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Four identical, uniformly separated particles interconnected by ideal anharmonic springs are constrained to move on a fixed, frictionless circular track. The Lagrangian for the system is written and then transformed by matrix operations suggested by the symmetry of the arrangement of springs and particles. The equations of motion derived from the transformed Lagrangian yield four natural **frequencies** of motion.

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According to astronomical theory, ice ages are caused by variations in the Earth's orbit. However, ice core data shows strong fluctuations in ice volume at a low **frequency** not significantly present in orbital variations. To understand how this might occur, the dynamics of a two dimensional nonlinear differential equation representing glacier/temperature interaction of an idealized climate was studied. Self sustained **oscillation** of the autonomous equation was used to model the internal mechanisms that could produce these fluctuations. Periodic parametric modulation of a damped internal **oscillation** was used to model periodic climate response at double the external modulation period. Both phenomena rely on bounded, structurally stable invariant manifolds that occur when a constant equilibrium solution becomes unstable. For the autonomous formulation, asymptotic analysis was performed to obtain analytic approximations. An outflowing manifold of a second saddle equilibrium formed a heteroclinic connection to the small amplitude periodic orbit of the self sustained **oscillation**. This connection bifurcated to a homoclinic orbit when the periodic orbit intersected the saddle equilibrium. For periodic parametric modulations, internal **frequencies** that give rise to the period doubling phenomena were identified. The Poincare map showed cases where the bounded outflowing manifold intersects transversally with the unbounded inflowing manifold, a geometry indicative of chaotic dynamics.

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Bistable structures have two stable equilibrium positions and can be utilized to maintain a specific static shape with no energy consumption. This dissertation focuses on the minimum required energy for performing snap-through of a bistable structure. Snap-through is the motion of a bistable structure from one stable equilibrium position to the other. This research uses the Duffing-Holmes equation as a one-degree-of-freedom representative model of a bistable structure, and this nonlinear equation is solved to calculate the required energy for cross-well **oscillation**. The research identifies several unique features of the response of a bistable system subjected to force and energy constraints. The research also shows how the required energy for cross-well **oscillation** varies as a function of damping ratio, **frequency** ratio, and for different values of excitation force amplitudes. The response of the bistable system is compared to a mono-stable linear system with the same parameters. A magneto-elastic bistable beam was fabricated and tested to validate theoretical predictions.

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A **frequency** domain solution method for nonlinear panel flutter with thermal effects using a consistent finite element formulation has been developed. The von Karman nonlinear strain-displacement relation is used to account for large deflections, the quasi-steady first-order piston theory is employed for aerodynamic loading and the quasi-steady thermal stress theory is applied for the thermal stresses with a given change of the temperature distribution, ΔΤ (x, y, z). The equation of motion under a combined thermal-aerodynamic loading can be mathematically separated into two equations and then solved in sequence: (1) thermal-aerodynamic postbuckling and (2) limit-cycle **oscillation**. The Newton-Raphson iteration technique is used to solve the nonlinear algebraic equations and an updated linearized eigen-solution procedure is adopted to solve the nonlinear differential equations. The finite-element **frequency** domain solution results are compared with numerical time integration results. Limit-cycle responses, flutter boundaries, snap-through areas and stress distributions are obtained from the present analyses. The effects of different temperature distributions, panel aspect ratios and boundary support conditions are investigated.
The influence of temperature and dynamic pressure on panel fatigue life is also presented. The relation of dynamic pressure versus panel life time at a given temperature is established and an endurance and failure dynamic pressures on panel fatigue life can be estimated.

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When holding an outstretched limb or aiming at a target, humans produce small involuntary fluctuations that may hamper performance. Current strategies for minimizing the impact of tremulous **oscillations** predominantly include both extrinsic and intrinsic support. The aim of the current dissertation is to better understand the parameters of physiological tremor associated with handgun aiming with the end goal of improving shooting accuracy. Experiment 1 focused on handgun aiming and the influence of different arm posture adopted during aiming. Experiment 2 expanded upon the findings of experiment 1 by comparing tremor during finger pointing, handgun aiming, and handgun shooting. Experiment 3 attempted to confirm that both mechanical support and proprioceptive feedback play a role in both attenuation of tremor amplitude and handgun shooting accuracy.
In experiment 1, thirty volunteers stood 6.4 meters from a target and aimed a weighted mock handgun for 10 seconds per trial. Two hand grips (bilateral, unilateral) and two arm positions (bent elbow, straight elbow) were assessed for acceleration in the anterior-posterior (AP), medial-lateral (ML), and vertical (VT) directions. Amplitude, regularity, and a **frequency** spectrum analysis of the acceleration signals were analyzed. Tremor amplitudes (VT, ML) were reduced using a bilateral grip and by bending the elbows. The irregularity of the tremor signal was increased by using two hands to support the handgun. Interestingly, irrespective of the posture adopted, ML accelerations were of greater amplitude than VT **oscillations**. AP **oscillations** were markedly smaller compared to VT and ML tremor, did not display consistent **frequency** peaks, and were not altered by the arm conditions.
During experiment 2, twenty volunteers, in a counterbalanced order, pointed their finger, aimed a training handgun, or shot a training handgun, for 10 seconds at a bullseye target 6.4 meters away. Amplitude, regularity, and **frequency** spectrum analysis of the acceleration signals were computed. Aiming with the mass of a gun in the hand has primarily a damping effect on the amplitude of tremor in the distal segments as well as resulting in more regular movements. Overall, aiming with a gun and pointing with a finger were similar tasks except for the added mass of the handgun aiming condition. Shooting accuracy and handgun shooting experience were also assessed for correlations with acceleration amplitude and regularity. Both handgun shooting accuracy and experience revealed a stronger correlation with increased irregularity of the acceleration signal than decreased acceleration amplitude. A correlation was also run between shooting accuracy and handgun shooting experience. An increase in accuracy had a significant, moderate relationship with an increase in handgun shooting experience.
Experiment 3 had twenty volunteers aim as well as shoot a training handgun at a bullseye target 6.4 meters away during two limb support conditions and two weight conditions for a total of four combinations. Amplitude, regularity, and **frequency** spectrum analysis of the acceleration signals were computed. Bilateral limb support again reduced tremor amplitude and increased the irregularity of the acceleration signal over unilateral conditions. Bilateral limb support also contributed to a significantly improved handgun shooting accuracy when compared to unilateral limb support conditions. By manipulating the weight of the handgun, the third study also indicated the addition of a second limb reduced acceleration amplitude through both mechanical support and proprioceptive feedback.
The experiments demonstrate that finger pointing and handgun aiming share similar tremulous characteristics in all three directions (VT, ML, AP). These experiments also indicate that acceleration amplitude can be reduced while acceleration regularity and shooting accuracy are increased through the use of a bilateral limb support posture.

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In the extensive published literature on panel flutter, a large number of papers are dedicated to investigation of flat plates in the supersonic flow regime. Very few authors have extended their work to flutter of curved panels. The curved geometry generates a pre-flutter behavior, triggering a static deflection due to a static aerodynamic load (SAL) over the panel as well as dynamic characteristics unique to this geometry. The purpose of this dissertation is to provide new insights in the subject of flutter of curved panels. Finite element **frequency** and time domain methods are developed to predict the pre/post flutter responses and the flutter onset of curved panels under a yaw flow angle. The first-order shear deformation theory, the Marguerre plate theory, the von Karman large deflection theory, and the quasi-steady first-order piston theory appended with SAL are used in the formulation. The principle of virtual work is applied to develop the equations of motion of the fluttering system in structural node degrees of freedom. In the **frequency** domain method, the Newton-Raphson method is used to determine the panel static deflection under the SAL, and an eigen-value solution is employed for the determination of the stability boundary margins at different panel height-rises and yaw flow angles. Pre-flutter static deflection shape, flutter coalescence **frequency**, and damping rate of various cylindrical panels are thoroughly investigated. The main results revealed that the pre-flutter static response of cylindrical panels is fundamentally different from the one associated with flat plates. It is shown that curvature has a detrimental effect for 2-dimensional (2-D) curved panels, and is beneficial for 3-D components at an optimum height-rise. In the time domain method, the system equations of motion are transformed into modal coordinates, and solved by a fourth-order Runge-Kutta numerical scheme. Time history responses, phase plots, power spectrum density plots, and bifurcation diagrams uncovered the pre/post flutter responses of cylindrical panels. The computed stability boundary margins and onset **frequencies** matched very well with the ones computed by the **frequency** domain method. Bifurcation diagrams revealed limit-cycles **oscillations** (LCO) and chaotic motion. It was found that 2-D cylindrical panels settle in a multiplicity of LCO as the height-rise of the panel increases, whereas chaotic motion characterize the dynamic behavior of 3-D cylindrical panels at high height-rises.

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Bistability is the property of structures showing the ability to attain two statically stable states. Due to dynamic and static advantages such as no energy demand at stable positions and providing higher deflections compared to a monostable structure, bistability may be appealing in control surface design for aircraft structures and load alleviation for wind turbine blades. The dynamics of bistable structures is nonlinear because of the snap-through occurring during the cross-well **oscillation** between two stable states. A new control strategy called hybrid position feedback control is developed based on the conventional positive position control to exploit linear dynamics of bistable structures around stable equilibrium positions.
In this thesis, complementary stability, performance and energy analysis of bistable structures controlled by the hybrid controller are investigated using numerical time domain and **frequency** methods. The stability regions, energy variance by parameters, and the operational regions providing state transition are determined. As a result of the analyses, two alternative design options are proposed and necessary stability regions are indicated.
In addition, experimental analysis is conducted on an unsymmetric cross-ply bistable composite plate to show the feasibility of the hybrid control strategy. Various analyses such as stability and energy consumption are performed.

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Computations have been performed to simulate turbulent supersonic, transonic, and subsonic flows past three-dimensional deep, transitional, and shallow cavities. Simulation of these self sustained oscillatory flows has been generated through time accurate solutions of Reynolds averaged full Navier-Stokes equations using the explicit MacCormack scheme. The Reynolds stresses have been modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses have been performed for the instantaneous pressure values on the cavity floor. Comparison with experimental data is made in terms of the mean static pressure and the **frequency** spectra of the **oscillation** along the cavity floor. The time-averaged computational results show good agreement with the experimental data along the cavity walls. The features of open, transitional and closed cavity flows and effects of the third dimension have been illustrated through computational graphics. The three-dimensionality of cavity flows has been elucidated pictorially.

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At high angles of attack, the flowfield over slender forebodies becomes asymmetric with substantial side force, which may exceed the available control capability. The unsteady compressible Navier-Stokes equations are used to investigate the effectiveness of different active control methods to alleviate and possibly eliminate the flow asymmetry and the subsequent side force. Although the research work focuses on active control methods, a passive control method has been investigated. The implicit, Roe flux-difference splitting, finite volume scheme is used for the numerical computations. Both locally-conical and three-dimensional solutions of the Navier-Stokes equations are obtained.
The asymmetric flow over five-degree semi-apex angle cone is used as a reference case to which the different control methods are applied and compared. For the passive control method, the side-strakes control is investigated. The parametric study includes the control effectiveness of the strake span length.
For the active control methods, flow injection in the normal and tangential directions to the body surface has been investigated. Both uniform and pressure-sensitive mass flow injection are applied, and the effects of mass flow rate, injection angle and injection length have also been studied. Injection, with a parabolic profile, is applied from the cone sides tangent to its surface. Surface-heating, where temperature of the cone surface is increased, is also investigated. The effectiveness of a hybrid method of flow control which combines injection with surface heating has been studied. The cone spinning and rotary **oscillation** around its axis are applied as an active control method. The computational applications include the effects of uniform spinning rates and periodic rotary **oscillations** at different amplitudes and **frequencies** on the flow asymmetry.

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This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts.
First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained.
In the second part the equilibrium solutions are obtained and a local stability analysis is performed. The system of rate equations is solved numerically and the effects, on the solution, of varying physical parameters is discussed.
Finally, the third part addresses the oscillatory behavior of the system by "tracking" the eigenvalues of the linearized system. A comparison is made between the **frequency** of **oscillations** in the linear and nonlinear system. Pertinent physical processes--back transfer, Q-switching, and up-conversion--are then examined.
The laser system consists of thulium and holmium ions in a YAG crystal operated in a Fabrey-Perot cavity. All computer programs were written in FORTRAN and currently run on either an IBM-PC or a DEC VAX 11/750.

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