 0.3 to 6 W/m2 for the second thermosyphon.
Internal flow regimes were characterized using temperature transient profiles and compared to existing flow regime maps for closed thermosyphons suggested by Smith et al. (2018: Part a and Part b) and Terdoon et al. (1997). The temperature transients along the evaporator for the first thermosyphon settled to a more uniform profile as heat flux was increased. For the second thermosyphon the temperature profiles suggested a change to a more dynamic flow in the evaporator at heat flux of approximately 6 W/m2. The elbow thermosyphon showed evidence of a significant hysteresis in the evaporator performance at moderate heat fluxes between 2 and 8 W/cm2. Comparisons were made between the two thermosyphons to study the effects of inclination angle and the feasibility of angle corrections to the Nusselt film condensation model from Guichet and Jouhara (2020). A modification to the Rohsenow condensation model from Guichet and Jouhara (2020) was recommended for the first thermosyphon showing good representation of the condenser performance. The evaporator performance results were compared to existing models from the literature. / Thesis / Master of Applied Science (MASc)
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Hysteresis modeling of wood joints and structural systemsFoliente, Greg C. 29 September 2009 (has links)
Difficulties in characterizing the dynamic behavior of wood structures have hindered investigations into their performance under dynamic loading. Because of this, wood structures are treated unfavorably in seismic design codes, even though past damage assessment surveys after seismic events indicated generally satisfactory performance.
To allow investigations into their performance and safety under dynamic loading, the energy dissipation mechanisms of wood joints and structural systems must be known and the hysteretic behavior modeled properly. This thesis presents a general hysteresis model for wood joints and structural systems, based on a modification of the Bouc-Wen-Baber-Noori (BWBN) model. The hysteretic constitutive law, based on the endochronic theory of plasticity and characterized by a single mathematical form, produces a versatile, smoothly varying hysteresis that models previously observed behavior of wood joints and structural systems, namely, (1) nonlinear, inelastic behavior, (2) stiffness degradation, (3) strength degradation, (4) pinching, and (5) memory. The constitutive law takes into account the experimentally observed dependence of wood joints' response to their past history (Le., the input and response at earlier times, or memory). Practical guidelines to estimate the hysteresis parameters of any wood joint or structural system are given. Hysteresis shapes produced by the proposed model are shown to compare reasonably well with experimental hysteresis of wood joints with: (1) yielding plate, (2) yielding nails, and (3) yielding bolts. To demonstrate its use, the proposed model is implemented in a nonlinear dynamic analysis program for single-degree-of-freedom (SDF) systems. System response from arbitrary dynamic loading, such as cyclic or earthquake-type loadings, can be computed. Three SDF wood systems are subjected to the Loma Prieta accelerogram to obtain their response time histories. Advantages of using the proposed model over currently available models in nonlinear dynamic analysis of more complex systems are identified. A multidegree-of-freedom shear building model incorporating the proposed hysteresis model is formulated but not implemented on a computer. / Master of Science
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Stochastic response of single degree of freedom hysteretic oscillatorsMaldonado, Gustavo Omar 17 November 2012 (has links)
During strong ground shaking structures often become inelastic and respond hysteretically. Therefore, in this study some hysteretic models commonly used in seismic structural analysis are studied. In particular the characteristics of a popular endochronic model proposed by Bouc and Wen are examined in detail. In addition, analytical expressions have also been developed for most commonly used bilinear model as well as another model, herein called as the hyperbolic model.</p> / Master of Science
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MODELING IRON LOSS IN ELECTRIC DRIVE SYSTEMS UNDER DC BIASED MAGNETICSMohammed Hassan M Alzahrani (14216648) 09 December 2022 (has links)
<p>Predicting core losses in electromagnetic and electromechanical devices such as electric machines is crucial to avoid overheating or oversizing. This work focuses on predicting core loss under a dc bias condition which results in hysteresis loop distortion and an increase in the core loss. The interest in dc biased materials is to facilitate design of electric drive systems wherein the electric machine core is subject to a dc bias such as in homopolar machines. Owing to their simplicity and ease of use, Steinmetz-based models are considered in this work. Herein, four models based on Steinmetz Equations are studied and compared for dc offset sinusoidal field intensity waveforms. The model parameters are then characterized for a sample of M15 steel. Finally, the four models are compared with regards to their accuracy and performance under saturated conditions.</p>
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