Previous decades of cartilage research have predominantly focused on decoupling the solid and fluid interactions of the mechanical response. The resulting biphasic and triphasic models are widely used in the biomechanics community. However, a simple viscoelastic model is able to account for the stress-relaxation behavior of cartilage, without the added complexity of solid and fluid interactions. Using a viscoelastic model, cartilage is considered a single material with elastic and dissipative properties. A mechanical characterization is made with fewer material parameters than are required by the conventional biphasic and triphasic models. This approach has tremendous utility when comparing cartilage of different species and varying healths. Additionally, the viscoelastic models can be easily extended in dynamic analysis and FEA programs. Cartilage primarily experiences compressive motion during exercise. Therefore, to mimic biological function, a mechanical test should also compress the cartilage. One such test is a viscoelastic stress-relaxation experiment. The Prony and fractional calculus viscoelastic models have shown promise in modeling stress-relaxation of equine articular cartilage. The elastic-viscoelastic correspondence principle is used to extend linear viscoelasticity to the frequency domain. This provides a comparison of articular cartilage based on stored and dissipated moduli. The storage and loss moduli metrics are hypothesized to serve as benchmarks for evaluating osteoarthritic cartilage, and provide guidelines for newly engineered bio-materials. The main goal of the current study is to test the applicability of modeling articular cartilage with viscoelastic models. A secondary goal is to establish a rigorous set of harvesting techniques that allows access to fresh explants with minimal environmental exposure. With a complex substance like cartilage, it is crucial to avoid unnecessary emph{in vitro} environmental exposure. Additional areas of study include: determining the strain-dependency of the mechanical response, exploring the response of cartilage in different fluid mediums such as saline, synovial fluid, and synthetic substitutes, and studying the time-dependent properties of cartilage during stress-relaxation experiments. Equine stifle joints, which are mechanically analogous to human knees, are harvested and used for analysis in this study. It is believed that the proposed viscoelastic models can model other articulating joints as well. If viscoelastic theory can be used to characterize cartilage, then comparisons can be drawn between real and artificial cartilage, leading to better joint replacement technology.

This work presents a method for screening synchrophasor data to search for power system events of interest. The method employs prony algorithm to perform modal analysis and estimate mode amplitude, frequency, and damping ratio on the data obtained from the Texas Synchrophasor Network. The procedure uses seven different Linear Prediction Model (LPM) orders, plus a 10 second window width that slides in steps of 1 second, to minimize the possibility of overlooking events of interest. Further, the algorithm is extended to include user defined modal characteristics thresholds, window length and step size to capture specific power system events. / text

The objective of this study was to develop a model to predict the viscoelastic material functions of a vinyl ester (VE) polymer (Derakane 441-400, Ashland Co.,) with variations in its material properties. Short-term tensile creep/creep recovery experiments were conducted at two stress levels and at four temperatures below the glass transition temperature of the VE polymer, with 10 replicates for each test configuration. Experimental strains in both the longitudinal and transverse directions were measured using a digital image correlation technique. The measured creep strain versus time responses were subsequently used to determine the creep compliances using the generalized viscoelastic constitutive equation with a Prony series representation. The variation in the creep compliances of Derakane 441-400 was described by formulating the probability density functions (PDFs) and the corresponding cumulative distribution functions (CDFs) of the creep compliances using the two-parameter Weibull and log-normal distributions. The maximum likelihood estimation technique was used to obtain the Weibull shape and its scale parameters and the log-normal location and its scale parameters. The goodness-ofit of the distributions was determined by performing Kolmogorov-Smirnov (K-S) hypothesis tests. Based on the K-S test results, the Weibull distribution is a better representation of the creep compliances of Derakane 441-400 when compared to the log-normal distribution. Additionally, the Weibull scale and shape parameters of the creep compliance distributions were shown to be time and temperature dependent. Therefore, two-dimensional quadratic Lagrange interpolation functions were used to characterize the Weibull parameters to obtain the PDFs and subsequently the CDFs of the creep compliances for the complete design temperature range during steady state creep. At each test temperature, creep compliance curves were obtained for CDF values of 0.05, 0.50 and 0.95 and compared with the experimentally obtained lowest, mean and highest creep compliances, respectively. The predicted creep compliances of Derakane 441-400 in the design space are in good agreement with the experimental data.

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Traditional large space structure construction incorporates the use of lightweight tubular metal alloys that have good strength to weight and stiffness to weight ratio. Recently, however, space structure construction has shifted focus on materials that are ultra lightweight, have high strength, have low package volume and possess excellent damping characteristics. Substantial damping is required in space since there is no surrounding medium to provide damping. Such a construction uses composites in a fabric form that displays viscoelastic behavior. The viscoelastic behavior is attributed to energy dissipation because of the shear stresses between the various fibrous strands that are kept in place by constraining viscoelastic layers. This type of vibration control falls under the rubric of passive damping of structures and has been found to have certain advantages over active damping such as less complexity as it does not require sensors, actuators and power supply that are needed for active damping. One such material consists of woven carbon strands constrained by layers of viscoelastic damping material. Dynamics and buckling behavior of a structure in the form of a tube made from this material with metallic end caps is modeled and analyzed using commercially available Finite Element Analysis code ABAQUS®. The current analysis deals with the non-pressurized tube since the structure can maintain the tubular configuration as well as support end caps on account of the stiffness provided by the composites. Since no simple analytical approaches are available to predict damping of these materials, experimental data was used to estimate the damping characteristics of the material. The mass of the end cap was also estimated from the experimental impulse response as exact mass of the end cap (that was rigidly fixed to the tube) was unknown. / Master of Science

As power system grids continue to grow in order to support an increasing energy demand, the system's behavior accordingly evolves, continuing to challenge designs for maintaining security. It has become apparent in the past few years that, as much as discovering vulnerabilities in the power network, accurate simulations are very critical. This study explores a classification method for validating simulation models, using disturbance measurements from phasor measurement units (PMU). The technique used employs the Random Forest learning algorithm to find a correlation between specific model parameter changes, and the variations in the dynamic response. Also, the measurements used for building and evaluating the classifiers were characterized using Prony decomposition. The generator model, consisting of an exciter, governor, and its standard parameters have been validated using short circuit faults. Single-error classifiers were first tested, where the accuracies of the classifiers built using positive, negative, and zero sequence measurements were compared. The negative sequence measurements have consistently produced the best classifiers, with majority of the parameter classes attaining F-measure accuracies greater than 90%. A multiple-parameter error technique for validation has also been developed and tested on standard generator parameters. Only a few target parameter classes had good accuracies in the presence of multiple parameter errors, but the results were enough to permit a sequential process of validation, where elimination of a highly detectable error can improve the accuracy of suspect errors dependent on the former's removal, and continuing the procedure until all corrections are covered. / Ph. D.

A power system stability is essential for maintaining the power system oscillation frequency within a small and acceptable interval around its nominal frequency. Hence, it is necessary to study and control the frequency for stable operation of a power system by knowing the characteristics within a power system. One approach is to understand the effectiveness of frequency and damping characteristics of generators in power systems. Hence, the simulation analysis of IEEE 118-bus power system is used for this study. The analysis includes theoretical analysis with a mathematical approach and simulation studies of swing equation to determine the characteristics of damped single-machine infinite bus, which is represented as a generator connects to a large network system with a small signal disturbance by line losses. Additionally, mathematical derivation of Prony analysis is presented in order to estimate the frequency and damping ratio of the simulation results. In the end, the results demonstrate that the frequency and damping characteristics of generators are highly dependent on the system inertia constant. Therefore, the higher inertia constant is a critical factor to ensure the system is more stable. / Master of Science

Ce manuscrit est consacré à l’étude de la méthode du développement en singularités (SEM) appliquée aux antennes. Dans la première partie de ce travail, trois méthodes d’extraction des pôles de résonance sont présentées et comparées : les méthodes de Prony et Matrix Pencil dans le domaine temporel et la méthode de Cauchy dans le domaine fréquentiel. Une procédure est établie pour optimiser l’extraction avec chaque méthode et une étude de robustesse montre que la méthode Matrix Pencil permet d’obtenir plus de pôles et avec une meilleure précision que les deux autres méthodes en présence de bruit. Dans un second temps, la méthode Matrix Pencil est appliquée sur des réponses d’antennes, obtenues en rayonnement et en Surface Equivalente Radar (SER), et les pôles de résonance extraits sont identiques pour les deux approches. Cette étude valide donc la possibilité d’extraire les pôles de résonance d’une antenne directement à partir de sa SER. La variation de la position des pôles de résonance en fonction des dimensions et de la charge de deux antennes est ensuite étudiée et met en évidence le lien entre l’impédance d’entrée de l’antenne et ses pôles de résonance. Enfin, les mesures de la SER de trois antennes valident expérimentalement l’extraction des pôles de résonance à partir de la SER d’une antenne. Ce travail pose donc les bases de la caractérisation d’antennes à l’aide de la SEM appliquée à la SER de l’antenne. / This manuscript deals with the Singularity Expansion Method (SEM) applied to antenna characterization. In the first part of this work, three resonant poles extraction methods are presented and compared: the Prony and Matrix Pencil methods in the transient domain and the Cauchy method in the frequency domain. A procedure is defined to optimize the extraction with each method and a robustness study shows that Matrix Pencil method allows obtaining more physical poles with a better accuracy than the two other methods in presence of noise. In a second part, the Matrix Pencil algorithm is applied on radiated and backscattered antenna responses. Extracted resonant poles from both responses are exactly the same. This study validates the possibility to extract poles directly from its backscattered response. The position of resonant poles is analyzed with respect to antenna’s dimension and its load for two different cases. This emphasizes the link between antenna poles and antenna input impedance. Finally, RCS measurements of three antennas validate antenna poles extraction directly from its RCS. This work lays the foundations of antenna characterization using the SEM applied to RCS measurements.