Rigidizable/Inflatable space structures have been the focus of renewed interest in recent years due to efficient packaging for transport. In this work, we examine new mathematical systems used to model small-scale joint dynamics for inflatable space truss structures. We investigate the regularity and asymptotic behavior of systems resulting from various damping models, including Kelvin-Voigt, Boltzmann, and thermoelastic damping. Approximation schemes will also be introduced. Finally, we look at optimal control for the Kelvin-Voigt model using a linear feedback regulator. / Ph. D.

Metal matrix composites offer unique opportunities for achieving multi-functionality in materials. In an attempt to investigate the possibility of enhancing damping characteristics of structural metals, copper was reinforced with tetragonal ferroelectric BaTiO3 particulates (Cu-BaTiO3 composites) using powder metallurgy techniques. The effect of particulate size and three processing conditions, sintering atmosphere, cooling rate and, uniaxial compaction pressure on the tetragonality and hence the ferroelectric properties of barium titanate powder were investigated using differential scanning calorimetry (DSC) and x-ray diffraction (XRD). The results show that sintering atmosphere and cooling rates have little effect on the tetragonality of barium titanate powder. Tetragonality of barium titanate powder decreased gradually with decreasing particle size. The decrease in tetragonality with decreasing particle size, however, was only severe in the very fine powders. Although no direct relationship was found between uniaxial compaction pressure and tetragonality, uniaxial pressure may also decrease the tetragonality of barium titanate. Three Cu-BaTiO3 composites, D1, D2 and D3 reinforced with 40vol% barium titanate particles of average sizes 209μm, 66μm and 2μm were respectively fabricated. The retention of the ferroelectric tetragonal phase of barium titanate after composite processing was confirmed by DSC. Composite microstructures observed using optical and scanning electron microscopy revealed uniform dispersions of barium titanate particles in D1 and D2. In D3, the barium titanate formed a chain-like structure because of extensive agglomeration of the fine reinforcement particles. Damping characteristics of the composites were evaluated between 25oC and 165oC at a frequency of 1Hz using dynamic mechanical analysis (DMA). The relative damping capacities (tanδ) in the composites were higher than the unreinforced metal. The damping capacity of composites D1 and D2 was also found to be dependent on temperature. Damping capacity was high from room temperature up to the Curie point of barium titanate, after which there was a slight drop in damping values probably due to a loss in ferroelectric properties. The small drop in damping values recorded in excess of the Curie temperature is an indication that ferroelectricity contributes little to the overall damping capacity of the Cu-BaTiO3 composites. This results from either a reduced ferroelectric damping in barium titanate particles or, poor stress transfer from matrix to reinforcement because of the weak and porous copper-barium titanate interface. / Master of Science

The purpose of this activity is to investigate how the PageRank algorithm behaves in relation to the damping factor when applied to small graphs and certain special graph types. The PageRank algorithm involves the calculation of eigenvalues and eigenvectors of the Google matrix for both directed and undirected graphs. This discussion will focus on all directed graphs with up to four vertices and select special graphs. Our primary objective is to observe how the damping factor influences the dominant eigenvector for each graph and, consequently, how it impacts PageRank. We have calculated PageRank for all the graphs and conducted an analysis, particularly focusing on the effect of the damping factor, denoted as "c," in our discussions. To compute the PageRank algorithm, we constructed a probability matrix for all the graphs and performed the calculations using MATLAB. This process yielded eigenvalues and eigenvectors associated with the Google matrix. The theoretical section of this thesis encompasses the PageRank theory, including essential proofs, theorems, and definitions that serve as foundational elements throughout the thesis. Additionally, we delve into the historical context and practical applications of PageRank. In our study, we present a comparative analysis of the results, specifically examining the impact of a damping factor on the dominant PageRank eigenvector.

In this study three types of optimized controllers are developed and tested on two laboratory structures. The two structures represented a progression in complexity and challenge to the controllers. The first structure was simple enough to be accurately modeled so the analytical frequencies and mode shapes agreed with the experimental measurements. The second structure being more complex was more difficult to model so differences between the analytical results and experimental measurements were present. These differences required the application a correction method to the reduced models developed for the second structure. The correction method was shown to work with good results on one reduced model and with poor results on the second reduced model. Two direct rate feedback control laws and a linear quadratic regulator with state estimation (LQG controller) were designed and implemented on both structures. It was shown that the performance of the LQG controller can be approached with a much simpler direct rate feedback controller with better analytical-experimental agreement. The best analytical-experimental agreement occurred with the simplest controller applied analytically to the corrected reduced model demonstrating the validity of the correction method as well as giving a strong reason to use simpler controller designs. / Ph. D.

Active Magnetic Bearings (AMB) are a relatively recent innovation in bearing technology. Unlike conventional bearings, which rely on mechanical forces originating from fluid films or physical contact to support bearing loads, AMB systems utilize magnetic fields to levitate and support a shaft in an air-gap within the bearing stator. This design has many benefits over conventional bearings. The potential capabilities that AMB systems offer are allowing this new technology to be considered for use in state-of-the-art applications. For example, AMB systems are being considered for use in jet engines, submarine propulsion systems, energy storage flywheels, hybrid electric vehicles and a multitude of high performance space applications. Many of the benefits that AMB systems have over conventional bearings makes them ideal for use in these types of vehicular applications. However, these applications present a greater challenge to the AMB system designer because the AMB-rotor system may be subjected to external vibrations originating from the vehicle's motion and operation. Therefore these AMB systems must be designed to handle the aggregate vibration of both the internal rotor dynamic vibrations and the external vibrations that these applications will produce. This paper will focus on the effects of direct base excitation to an AMB/rotor system because base excitation is highly possible to occur in vehicular applications. This type of excitation has been known to de-stabilize AMB/rotor systems therefore this aspect of AMB system operation needs to be examined. The goal of this research was to design, build and test a test rig that has the ability to excite an AMB system with large amplitude base excitation. Results obtained from this test rig will be compared to predictions obtained from linear models commonly used for AMB analysis and determine the limits of these models. / Master of Science

In this thesis the characteristics of pitch and roll damping coefficients of missile models are investigated by using Computational Fluid Dynamics (CFD) techniques. Experimental data of NACA0012 airfoil, Basic Finner (BF) and Modified Basic Finner (MBF) models are used for validation and verification studies. Numerical computations are performed from subsonic to supersonic flow regimes. Grid refinement and turbulence model selection studies are conducted before starting the dynamic motion simulations. Numerical method of dynamic motion simulation is validated with a 2D NACA0012 airfoil. After the validation of numerical method, forced-oscillation motion is given to the BF and MBF models. In order to get deeper understandings about the characteristics of dynamic pitching and rolling motions, parametric studies are performed. The amplitude and frequency of forced-oscillation motions are investigated one by one. The effects of angle of attacks are also investigated for both pitching and rolling motions. The results of CFD simulations are compared with experimental data obtained from different wind tunnel and free flight tests. It is seen from these comparisons that experimental and numerical results are in good agreement throughout the whole flow regime. In conclusion, the numerical method presented in this study is validated and can be used for the prediction of pitch and roll damping coefficient of any missile configurations.

This thesis develops a finite element based dynamic modeling method for design and analysis of compliant mechanisms which transfer input force, displacement and energy through elastic deformations. Most published analyses have largely based on quasi-static and lump-parameter models neglecting the effects of damping, torsion, complex geometry, and nonlinearity of deformable contacts. For applications such as handling of objects by the robotic hands with multiple high-damped compliant fingers, there is a need for a dynamic model capable of analyzing the flexible multibody system. This research begins with the formulation of the explicit dynamic finite element method (FEM) which takes into account the effects of damping, complex geometry and contact nonlinearity. The numerical stability is considered by evaluating the critical time step in terms of material properties and mesh quality. A general framework incorporating explicit dynamic FEM, topology optimization, modal analysis, and damping identification has been developed. Unlike previous studies commonly focusing on geometry optimization, this research considers both geometric and operating parameters for evaluation where the dynamic performance and trajectory of the multibody motion are particularly interested. The dynamic response and contact behavior of the rotating fingers acting on the fixed and moving objects are validated by comparing against published experimental results. The effectiveness of the dynamic modeling method, which relaxes the quasi-static assumption, has been demonstrated in the analyses of developing an automated transfer system involved grasping and handling objects by the compliant robotic hands. This FEM based dynamic model offers a more realistic simulation and a better understanding of the multibody motion for improving future design. It is expected that the method presented here can be applied to a spectrum of engineering applications where flexible multibody dynamics plays a significant role.

Das Ziel dieser Arbeit war die Aufklärung der Dämpfungsmechanismen partikelgefüllter Hohlkugelstrukturen und die Charakterisierung ihres Dämpfungsvermögens, um werkstoffgerechte Konstruktionen zur Schwingungsdämpfung zu ermöglichen. Seit die Reduktion der Masse bewegter Baugruppen zur Reduktion des Energieverbrauchs von Maschinen in den Fokus der Entwicklung im Maschinenbau gerückt ist, und gleichzeitig der Anspruch an die Genauigkeit und Oberflächengüte der zu fertigenden Bauteile steigt, hat sich die Dämpfung mechanischer Schwingungen von einem dem Komfort dienenden Thema zu einer essentiellen Aufgabe vor allem in der Konstruktion von Werkzeugmaschinen gewandelt. In der Literatur werden viele Verfahren zur aktiven, semiaktiven und passiven Dämpfung mechanischer Schwingungen diskutiert. Industriell etabliert haben sich bisher hauptsächlich Verfahren, die auf der Dämpfung im Gefüge der Werkstoffe beruhen. Zur Aktivierung der Dämpfungsmechanismen im Gefüge ist immer eine Verformung des Werkstoffs notwendig. Die in der Arbeit untersuchten partikelgefüllten Hohlkugeln dagegen ermöglichen eine Starrkörperdämpfung. Ausgehend von der Erfahrung, dass eine fallen gelassene partikelgefüllte Hohlkugel kaum oder gar nicht hüpft, wurde ein Verfahren zur Messung der Dämpfungsfähigkeit von Einzelkugeln entwickelt. Es wurden die Parameter der partikelgefüllten Hohlkugeln identifiziert, die durch ihre Veränderung Rückschlüsse auf deren Dämpfungswirkung erwarten ließen. Von den Eigenschaften der Partikel, über technologische Messungen an den Pulvern, die Messung des Dämpfungsvermögens der Einzelkugel und der Dämpfung von Probekörpern bis hin zum Einsatz im Frässchlitten einer Beispielmaschine wurde das Dämpfungsverhalten des realen Werkstoffs untersucht. Durch die Abschätzungen anhand eines Modellsystems wurde eine vertiefte Vorstellung der in den partikelgefüllten Hohlkugeln ablaufenden Vorgänge erreicht. Anhand eines Frässchlittens einer Beispielmaschine konnte die Schwingungsdämpfung im Leichtbau nachgewiesen werden.:1 Einleitung 5 2 Literatur und Stand der Technik 7 2.1 Dämpfung mechanischer Schwingungen 7 2.1.1 Begriffsbestimmungen 7 2.1.2 Dämpfung im Gefüge von Werkstoffen 9 2.1.3 Besonderheiten der Dämpfung in zellularen metallischen Werkstoffen (ZMW) 13 2.1.4 Dämpfung durch Reibung zwischen Bauteilen 15 2.1.5 Modelluntersuchungen an Schlag- und Partikeldämpfern 15 2.1.6 Reibung in Pulvern und Schüttgütern 21 2.2 Kombination von Leichtbau und Schwingungsdämpfung im Maschinenbau 29 2.2.1 Notwendigkeit und Potential 29 2.2.2 Sandwichbauweise 29 2.3 Technologie 35 2.3.1 Herstellung ungefüllter Hohlkugeln und Hohlkugelstrukturen 35 2.3.2 Herstellung gefüllter Hohlkugeln im Labormaßstab 37 3 Ziel der vorliegenden Arbeit 39 4 Methoden 41 4.1 Probenherstellung 41 4.1.1 Ausgangsmaterialien 41 4.1.2 Beschichtung 42 4.1.3 Entbinderung und Sinterung 43 4.1.4 Partikelgefüllte keramische Hohlkugeln 44 4.1.5 Herstellung von Probekörpern 45 4.2 Charakterisierungsmethoden 47 4.2.1 Pulvercharakterisierung 47 4.2.2 Dämpfung von Einzelkugeln 52 4.2.3 Resonanzfrequenz – Dämpfungsanalyse (RFDA) 54 5 Ergebnisse 58 5.1 Partikelbewegung in gefüllten Hohlkugeln 58 5.2 Dämpfungspulver 61 5.2.1 Partikelform 61 5.2.2 Partikelgrößenverteilung 62 5.2.3 Pulverdichten 64 5.2.4 Veränderung der Partikeloberfläche 66 5.3 Dämpfung bei geringem Energieeintrag 67 5.4 Dämpfung der Partikel bei hohem Energieeintrag 69 5.4.1 Einfluss der Hausnerzahl 69 5.4.2 Einfluss der Fähigkeit zur Fluidisierung 71 5.4.3 Abhängigkeit vom Masseverhältnis 75 5.4.4 Abhängigkeit von der Partikelgröße 76 5.4.5 Abhängigkeit von der spezifischen Oberfläche 78 5.4.6 Abhängigkeit von der Kugelschale 79 5.5 Dämpfung von Bauteilen 81 5.5.1 Dämpfung von Probekörpern in Abhängigkeit von der Dämpfung der Einzelkugeln 81 5.5.2 Dämpfung von Probekörpern in Abhängigkeit vom Masseverhältnis Partikel – Probekörper 83 5.5.3 Volumenanteil der Einzelkugeln im Probekörper 84 5.5.4 Dämpfung in Abhängigkeit von der Anzahl der Dämpfungszentren 85 6 Diskussion 87 6.1 Analyse der Bewegungszustände der Partikel 87 6.2 Analyse der wirkenden Kräfte 89 6.3 Modellierung der Dämpfung 93 6.4 Folgerungen aus dem Modell 94 6.5 Vergleich mit experimentellen Ergebnissen 98 6.5.1 Energiedissipation im Pulverbett 99 6.5.2 Fluidisierung des Pulverbettes 100 6.5.3 Gasartige Partikelbewegung 102 6.5.4 Füllgrad 103 6.5.5 Dämpfung im Verbundwerkstoff 106 6.6 Abschätzungen zur Bauteildämpfung 108 6.7 Anwendungsbeispiel Frässchlitten 109 6.7.1 Technische Ergebnisse 109 6.7.2 Kostenabschätzung im Manufakturbetrieb 113 7 Zusammenfassung 117 8 Danksagung 120 9 Anhang 122 9.1 Literaturverzeichnis 122 9.2 Berechnungen 130 9.2.1 Berechnung der Stoßzahl 130 9.2.2 Partikeloberfläche pro Hohlkugel 130 9.2.3 Füllgrad von Einzelkugeln 132 9.3 Verzeichnis der Abkürzungen und Symbole 135 9.4 Verzeichnis der Abbildungen 139

During aircraft development, the impact of vibrations is examined and how this affects the aircraft structure under different conditions. Those vibrations can damage electronic equipment that are installed within the fuselage and can even lead to material fatigue within the structure. To reduce vibrations there are two approaches that are preferred to use, installing vibration insulators attached between the structure and the electrical component or change the design of the structure to a stiffer one. Those methods are easiest to implement in an early stage of the development but in later stages, when vibration problems usually are detected, it is too difficult and expensive to do major changes of the structure and there is lack of space to implement vibration insulators. A third method is then to apply passive damping in form of damper mats to surfaces on structures where critical vibrations occurs.    The effects on the structural behavior when damper mats are applied to a certain structure are studied in this thesis work. The purpose is to get deeper knowledge about how damper mats can be used to reduce vibrations in aircraft structures. The type of damper mat that is studied is known as Constrained Layer Damping, CLD, which is a sandwich of a visco-elastic material layer and a stiffer constraining material layer. Modelling and simulation methods that are based on commercial FE-software have been developed. The analysis method is based on doing a modal analysis with structural damping taken into account. This makes it possible to predict the overall global damping at each structural mode. The models for damper mats have in this project been verified with experimental testing using typical damper mats. The methodology can be used to predict the behavior of damped structures in order to obtain an effective and lightweight passive damping solution. / Under utvecklingen av flygplan undersöks hur vibrationer påverkar flygplansstrukturen under olika förutsättningar. Dessa vibrationer kan skada elektronisk utrustning som är monterad i flygplanskroppen och kan även göra så att materialutmattning uppstår i flygplansstrukturen. För att motverka vibrationer finns det två metoder som är att föredra, antingen att montera vibrationsisolatorer mellan de elektroniska utrustningarna och strukturen eller att ändra designen på strukturer till en styvare. Dessa metoder är enkla att implementera i ett tidigt steg i utvecklingsprocessen men i senare steg, då vibrationsproblem ofta upptäcks, så är det för komplicerat och för dyrt att göra större ändringar på strukturen och så är det ont om plats för att kunna installera vibrations isolatorer. En tredje metod är istället att implementera passiv dämpning i form av dämpningsmattor på ytor av strukturen där kritiska vibrationer uppstår. Effekterna av det strukturella uppförandet när dämpningsmattor är applicerade på en viss struktur har studerats i det här examensarbetet. Syftet är att få en fördjupad kunskap om hur dämpningsmattor kan användas för att reducera vibrationer i flygplan strukturer. Den typ av dämpningsmatta som har studerats är känd som Constrained Layer Damping, CLD, vilken är en sandwich av ett visko-elastiskt lager samt ett styvare lager.  Modellerings och simuleringsmetoder som är baserade på kommersiella FE-mjukvaror har utvecklats. Analysmetoderna är baserade på att utföra modalanalys tillsammans med strukturell dämpning. Detta möjliggör att förutse den övergripande dämpningen vid varje strukturell mod. Modellerna för dämpningsmattorna har i det här projektet verifierats med experimental testning av typiska dämpningsmattor. Metodiken kan användas till att prediktera beteendet av dämpade strukturer för att uppnå en effektiv och lättviktig passiv dämpningslösning.

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