Vibrations resulting from earthquakes, machinery, or unanticipated shocks may be very damaging and costly to structures. To avoid such damage, designers need a structural system that can dissipate the energy caused by these vibrations. Using elastically buckled struts may be a viable means to reduce the harmful effects of unexpected vibrations. Post-buckled struts can support high axial loads and also act as springs in a passive vibration isolation system by absorbing or dissipating the energy caused by external excitation. When a base excitation is applied, the buckled strut may act to reduce the dynamic force transmitted to the system, thus reducing the structural damage to the system. Several models of buckled and pre-bent struts are examined with different combinations of parameters and end conditions. The models include pinned or fixed columns supporting loads above their buckling load, and columns with an initial curvature supporting various loads. The varying parameters include external damping, internal damping, and stiffness. The columns will be subjected to simple harmonic motion applied at the base or to a multi-frequency base excitation. The response of each model is measured by the deflection transmissibility of the supported load over a large range of frequencies. Effective models reduce the motion of the supported load over a large range of frequencies. / Master of Science

In this thesis, the Josephson effect in mercury telluride based superconducting quantum point contacts (SQPCs) is studied. Implementing such confined structures into topological superconductors has been proposed as a means to detect and braid Majorana fermions. For the successful realization of such experiments though, coherent transport across the constriction is essential. By demonstrating the Josephson effect in a confined topological system, the presented experiments lay the foundation for future quantum devices that can be used for quantum computation. In addition, the experiments also provide valuable insights into the behavior of the Josephson effect in the low-channel limit (N<20). Due to the confinement of the weak link, we can also study the Josephson effect in a topological insulator, where the edge modes interact. In conclusion, this thesis discusses the fabrication of, and low-temperature measurements on mercury telluride quantum point contacts embedded within Josephson junctions. We find that the merging of the currently used fabrication methods for mercury telluride quantum point contacts and Josephson junctions does not yield a good enough device quality to resolve subbands of the quantum point contact as quantization effects in the transport properties. As we attribute this to the long dry etching time that is necessary for a top-contact, the fabrication process was adapted to reduce the defect density at the superconductor-semiconductor interface. Employing a technique that involves side contacting the mercury telluride quantum well and reducing the size of the mercury telluride mesa to sub-micrometer dimensions yields a quantized supercurrent across the junction. The observed supercurrent per mode is in good agreement with theoretical predictions for ballistic, one-dimensional modes that are longer than the Josephson penetration depth. Moreover, we find that oscillatory features superimpose the plateaus of the supercurrent and the conductance. The strength of these oscillatory features are sample-dependent and complicate the identification of plateaus. We suggest that the oscillatory features originate mainly from local defects and the short gate electrode. Additionally, resonances are promoted within the weak link if the transparency of the superconductor-HgTe interface differs from one. Furthermore, the research explores the regimes of the quantum spin Hall effect and the 0.5 anomaly. Notably, a small yet finite supercurrent is detected in the QSH regime. In samples fabricated from thick mercury telluride quantum wells, the supercurrent appears to vanish when the quantum point contact is tuned into the regime of the 0.5 anomaly. For samples fabricated from thin mercury telluride quantum wells, the conductance as well as the supercurrent vanish for strong depopulation. In these samples though, the supercurrent remains detectable even for conductance values significantly below 2 e²/h. Numerical calculation reproduce the transport behavior of the superconducting quantum point contacts. Additionally, the topological nature of the weak link is thoroughly investigated using the supercurrent diffraction pattern and the absorption of radio frequency photons. The diffraction pattern reveals a gate independent, monotonous decay of $I_\text{sw}(B)$, which is associated with the quantum interference of Andreev bound states funneled through the quantum point contact. Interestingly, the current distribution in the weak link appears unaffected as the quantum point contact is depleted. In the RF measurements, indications of a 4π periodic supercurrent are observed as a suppression of odd Shapiro steps. The ratio of the 4π periodic current to the 2π periodic current appears to decrease for smaller supercurrents, as odd Shapiro steps are exclusively suppressed for large supercurrents. Additionally, considering the observation that the supercurrent is small when the bulk modes in the quantum point contact are fully depleted, we suggest that the re-emerging of odd Shapiro steps is a consequence of the group velocity of the edge modes being significantly suppressed when the bulk modes are absent. Consequently, the topological nature of the superconducting quantum point contact is only noticeable in the transport properties when bulk modes are transmitted through the superconducting quantum point contact. The shown experiments are the first demonstration of mercury telluride superconducting quantum point contacts that exhibit signatures of quantization effects in the conductance as well as the supercurrent. Moreover, the experiments suggest that the regime of interacting topological edge channels is also accessible in mercury telluride superconducting quantum point contacts. This is potentially relevant for the realization of Majorana fermions and their application in the field of quantum computation. / Gegenstand dieser Arbeit ist der Josephson-Effekt in supraleitenden Quantenpunktkontakten (SQPCs) aus Quecksilbertellurid. Grundsätzlich wurde postuliert, dass räumlich eingeschränkte topologische Supraleitung in Quantenpunktkontakten verwendet werden kann, um Majorana-Fermionen zu realisieren und zu manipulieren. Dafür ist allerdings kohärente Supraleitung durch die Verjüngung des Quantenpunktkontaktes unerlässlich. Dies wird durch die Beobachtung des Josephson-Effektes durch den Quecksilbertellurid-Quantenpunktkontakt demonstriert. Somit legen die präsentierten Experimente den Grundstein für zukünftige Quanten-Bauelemente mit Anwendung im Bereich des Quantencomputings. Darüber hinaus liefern die Experimente auch einen Einblick in das Verhalten eines Josephson-Kontaktes, wenn dessen Verbindungsstück nur eine kleinen Anzahl an Transportmoden befördern kann (N<20). Durch die räumliche Nähe der Randkanäle des zwei-dimensionalen topologischen Isolators in der Verjüngung wird außerdem untersucht, wie sich der Josephson-Effekt unter Interaktion der helikalen Randkanäle verhält. Grundsätzlich behandelt diese Arbeit die Herstellung und Vermessung von supraleitenden Quecksilbertellurid-Quantenpunktkontakten, welche in einen Josephson-Kontakt eingebettet sind. Zunächst wird gezeigt, dass bei dem Versuch einen supraleitenden Quecksilbertellurid-Quantenpunktkontakt durch Anwenden der bekannten Fabrikationsprozesse von Quecksilbertellurid-Quantenpunktkontakten und Josephson-Kontakten herzustellen, die Qualität der Probe nicht gut genug ist, um quantisierten Transport durch einzelne Subbänder des Quantenpunktkontaktes aufzuweisen. Dies wird auf das lange Trockenätzen zurückgeführt, welche für einen Kontakt von oben notwendig ist. Daher wurde der Strukturierungsprozess angepasst, um die Defektdichte an dem Supraleiter-Halbleiter-Kontakt zu verringern. Durch das seitliche Kontaktieren des Quecksilbertellurid-Quantentroges und die Verkleinerung der Mesa auf submikrometer Größe, wird ein quantisierter Suprastrom durch den Josepshon-Kontakt beobachtet. Hierbei stimmt der von den Transportmoden getragene Suptrastrom gut mit den theoretischen Vorhersagen für ballistische, eindimensionale Moden überein, wenn deren Modenlänge größer als die Josephson-Eindringtiefe ist. Darüber hinaus wird beobachtet, dass die Stufen im Suprastrom und im Leitwert von Oszillationen überlagert werden. Die Stärke der Oszillationen ist hierbei probenabhängig, was die Identifikation einzelner Stufen erschwert. Die Oszillationen sind auf lokale Defekte und die kurze Gateelektrode zurückzuführen. Zusätzlich entstehen Resonanzen im Verbindungsstück des Josephson-Kontaktes, wenn die Transparenz der Supraleiter-HgTe-Kontaktes von eins abweicht. Des Weiteren werden die Bereiche des Quanten-Spin-Hall-Effektes und der 0.5-Anomalie untersucht. Bemerkenswerterweise wird im Quanten-Spin-Hall-Regime ein kleiner, aber endlicher Suprastrom detektiert. In Proben aus dicken Quecksilbertellurid-Quantentrögen verschwindet der Suprastrom, wenn der Quantenpunktkontakt in das Regime der 0.5-Anomalie gebracht wird. Bei dünnen Quecksilbertellurid-Quantentrögen verschwinden sowohl Leitwert als auch Suprastrom, wenn die Ladungsträgerdichte über das Quanten-Spin-Hall-Regime hinaus verringert wird. In diesen Proben bleibt allerdings der Suprastrom selbst für Leitwerte, die deutlich unter G=2 e²/h liegen, eindeutig erhalten. Das Transportverhalten der supraleitenden Quantenpunktkontakte wird durch numerische Simulationen reproduziert. Letztendlich werden die topologischen Eigenschaften des Verbindungsstückes auch durch das Beugungsbild des Suprastromes und durch die Absorption von RF-Photonen untersucht. Das Beugungsbild des Suprastromes zeigt einen monotonen Abfall von ebendiesem bei ansteigendem Magnetfeld, welcher unabhängig von der angelegten Gatespannung ist. Dieses Verhalten basiert auf Interferenzeffekten von gebundenen Andreev-Zuständen, welche die Verjüngung passieren. Interessanterweise scheint die Stromverteilung in dem Verbindungsstück unverändert zu bleiben, wenn der Quantenpunktkontakt entleert wird. In den RF-Messungen wird mit der Unterdrückung von ungeraden Shapiro-Stufen ein Anzeichen für einen 4\π-periodischen Suprastroms beobachtet. Das Verhältnis des 4π-periodischen Anteils des Suprastroms zum 2π-periodischen Anteil des Suprastroms wird kleiner, wenn der gesamte Suprastrom verringert wird. Demnach sind ungerade Shapiro-Stufen nur für große Supraströme unterdrückt. Wenn man darüber hinaus berücksichtigt, dass der Suprastrom klein ist, wenn die Volumenzustände im Quantenpunktkontakt entleert sind, liegt es nahe, dass das Wiederauftreten der ungeraden Shapiro-Stufen eine Konsequenz daraus ist, dass die Gruppengeschwindigkeit der helikalen Randkanäle unter Abwesenheit von Volumenzuständen deutlich verringert ist. Demzufolge sind die topologischen Eigenschaften des Verbindungsstückes nur bemerkbar, wenn auch Volumenzustände die Verjüngung passieren. Die gezeigten Experimente sind der erste Nachweis von supraleitenden Quantenpunktkontakten im zwei-dimensionalen topologischen Isolator Quecksilbertellurid, welche Kennzeichen von Quantisierungseffekte sowohl im Leitwert als auch im Suprastrom aufzeigen. Darüber hinaus implizieren die Experimente, dass der Bereich von interagierenden topologischen Randkanälen auch in supraleitenden Quecksilbertellurid-Quantenpunktkontakten zugänglich ist. Dies hat potenziell Relevanz für die Realisierung von Majorana-Fermionen in vergleichbaren Systemen und deren Anwendung im Bereich des Quantencomputing.

A vibration isolator is designed to reduce the vibration and structure borne noise transmitted from a vibratory source, such as machinery and equipment, to the supporting structure. The vibration and structure borne noise transmitted depends upon the dynamic properties of the foundation, the source mounting point and the vibration isolator. Therefore knowledge of the frequency dependent dynamic properties of vibration isolators is a necessary part of the acoustic prediction and control/reduction process. Vibration isolators may be characterised by measuring their four-pole parameters. A measurement procedure is proposed that employs the floating mass method, measures the direct forces and corrects for the errors introduced by the direct force measurement. Compared to the basic method, it extends the frequency limits of measurement in both directions. The development of a novel vibration isolator test facility that implements the proposed measurement procedure is described, and its satisfactory operation is experimentally demonstrated. The vibration isolator test facility is capable of characterizing vibration isolators commonly used in industrial and maritime applications, under service conditions. A method is proposed for measuring the four-pole parameters of a uni-directional asymmetrical vibration isolator under static load. The method is called the two masses method, and is suitable for determining the four???pole parameters of active vibration isolators with feedback control. The method is also applicable to uni-directional symmetrical and bi-directional symmetrical and bi-directional asymmetrical vibration isolators. It may be regarded as a universal method for characterising vibration isolators. Experimental data is presented and the method is validated. Modelling of vibration isolators is complicated by the highly non-linear nature of their rubber elements. The notion of an effective rubber cylinder is proposed to account for the barrelling of rubber elements under static load. Consequently, a general static compression model is proposed that applies to vibration isolators having unfilled and filled rubber elements of regular prismatic shapes. The model predicts the dependence of the four-pole parameters on the compression ratio of the rubber element. The predictions derived from the effective rubber cylinder and general static compression model agree excellently with experimental work of this study and other researchers.

In this thesis, a process is developed for designing elastomeric vibration isolators in order to provide vibration isolation for sensitive equipment being used in ROKETSAN A.S.&rsquo / s products. For this purpose, first of all, similar isolators are examined in the market. After that, appropriate elastomeric materials are selected and their temperature and frequency dependent dynamic properties are experimentally obtained. Parametric finite element model of the isolator is then constituted in ANSYS APDL using the properties of elastomeric materials and the conceptual design of the isolator. Then, according to design requirements, final design parameters of the vibration isolator are determined at the end of design iterations. In the next step, vibration isolator that was designed is manufactured using the elastomeric material chosen, by a local rubber company. Finally, design process is verified by comparing analysis and test results.

A vibration isolator is designed to reduce the vibration and structure borne noise transmitted from a vibratory source, such as machinery and equipment, to the supporting structure. The vibration and structure borne noise transmitted depends upon the dynamic properties of the foundation, the source mounting point and the vibration isolator. Therefore knowledge of the frequency dependent dynamic properties of vibration isolators is a necessary part of the acoustic prediction and control/reduction process. Vibration isolators may be characterised by measuring their four-pole parameters. A measurement procedure is proposed that employs the floating mass method, measures the direct forces and corrects for the errors introduced by the direct force measurement. Compared to the basic method, it extends the frequency limits of measurement in both directions. The development of a novel vibration isolator test facility that implements the proposed measurement procedure is described, and its satisfactory operation is experimentally demonstrated. The vibration isolator test facility is capable of characterizing vibration isolators commonly used in industrial and maritime applications, under service conditions. A method is proposed for measuring the four-pole parameters of a uni-directional asymmetrical vibration isolator under static load. The method is called the two masses method, and is suitable for determining the four???pole parameters of active vibration isolators with feedback control. The method is also applicable to uni-directional symmetrical and bi-directional symmetrical and bi-directional asymmetrical vibration isolators. It may be regarded as a universal method for characterising vibration isolators. Experimental data is presented and the method is validated. Modelling of vibration isolators is complicated by the highly non-linear nature of their rubber elements. The notion of an effective rubber cylinder is proposed to account for the barrelling of rubber elements under static load. Consequently, a general static compression model is proposed that applies to vibration isolators having unfilled and filled rubber elements of regular prismatic shapes. The model predicts the dependence of the four-pole parameters on the compression ratio of the rubber element. The predictions derived from the effective rubber cylinder and general static compression model agree excellently with experimental work of this study and other researchers.

<p> Steel-reinforced elastomeric isolator (SREI) bearings are currently the most commonly used type of seismic isolators. However, high manufacturing and associated installation costs prohibit their application in ordinary residential and commercial buildings. Fiber-reinforced elastomeric isolator (FREI) bearings are comprised of alternating layers of elastomer bonded to fiber-reinforcement layers. Research studies have shown that FREI bearings can be used as an alternative to SREI-bearings with comparable performance.</p> <p> FREis are much lighter in weight than traditional SREIs. In addition, their manufacturing cost can be lower, if individual FREI bearings, with the required size, are cut from a large sheet or a long strip, fabricated through mass production manufacturing techniques. An appealing application which simplifies the installation of FREI bearings is when they are placed between the substructure and superstructure with no bonding at their contact surfaces. This specific application is denoted as "unhanded application".</p> <p> When an unbonded FREI bearing is deformed laterally, it shows "rollover deformation" due to lack of flexural rigidity in the fiber-reinforcement sheets. The rollover deformation, as a beneficial feature, reduces the lateral stiffness of the bearing and enhances its seismic isolation efficiency, compared to the same bearing employed with bonded contact surfaces. However, it is important that the bearing is properly sized to maintain its lateral stability and hence exhibit ''stable rollover" (SR) deformation. Such a bearing is termed in this thesis as "stable unbonded" (SU)-FREI bearing.</p> <p> The main objectives of this research were to investigate the influence of geometry on the lateral response behavior of unbonded FREI bearings, and to evaluate the feasibility of employing SU-FREI bearings for seismic mitigation of low-rise buildings. The first objective was accomplished by conducting an experimental study on full-scale square FREI bearings. To achieve the latter objective a shake table study was performed on a 1/4 scale 2-storey steel frame which was seismically isolated with 1/4 scale SU-FREI bearings. The mechanical properties, including vertical and lateral stiffnesses and effective damping, of prototype samples of the 1/4 scale SU-FREI bearings were evaluated by vertical compression testing and cyclic lateral shear (under constant compression) testing. In addition, the influence of parameters such as lateral displacement amplitude and rate, amplitude history, and variations in the vertical pressure on the lateral response of the 1/4 scale SU-FREI bearings, were investigated.</p> <p> It was found that for FREI bearings having identical material properties and shape factor (the plan area of the bearing divided by the perimeter area of a single elastomer layer) the aspect ratio (length to total height of the bearing, also called second shape factor) plays an important role in achieving stable lateral response. All tested prototype 1/4. scale SU-FREI bearings exhibited SR-deformation with sufficient lateral flexibility and damping. Lateral response was found to be nonlinear and dependent on the amplitude and history of lateral displacement. However, due to the application of a relatively low design vertical pressure of 1.6 MPa, the influence of ±50% variation in the design vertical pressure on the lateral response was found to be insignificant. Lateral displacement capacity of the SU-FREI bearings was attained when their originally vertical faces fully contacted the upper and lower horizontal supports. This was accompanied with a significant increase in the lateral stiffness of the bearings which maintains the overall stability of the bearing to unexpectedly large ground motions. Shake table tests clearly demonstrated that SU-FREI bearings were efficient in seismic mitigation of the test-structure.</p> <p> The final component of this thesis involves investigating the applicability of two simplified analytical models in seismic response prediction of a base isolated structure. The two models use different techniques to simulate the lateral load-displacement hysteresis loops of prototype SU-FREI bearings which are obtained from cyclic shear tests (under constant compression). Model 1 includes the rate and the amplitude of bearings' lateral displacements to simulate the hysteresis loops through a multi-parameter curve fitting function. Model 2 uses bilinear idealization to simulate the hysteresis loops. Due to the highly nonlinear lateral response of SU-FREI bearings, these models utilize an iterative time history analysis approach to improve their accuracy. Comparisons with shake table results of a 1A scale structure show that both models can be used in response prediction of ordinary structures which are seismically isolated with SU-FREI bearings.</p>. / Thesis / Doctor of Philosophy (PhD)

This study of adaptable vibration isolating mounts sets out to capture the uniqueness of magnetorheological (MR) fluid's variable viscosity rate, and to physically alter the damping and stiffness when used inside an elastomeric mount. Apparent variable viscosity or rheology of the MR fluid has dependency on the application of a magnetic field. Therefore, this study also intends to look at the design of a compact magnetic field generator which magnetizes the MR fluid to activate different stiffness and damping levels within the isolator to create an adaptable and tunable feature. To achieve this adaptable isolator mount, a mold will be fabricated to construct the mounts. A process will then be devised to manufacture the mounts and place MR fluid inside the mount for later compatibility with the magnetic field generator. This process will then produce an MR fluid-elastic mount. Additionally for comparative purposes, passive mounts will be manufactured with a soft rubber casing and an assortment of metal and non-metal inserts. Next, the design of the magnetic field generator will be modeled using FEA magnetic software and then constructed. Stiffness or force/displacement measurements will then be analyzed from testing the isolator mount and magnetic field generator on a state-of-the-art vibration dynamometer. To vary the magnetic flux through the mount, an electro-magnet is used. To analyze the results, a frequency method of the stiffness will be used to show the isolators adaptation to various increments of magnetic flux over the sinusoidal input displacement frequencies. This frequency response of the stiffness will then be converted into a modeling technique to capture the essence of the dynamics from activating the MR fluid within the isolator mount. With this methodology for studying the adaptability of an MR fluid-elastic mount, the stiffness increases are dependent on the level of magnetic field intensity provided from the supplied electro-magnet. When the electro-magnet current supply is increased from 0.0 to 2.0 Amps, the mount stiffness magnitude increase is 78% in one of the MR fluid-elastic mounts. Through comparison, this MR fluid-elastic mount at off-state with zero magnetic field is similar to a mount made of solid rubber with a hardness of 30 Shore A. With 2 Amps of current, however, the MR fluid-elastic mount has a higher stiffness magnitude than a rubber mount and resembles a rubber casing with a steel insert. Moreover, when the current in the electro-magnet is increased from 0.0 to 2.0 Amps the equivalent damping coefficient in a MR fluid-elastic mount increases over 500% of the value at 0 Amps at low frequency. Through damping comparisons, the MR fluid-elastic mount with no current is similar to that of a mount made of solid rubber with a hardness of 30 Shore A. At full current in the electromagnet, however, the damping in the MR fluid-elastic mount is greater than any of the comparative mounts in this study. Therefore, the results show that the MR fluid-elastic mount can provide a wide range of stiffness and damping variation for real-time embedded applications. Since many aerospace and automotive applications use passive isolators as engine mounts in secondary suspensions to reduce transmitted forces at cruise speed, the MR fluid-elastic mount could be substituted to reduce transmitted forces over a wider range of speeds. Additionally, this compact MR fluid-elastic mount system could be easily adapted to many packaging constraints in those applications. / Master of Science

Transmissibility is the most common metric used for isolator characterization. However, engineers are becoming increasingly concerned about energy transmission through an isolator at high frequencies and how the compliance of the machine and foundation factor into the performance. In this study, the transfer matrix approach for isolator characterization is first reviewed. Two methods are detailed for determining the transfer matrix of an isolator using finite element simulation. This is accomplished by determining either the mobility or impedance matrix for the isolator and then converting to a transfer matrix. One of the more useful metrics to characterize the high frequency performance of an isolator is insertion loss. Insertion loss is defined as the difference in transmitted vibration in decibels between the unisolated and isolated cases. Insertion loss takes into account the compliance on the source and receiver sides. Accordingly, it has some advantages over transmissibility which is a function of the damping and mounted resonant frequency. A static analysis is to preload the isolator so that stress stiffening is accounted for. This is followed by modal and forced response analyses to identify the transfer matrix of the isolator. In this paper, the insertion loss of spring isolators is examined as a function of several geometric parameters including the spring diameter, wire diameter, number of active coils, and height. Results demonstrate how modifications to these parameters affect the insertion loss and the first surge frequency.

Vibrations are very common phenomenon. It influences structures and generates acoustic noise which might be harmful to human beings. The vibration isolator was invented to reduce the effect from vibrations. However, the behavior of rubber material, which many vibration isolators are made of, is hard to predict. Consequently, vibration tests are needed to obtain the dynamic properties of rubber isolator.In this case, a six-year old LORD 2204-5 rubber isolator provided by Atlas Copco was tested. The aim of this paper is to obtain the FRF (Frequency Response Function) diagram which can describe the property of the rubber material. Moreover, the influence of aging of rubber material on the dynamic properties was studied.As the vibration test should simulate the working environment of the isolators that are both a static load from the structure and a dynamic force from the engine, a new excitation method was designed. The camshaft with the shape of an epitrochoid induced the sinusoidal signal of the isolator and the frame transferred the static load from the hydraulic machine. The artificial aging was performed in a hot air oven in 90°C for 42 hours, which according to Arrhenius equation should be equivalent to six years of natural aging. The vibration isolator was tested again after being aged.The obtained data showed that the aging process decreased the stiffness of the material. The results were corresponding with other studies regarding aging of rubber.

Die Untersuchung stark korrelierter Elektronensysteme anhand des zweidimensionalen Hubbard-Modells bildet das zentrale Thema dieser Arbeit. Wir analysieren das Schicksal des Mott-Isolators bei Dotierung als auch bei Reduzierung der Wechselwirkungsstärke. Die numerische Auswertung erfolgt mit Hilfe von Quanten-Cluster-Approximationen, die eine thermodynamisch konsistente Beschreibung der Grundzustandseigenschaften garantieren. Der hier verwendete Rahmen der Selbstenergiefunktional-Theorie bietet eine große Flexibilität bei der Konstruktion von Cluster-Näherungen. Eine detaillierte Analyse gibt Aufschluss über die Qualität und das Konvergenzverhalten unterschiedlicher Cluster-Näherungen innerhalb der Selbstenergiefunktional-Theorie. Wir verwenden für diese Untersuchungen das eindimensionale Hubbard-Modell und vergleichen unsere Resultate mit der exakten Lösung. In zwei Dimensionen finden wir als Grundzustand des Teilchen-Loch-symmetrischen Modells bei Halbfüllung einen antiferromagnetischen Isolator unabhängig von der Wechselwirkungsstärke. Die Berücksichtigung kurzreichweitiger räumlicher Korrelationen durch unsere Cluster-Näherung führt, im Vergleich mit der dynamischen Mean-Field-Theorie, zu einer deutlichen Verbesserung des antiferromagnetischen Ordnungsparameters. Darüberhinaus beobachten wir in der paramagnetischen Phase einen Metall-Isolator-Übergang als Funktion der Wechselwirkungsstärke, der sich qualitativ vom reinen Mean-Field-Szenario unterscheidet. Ausgehend vom antiferromagnetischen Mott-Isolator zeigt sich ein füllungsgetriebener Metall-Isolator-Übergang in eine paramagnetische metallische Phase. Abhängig von der verwendeten Cluster-Approximation tritt dabei zunächst eine antiferromagnetische metallische Phase auf. Neben langreichweitiger antiferromagnetischer Ordnung haben wir in unseren Rechnungen auch Supraleitung berücksichtigt. Das Verhalten des supraleitenden Ordnungsparameters als Funktion der Dotierung ist dabei in guter Übereinstimmung sowohl mit anderen numerischen Verfahren als auch mit experimentellen Ergebnissen. / The central goal of this thesis is the examination of strongly correlated electron systems on the basis of the two-dimensional Hubbard model. We analyze how the properties of the Mott insulator change upon doping and with interaction strength. The numerical evaluation is done using quantum cluster approximations, which allow for a thermodynamically consistent description of the ground state properties. The framework of self-energy-functional theory offers great flexibility for the construction of cluster approximations. A detailed analysis sheds light on the quality and the convergence properties of different cluster approximations within the self-energy-functional theory. We use the one-dimensional Hubbard model for these examinations and compare our results with the exact solution. In two dimensions the ground state of the particle-hole symmetric model at half-filling is an antiferromagnetic insulator, independent of the interaction strength. The inclusion of short-range spatial correlations by our cluster approach leads to a considerable im\-prove\-ment of the antiferromagnetic order parameter as compared to dynamical mean-field theory. In the paramagnetic phase we furthermore observe a metal-insulator transition as a function of the interaction strength, which qualitatively differs from the pure mean-field scenario. Starting from the antiferromagnetic Mott insulator a filling-controlled metal-insulator transition in a paramagnetic metallic phase can be observed. Depending on the cluster approximation used an antiferromagnetic metallic phase may occur at first. In addition to long-range antiferromagnetic order, we also considered superconductivity in our calculations. The superconducting order parameter as a function of doping is in good agreement with other numerical methods, as well as with experimental results.