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In this Dissertation, we develop, and provide proof of principle for, parameter identification techniques for structural systems that can be described in terms of one or two nonlinear normal modes. We model the dynamics of these modes by second-order ordinary-differential equations based on the principles of mechanics, past experience, and engineering judgment. We perform a number of separate experiments on a two-mass structure using several different types of excitation. For the linear tests, the theoretical system response is known in closed-form. For the nonlinear test, we use the method of multiple scales to determine second-order uniform expansions of the model equations and hence determine the approximations to responses of the structure. Then, we estimate the linear and nonlinear parameters by regressive fits between the theoretically and experimentally obtained response relations. We report deviations and agreements between model and experiment. / Ph. D.

The advent of synchronized wide-area frequency measurements obtained from frequency disturbance recorders and phasor measurement units has presented the power industry with special opportunities to study power system dynamics. I propose the use of wide-area frequency measurements in identifying system disturbances based on power system post-event modal properties. In this work, power system dynamics are examined from an internal system energy viewpoint. Since an electric power system is composed of coupled rotating machines (large generators) which have air gap magnetic fields that are essentially static, or quasi-static, the power system may be modeled as a system with energy stored in quasi-static magnetic fields. The magnetic fields in the machines do change with time but may be modeled as static as far as wave propagation is concerned. The dynamic model that I develop treats this magnetic energy specifically as potential energy. Each rotating machine also contains an inertia due to the mass and motion of its rotor train and so each machine contains a rotational kinetic energy. Thus the internal system energy for a power system dynamic model may be considered to be contained in potential (magnetic) and kinetic (rotating mass) energies. This notion of internal energy lends itself to the use of a state-space model where each system state is associated with either a kinetic energy or a potential energy. An n-machine system would have a total of 2n states and would thus be a 2n-th order system. For many power system disturbances, I postulate that a linearized version of this model may be used to examine system natural response in terms of frequency and phasor measurements. The disturbances that I will investigate include generator and line outages. For any particular outage, the power system exhibits a very specific natural response in terms of its kinetic and potential energies. Kinetic energy in the system is directly related to each specific machine's rotational speed. I propose that the kinetic energy corresponds directly with bus frequencies through a linear transformation. Likewise magnetic field energy in each machine corresponds directly with a torque angle. The potential energy in the system thus corresponds directly with bus angles through a linear transformation. The primary focus of this work is on frequency deviation modal characteristics – specifically damped oscillation frequencies, mode shapes, and damping ratios. This work presents how specific disturbances on a power system will lead to specific oscillation frequencies in the deviation quantities and that these oscillation frequencies may be used to identify the disturbance. The idea of disturbance identification stems out of previous work done in locating disturbances by using a distributed parameter (DP) model of an electric power system. This DP model, which assumes a wave-like motion of frequency and phase quantities, was used to locate disturbances via a triangulation method. This present work, instead of using a DP model of the power system, assumes lumped parameters and focuses on disturbance identification strictly via modal characteristics – particularly oscillation frequency in the frequency deviations. This model is not concerned with geographic location but focuses on system topology, loading, and machine mass as lumped parameters. Advantages of disturbance identification include mainly reliability enhancements but can also be used in marketing applications. The state-space model used to realize this theory is verified via simulation using small, "academic" systems which should prove useful in classroom settings. Additionally the model is verified on a larger test system in order prove its validity and potential usefulness on large power systems. / Ph. D.

Digital models are essential to quantifying the behavior of structural systems. In many cases, the creation of these models involves manual measurements taken in the field, followed by a manual creation of this model using these measurements. Both of these steps are time consuming and prohibitively expensive, leading to a lack of utilization of accurate models. We propose a framework built on the processing of 3D laser scanning data to partially automate the creation of these models. We focus on steel structures, as they represent a gap in current research into this field. Previous research has focused on segmentation of the point cloud data in order to extract relevant geometries. These approaches cannot easily be extended to steel structures, so we propose a novel method of processing this data with the goal of creating a full finite element model from the information extracted. Our approach sidesteps the need for segmentation by directly extracting the centerlines of structural elements. We begin by taking "slices" of the point cloud in the three principal directions. Each of these slices is flattened into an image, which allows us to take advantage of powerful image processing techniques. Within these images we use 2d convolution as a template match to isolate structural cross sections. This gives us the centroids of cross sections in the image space, which we can map back to the point cloud space as points along the centerline of the element. By fitting lines in 3d space to these points, we can determine the equations for the centerline of each element. This information could be easily passed into a finite element modeling software where the cross sections are manually defined for each line element. / Modern buildings require a digital counterpart to the physical structure for accurate analysis. Historically, these digital counterparts would be created by hand using the measurements that the building was intended to be built to. Often this is not accurate enough and the as-built system must be measured on site to capture deviations from the original plans. In these cases, a large amount of time must be invested to send personnel out into the field and take large amounts of measurements of the structure. Additionally, these "hand measurements" are prone to user error. We propose a novel method of gathering these field measurements quickly and accurately by using a technique called "laser scanning". These laser scans essentially take a 3D snapshot of the site, which contains all the geometric information of visible elements. While it is difficult to locate items such as steel beams in the 3D data, the cross sections of these structural elements are easily defined in 2D. Our method involves taking 2D slices of this 3D scan which allows us to locate the cross sections of the structural members by searching for template cross-sectional shapes. Once the cross sections have been isolated, their centers can be mapped back from the 2D slice to the 3D space as points along the centerlines of the structural elements. These centerlines represent one of the most time consuming requirements to building digital models of modern buildings, so this method could drastically reduce the total modeling time required by automating this particular step.

Metal buildings account for over 40% of low-rise construction in the US. Despite this, predictive fundamental period equations that were obtained empirically for mid-rise construction are used in seismic design. Analytical modeling of metal building frames implied that these equations significantly underpredict the period, which led to the development of a new predictive equation. However, experimental tests showed that these models may overestimate the measured period. In this work, further tests were carried out in order to single out possible causes. Buildings were tested during different stages of construction to evaluate how non-structural elements could affect the behavior. Both planar and three-dimensional models were developed to determine if design assumptions are accurate for the purpose of estimating the period. The results from tests showed that, unlike other single-story buildings, non-structural components seem to have negligible effect on the structural behavior. However, several buildings seemed to exhibit signs of fixed conditions at the column base. This assertion was corroborated by updating the analytical models. The two modeling approaches showed good agreement with each other as well, validating the use of planar models to predict the period. Finally, new predictive equations are proposed that take into account the type of cladding, as it was found to be an important variable not previously considered. However, low mass participation ratios coupled with the stiffness provided by the secondary framing put the use of the equivalent lateral force procedure into question. / Master of Science / When designing buildings for earthquake loads it is necessary to know their dynamic properties in order to define the equivalent forces that must be applied. Building codes provide predictive equations that were obtained empirically for typical mid-rise construction. Metal buildings do not fall within the range of buildings tested for their development, and so a new equation was proposed for them based on a database of planar models. However, previous tests implied that this equation was predicting larger periods than those obtained experimentally. In this work, further tests were carried out during different stages of construction to evaluate how non-structural elements could affect the behavior. Models were also created for each building in order to determine if the approach used to develop the metal building database was adequate for estimating the period. The results from tests showed that, unlike other single-story buildings, non-structural components seem to have negligible effect on the structural behavior, and the modeling assumptions within the database were validated. Further analysis showed that the type of cladding (concrete or metal sheeting) had a large influence on the properties of metal buildings. In consequence, a new set of predictive equations is proposed that takes this into account.

Modal analysis is the experimental characterization of the dynanlical behavior of a structure. Recent advances in laser velocimetery have made available to the experimentalist a rich, new source of vibration data. Data can now be obtained from many different spatial locations on a structure. A method is presented to use this new data for the analysis of beams. Two approaches are investigated: minimum residual methods and boundary condition methods. The minimum residual approaches include autoregressive methods and non-linear least squares techniques. Significant contributions to sample rate considerations for parametric sinusoidal estimation resulted from this research. The minimum residual methods provide a good connection between the measured data and the fitted model. However, they do not yield a true modal decomposition of the spatial data. The boundary condition approach provides a complete modal model that is based on the spatial data and is completely compatible with classical beam theory. All theoretical constraints are included in the procedure. Monte Carlo investigations describe the statistical characteristics of the methods. Experiments using beams validate the methods presented. Advantages and limitations of each approach are discussed. / Ph. D.

This thesis describes the test rig and results from a project expanding the field of rotor health monitoring by using Active Magnetic Bearings (AMBs) as actuators for applying a variety of known force inputs to a spinning. Similar to modal analysis and other nondestructive evaluation (NDE) techniques which apply input signals to static structures in order to monitor responses; this approach allows for the measurement of both input and output response in a rotating system for evaluation. However, unlike these techniques, the new procedure allows for multiple forms of force input signals to be applied to a rotating structure. This technique is used on a rotating shaft supported in conventional bearings with an AMB actuator added to the system. This paper presents the results from this project including shaft rub and notch. An EDM notch was also tested to attempt a breathing scenario similar to breathing cracks. / Master of Science

This master thesis deals with the optimal initial perturbation problem for a 1D unsteady self-similar ablation flow in an inertial confinement fusion context. The physical modelling consists of the compressible Euler equations with nonlinear heat conduction. The base flow and linear 3D perturbations are computed using a multidomain Chebyshev collocation method. Longitudinal optimal initial perturbations are computed by means of a non-modal analysis method for stationary perturbation evolution operators (Schmid, 2001 & 2007) after transformation of the time-dependent perturbation problem. Results of optimal gain and initial perturbation differ significantly from those produced by a non-stationary direct-adjoint method (Varillon, 2019). This discrepancy is analyzed to be a consequence of a diagonalization failure of the discrete perturbation evolution operator.