There is a need for a nonlinear flutter analysis method capable of predicting limit cycle oscillation in aeroelastic systems. A review is conducted of analysis methods and experiments that have attempted to better understand and model limit cycle oscillation (LCO). The recently developed method of nonlinear normal modes (NNM) is investigated for LCO calculation. Nonlinear normal modes were used to analyze a spring-mass-damper system with nonlinear damping and stiffness to demonstrate the ability and limitations of the method to identify limit cycle oscillation. The nonlinear normal modes method was then applied to an aeroelastic model of a pitch-plunge airfoil with nonlinear pitch stiffness and quasi-steady aerodynamics. The asymptotic coefficient solution method successfully captured LCO at a low relative velocity. LCO was also successfully modeled for the same airfoil with an unsteady aerodynamics model with the use of a first order formulation of NNM. A linear beam model of the Goland wing with a nonlinear aerodynamic model was also studied. LCO was successfully modeled using various numbers of assumed modes for the beam. The concept of modal truncation was shown to extend to NNM. The modal coefficients were shown to identify the importance of each mode to the solution and give insight into the physical nature of the motion. The quasi-steady airfoil model was used to conduct a study on the effect of the nonlinear normal mode's master coordinate. The pitch degree of freedom, plunge degree of freedom, both linear structural mode shapes with apparent mass, and the linear flutter mode were all used as master coordinates. The master coordinates were found to have a significant influence on the accuracy of the solution and the linear flutter mode was identified as the preferred option. Galerkin and collocation coefficient solution methods were used to improve the results of the asymptotic solution method. The Galerkin method reduced the error of the solution if the correct region of integration was selected, but had very high computational cost. The collocation method improved the accuracy of the solution significantly. The computational time was low and a simple convergent iteration method was found. Thus, the collocation method was found to be the preferred method of solving for the modal coefficients. / Ph. D.

This study compared the effects of selective cutting (SC) and the first shelterwood (SW) cut in oak (Quercus)-dominated forests of western Virginia. The specific attributes compared were: (1) tree species composition; (2) seedling, sapling, and overstory tree density; (3) overstory tree quality and size; (4) sapling crown class; and (5) canopy closure. Seedlings, saplings, and overstory trees were sampled at 22 SC and 28 SW sites. Significant differences identified between the two harvest types included: biodiversity of overstory and seedling layers; species densities for seedlings, saplings, and overstory trees; species composition across forest layers; and average canopy closure. Regeneration was poorer on SC than on SW, especially among oak species where SC oak seedling density averaged 5,651 stems ha-1 and SW oak seedling density averaged 9,843 stems ha-1. Selective cutting and SW may both contribute to mesophication of oak-dominated forests in the southern Appalachian Mountains; however, SC resulted in a higher percentage of mesic species post-harvest, and the SW tended to have more oak regeneration. / Master of Science / Selective cutting in the form of high-grading (harvesting only the most valuable trees in a forest) and diameter-limit cutting (harvesting all merchantable trees in a forest above a designated diameter at breast height) is the predominant timber harvest practice in the southern Appalachian Mountains. It is contributing to a shift in forest composition away from oak species toward tree species of lower commercial and wildlife value. In this study, although there were fewer seedlings and saplings after selective cuts than after shelterwoods (a partial harvest of trees aimed at encouraging the regeneration of desirable tree species such as oaks in the future forest), there was higher tree species diversity among the seedlings and saplings at selective cutting sites than at shelterwoods. Oak regeneration remains a challenging goal to meet, but silvicultural systems such as shelterwoods that are designed to promote oak regeneration are likely to be more successful than selective cutting at maintaining oak dominance in this forested region.

The research reported here explored the flammable range of gasification product “producer gas” in a combustion chamber to ensure complete combustion. Rising fuel prices has led to increased research in renewable energy sources. Biomass is a renewable resource whose use does not result in a net increase of CO₂ in the atmosphere. Wood was selected as the biomass for this research. Applications for wood as a fuel source includes crop drying, space heating, and power generation. Flammability limit and chemical equilibrium theory were used to model the flammable range of the gasification product in a combustion chamber. The model predicted an adiabatic flammable zone within an equivalence ratio of 0.56 to 1.67 for oak with 20 percent moisture content (w.b.), and a maximum adiabatic flame temperature of 2025°C for dry oak. Chemical equilibrium theory was used to predict gasification-combustion product concentration. Based on the analysis of the data, the following conclusions were made: (1) Flammability of gas-air mixture is largely determined by the amount of heat loss prior to combustion, (2) At equivalence ratios greater than 1.25, CO appears in the combustion products, (3) Adiabatic Flame Temperatures are largely influenced by moisture and excess air, (4) Combustion temperature is a critical parameter that influences composition distribution of the gasification-combustion product. (Product compositions are important to the designer, for both energy and environmental impact), and (5) Maximum benefit for a gasifier-combustor system could be obtained if heat loss, excess air, moisture content, mixing effectiveness, and residence time are optimized. / Master of Science

Pilot in-the-loop oscillation (PIO) is a phenomenon which occurs due to the dynamic interaction between pilot and aircraft. This detrimental aircraft handling quality appears through a variety of flight conditions and is very difficult to predict. Due to this complex behavior, PIO is not easily eliminated. This report describes a method of PIO analysis that is capable of examining multiple asymmetric nonlinearities acting simultaneously. PIO analyses are performed on a model based on the USAF NT-33A variable stability aircraft with nonlinearities including stick position limiting, elevator deflection limiting, and elevator rate limiting. These analyses involve the use of dual input describing functions which enable the prediction of frequency, amplitude, and mean point of oscillation. / Master of Science

Presence of nonlinearities may lead to limit cycle oscillations (LCOs) in aeroelastic systems. LCOs can result in fatigue in wings leading to catastrophic failures. Existence of LCOs for velocities less than the linear flutter velocity has been observed during flight and wind tunnel tests, making such subcritical behavior highly undesirable. The objective of this dissertation is to investigate the existence of subcritical LCOs in aeroelastic systems and develop state feedback controllers to suppress them. The research results are demonstrated on a two degree of freedom airfoil section model with stiffness nonlinearity. Three different approaches are developed and discussed. The first approach uses a feedback linearization controller employing the aeroelastic modal coordinates. The use of modal coordinates results in a system which is linearly decoupled making it possible to avoid cancellation of any linear terms when compared to existing feedback linearization controllers which use the physical coordinates. The state and control costs of the developed controller are compared to the costs of the traditional feedback linearization controllers. Second approach involves the use of nonlinear normal modes (NNMs) as a tool to predict LCO amplitudes of the aeroelastic system. NNM dynamics along with harmonic balance method are used to generate analytical estimates of LCO amplitude and its sensitivities with respect to the introduced control parameters. A multiobjective optimization problem is solved to generate optimal control parameters which minimize the LCO amplitude and the control cost. The third approach uses a nonlinear state feedback control input obtained as the solution of a multiobjective optimization problem which minimizes the difference between the LCO commencement velocity and the linear flutter velocity. The estimates of LCO commencement velocity and its sensitivities are obtained using numerical continuation methods and harmonic balance methods. It is shown that the developed optimal controller eliminates any existing subcritical LCOs by converting them to supercritical LCOs. / Ph. D.

Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. Specifically, we study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet. The equation for stability is derived and solved numerically using the Chebyshev collocation spectral method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability. The numerical solutions are compared with the analysis of the long wave limit and excellent agreement is shown between the analytical and the numerical solutions. We found flows which are long wave stable, but nevertheless unstable to wave numbers in a certain finite range. While elasticity is ultimately stabilizing, this effect is not monotone; there are instances where a small amount of elasticity actually destabilizes the flow. The linear stability in the short wave limit of shear flows bounded by two parallel free surfaces is investigated. Unlike the plane Couette flow which has no short wave instability, we show that plane Poiseuille flow has two unstable eigenmodes localized near the free surfaces which can be combined into an even and an odd eigenfunctions. The derivation of the asymptotics of these modes shows that our numerical eigenvalues are in agreement with the analytic formula and that the difference between the two eigenvalues tends to zero exponentially with the wavenumber. / Ph. D.

This research introduces a proposed model for predicting tilting angle and limit states of single-fastened cold-formed steel-to-steel shear connections. Predictions are validated through an experimental study considering ply configuration and a single Hex #10 -washer head fastener, centered in a 102 mm by 102 mm three boundary window. The fastener tilting angle is captured using an automated, optical non-contact measurement procedure. The results are used to identify cold-formed steel shear connection deformation as load progresses, including tilting, bearing, and combined tilting bearing at the plies and thread tension, shear and bearing fastener failure. Results shows that fastener tilting plays a kinematic affect for the connection. Fastener tilting is predicted in function of ply thickness and fastener pitch. Local ply bending deformation is reported to be the main deformation of the connection during fastener tilting. While fastener bending and shear failure occurred if the fastener does not tilt. / Master of Science

There has been a long history of violence between North and South Korea since the end of the Korean War in 1953 and North Korea is still a current threat to the South due to their missile launches and naval clashes. The purpose of this thesis is to analyze the interactions between North and South Korea from 1998 to 2006 and answer the question: What accounts for the difference in responses to North Korean threats by South Korean presidents from the same party with similar stands toward North Korea? Although South Korean Presidents Kim Dae Jung and Roh Moo Hyun shared similar approaches to North Korea, why did they not always respond in the same way? To answer this question, I examine a case in which North Korea test-launched a rocket and a case in which North Korean vessels cross the Northern Limit Line during each administration. By comparing these cases, I explain why the presidents continued their engagement policy and refrained from condemning the North in all but the case of the 2006 missile test. I test a set of explanations made by experts for South Korean approaches to North Korea to see which explanation best fits each case. I argue that each response was due to a combination of explanations rather than one single explanation. Even though each explanation had some merit, some explanations were more applicable than the others. Both Kim and Roh expressed concern over North Korea due to security and economic concerns. However, as the years and threatening behavior went on the public and international community started to take a greater notice to North Korea's activity and wanted the South Korean government to take action. As a result, public opinion and international pressure partially influenced Roh to shift his responses towards North Korea and halt aid after the 2006 missile launch. / Master of Arts

When designing aircraft wings shapes, it is important to ensure that the flight envelope does not overlap with regions of flutter or Limit Cycle Oscillation (LCO). A quick assessment of these dynamic aeroelastic for various design candidates is key to successful design. Flutter based design requires the sensitivity of flutter parameters to be known with the respect of design parameters. Traditionally, frequency domain based methods have been used to predict flutter characteristics and its sensitivity. However, this approach is only applicable for linear or linearized models and cannot be applied to systems undergoing LCO or other nonlinear effects. Though the time accurate approach can be implemented to overcome this problem, it is computationally expensive. Also, the unsteady adjoint formulation for sensitivity analysis, requires the state and adjoint variables to be stored at every time step, which prohibitively increases the memory requirement. In this work, these problems have been overcome by implementing a time spectral method based approach to compute flutter onset, LCOs and their design sensitivities in a computationally efficient manner. The time spectral based formulation approximates the solution as a discrete Fourier series and directly solves for the periodic steady state, leading to a steady formulation. This can lead to the time spectral approach to be faster than the time accurate approach. More importantly, the steady formulation of the time spectral method also eliminates the memory issues faced by the unsteady adjoint formulation. The time spectral based flutter/LCO prediction method was used to predict flutter and LCO characteristics of the AGARD 445.6 wing and pitch/plunge airfoil section with NACA 64A010 airfoil. Furthermore, the adjoint based sensitivity analysis was used to carry out aerodynamic shape optimization, with an objective of maximizing the flutter velocity with and without constraints on the drag coefficient. The resulting designs show significant increase in the flutter velocity and the corresponding LCO velocity profile. The resulting airfoils display a greater sensitivity to the transonic shock which in turn leads to greater aerodynamic damping and hence leading to an increase in flutter velocity. / Doctor of Philosophy / When designing aircrafts, dynamic aeroelastic effects such as flutter onset and Limit Cycle Oscillations need to considered. At low enough flight speeds, any vibrations arising in the aircraft structure are damped out by the airflow. However, beyond a certain flight speed, instead of damping out the vibrations, the airflow accentuates these vibrations. This is known as flutter and it can lead to catastrophic structural failure. Hence, during the aircraft design phase, it must be ensured that the aircraft would not experience flutter during the flight conditions. One of the contribution of this work has been to come up with a fast and accurate method to predict flutter using computational modelling. Depending on the scenario, it is also possible that during flutter, the vibrations in the structure increase to a certain amplitude before leveling off due to interaction of non-linear physics. This condition is known as limit cycle oscillation. While they can arise due to different kinds of non-linearities, in this work the focus has been on aerodynamic non-linearities arising from shocks in transonic flight conditions. While limit cycle oscillations are undesirable as they can cause structural fatigue, they can also save the aircraft from imminent structural fracture and hence it is important to accurately predict them as well. The main advantage of the method developed in this work is that the same method can be used to predict both the flutter onset condition and limit cycle oscillations. This is a novel development as most of the traditional approaches in dynamic aeroelasticity cannot predict both the effects. The developed flutter/LCO prediction method has then been used in design with the goal of achieving superior flutter characteristics. In this study, the shape of the baseline airfoil is changed with the goal of increasing the flutter velocity. This enables the designed system to fly faster without addition of weight. Since the design has been carried out using gradient based optimization approach, an efficient way to compute the gradient needs to be used. Traditional approaches to compute the gradient, such as Finite Difference Method, have computational cost proportional to the number of design variables. This becomes a problem for shape design optimization, where a large number of design variables are required. This has been overcome by developing an adjoint based sensitivity analysis method. The main advantage of the adjoint based sensitivity analysis is that it its computational cost is independent of the number of design variables, and hence a large number of design variables can be accommodated. The developed flutter/LCO prediction and adjoint based sensitivity analysis framework was used to carry out shape design for a pitch/plunge airfoil section. The objective of the design process was to maximize the flutter onset velocity with and without constraints on drag. The resulting optimized airfoils showed significant increase in the flutter velocity.

Motion sensitive operations at sea are conducted in an unpredictable environment. While occasionally these operations can be planned around suitable weather forecast or delayed until smoother motions are apparent, naval ships conducting flight operations may have little liberty in their mission planning and execution. Tools exist to translate the ocean's harsh conditions into discretely defined low motion operational periods. Particularly of interest, the identification of discrete lull periods or quiescence for shipboard helicopter operations can be better defined using a landing period indicator than with the current method of utilizing static deck angle measurements. While few of these systems exist, assessing their operational benefits is difficult due to a lack of well-defined performance metrics. This thesis defines and examines the use of two methodical approaches to evaluating Landing Period Indicators (LPIs) and their subject ship-helicopter dynamic interface system. First a methodology utilizing the comparison of a basic transparent algorithm is detailed and a case study employing this methodology is examined. Second, a system dynamics approach is taken to pilot workload analysis, utilizing a dynamic systems model characterizing a subset of the Dynamic Interface. This approach illustrates the realistic gains in understanding and development that can be accomplished by utilizing system dynamics in the analysis of the Dynamic Interface and LPI insertion. / Master of Science