This thesis describes an experimental investigation of the flame transfer function between flow disturbances and heat release oscillations in lean, premixed combustors. This research effort was motivated by the fact that modern gas turbines, operating fuel-lean to minimize exhaust emissions, are susceptible to self-excited combustion oscillations. These instabilities generally occur when the unsteady combustion process couples with the acoustic modes of the combustion chamber. The resultant flow and structural vibrations can substantially reduce hot section part life. As such, avoiding operating regimes where high dynamics occur often requires operating at lower power outputs and/or higher pollutant emissions than the turbine is otherwise capable. This work demonstrated nonlinearities in the chemiluminescence response at large amplitude velocity oscillations in a turbulent, swirling flame. It is observed that the nonlinear flame response can exhibit a variety of behaviors, both in the shape of the response curve and the forcing amplitude at which nonlinearity is first observed depending on the operating conditions of the combustor. The phase between the flow oscillations and heat release is also seen to have substantial amplitude dependence. In addition, the interactions between the fundamental frequency and the higher and subharmonics of the measured signals can significantly influence the flame as well as the frequency response of the system. The nonlinear flame dynamics are governed by different mechanisms in different frequency and flowrate regimes. Three mechanisms, vortex rollup, unsteady flame liftoff, and parametric instability, are identified to influence the nonlinear flame response in these combustors. Analysis of the results shows that the mechanisms responsible for nonlinearity in the flame response are influenced by the Strouhal number, the mean velocity at the combustor dump plane, and the ratio of the oscillating velocity amplitude to the laminar flame speed.

An understanding of the generation of higher harmonics in Lamb waves is of critical importance for applications such as remaining life prediction of plate-like structural components. The objective of this work is to use nonlinear Lamb waves to experimentally investigate inherent material nonlinearities in aluminum plates. These nonlinearities, e.g. lattice anharmonicities, precipitates or vacancies, cause higher harmonics to form in propagating Lamb waves. The amplitudes of the higher harmonics increase with increasing propagation distance due to the accumulation of nonlinearity while the Lamb wave travels along its path. Special focus is laid on the second harmonic, and a relative nonlinearity parameter is defined as a function of the fundamental and second harmonic amplitude. The experimental setup uses an ultrasonic transducer and a wedge for the Lamb wave generation and laser interferometry for detection. The experimentally measured Lamb wave signals are processed with a short-time Fourier transformation (STFT) and a chirplet transformation-based algorithm, which yield the amplitudes of the frequency spectrum as functions of time, allowing the observation of the nonlinear behavior of the material. The increase of the relative nonlinearity parameter with propagation distance as an indicator of cumulative second harmonic generation is shown in the results for two different aluminum alloys. The difference in inherent nonlinearity between both alloys as determined from longitudinal wave measurements can be observed for the Lamb wave measurements, too.

This thesis contains two major components of research: numerical simulation of optical-parametric amplification cross correlation of Frequency-Resolved Optical Gating (OPA-XFROG) and numerical simulation of GRENOUILLE and its related issues. Recently, an extremely sensitive technique--OPA-XFROG has been developed. A short pump pulse serves as the gate by parametrically amplifying a short segment of the signal pulse in a nonlinear crystal. High optical parametric gain makes possible the complete measurement of ultraweak, ultrashort light pulses. Unlike interferometric methods, it does not carry prohibitively restrictive requirements, such as perfect mode-matching, perfect spatial coherence, highly stable absolute phase, and a same-spectrum reference pulse. We simulate the OPA-XFROG technique and show that by a proper choice of the nonlinear crystal and the noncollinear mixing geometry it is possible to match the group velocities of the pump, signal, and idler pulses, which permits the use of relatively thick crystals to achieve high gain without measurement distortion. Gain bandwidths of ~100 nm are possible, limited by group velocity dispersion. In the second part of the thesis, we numerically simulate the performance of the ultrasimple ultrashort laser pulse measurement device- GRENOUILLE. While simple in practice, GRENOUILLE has many theoretical subtleties because it involves the second-harmonic generation of relatively tightly focused and broadband pulses. In addition, these processes occur in a thick crystal, in which the phase-matching bandwidth is deliberately made narrow compared to the pulse bandwidth. We developed a model that include all sum-frequency-generation processes, both collinear and noncollinear. We also include dispersion using the Sellmeier equation for the crystal BBO. Working in the frequency domain, we compute the GRENOUILLE trace for practical-and impractical-examples and show that accurate measurements are easily obtained for properly designed devices. For pulses far outside a GRENOUILLE's operating range (on the long side), we numerically deconvolve the GRENOUILLE trace with the response function of GRENOUILLE to improve its spectral resolution. In the last part of the thesis, we simulate the second harmonic generation with tightly focused beams by use of lens. Thus, we are able to explain the `weird' focusing effect that has been a `puzzles' for us in the GRENOUILLE measurement.

The aim of this study is to develop a seawater desalination system that uses sea-wave energy as the sole energy source for system operation. This system is composed of a sea-wave energy acquisition system, a reverse-osmosis device, and a proposed mechanism linking the system to function synchronously. The relationships between various system parameters and system characteristics are analyzed. The limitations and constraints of system operations are then suggested. For the purpose of comparison, another system, which indirectly drives the reverse-osmosis system through an additional stage of energy storage, is introduced. To analyze the system dynamic properties, the following steps are implemented. First, a mathematical model than can properly describe the system characteristics is derived. This model is found to be a nonlinear one, which increase the difficulties of system analysis enormously. However, it is also noted through a preliminary examination that the effect of system nonlinearity becomes insignificantly if the system parameters are properly adjusted. Under these parameters, the linearied model is analyzed. The effects of different system parameters on the amount of energy acquisition and desalinated water are investigated. The analysis indicates that the amount of energy acquisition or desalinated water is closely related to both the selected energy acquisition system and the desalination system. For a given energy acquisition system and sea wave condition, an improper system parameter selection of desalination system will either make the whole system operation inefficient or devastate the functioning of acquisition system. This suggests that certain parameters of the desalination system must be adjustable in a real operation. The study also shows that the linearied system can be approximated by a model with two degrees of freedom. This model may offer the convenience for the optimization of system parameters.

This thesis studies the mechanics which can be associated with asphalt concrete compaction and develops continuum models in a general thermo-mechanical setting which can be used in future work to corroborate experimental compaction experiment results. Modeling asphalt concrete compaction, and also the ability to thereby predict response of mixes, is of great importance to the pavement industry. Asphalt concrete exhibits nonlinear response even at small strains and the response of asphalt concrete to different types of loading is quite different. The properties of asphalt concrete are highly influenced by the type and amount of the aggregates and the asphalt used. The internal structure of asphalt concrete continues to evolve during the loading process. This is due to the influence of different kinds of activities at the micro-structure level and to the interactions with the environment. The properties of asphalt concrete depend on its internal structure. Hence, we need to take into account the evolution of the internal structure in modeling the response of asphalt concrete. A theoretical model has been developed using the notion of multiple natural configurations to study a variety of non-linear dissipative responses of real materials. By specifying the forms for the stored energy and the rate of dissipation function of the material, a specific model was developed using this framework to model asphalt compaction. A compressible model is developed by choosing appropriate forms of stored energy and rate of dissipation function. Finally, a parametric study of the model is presented for a simple compression deformation. It is anticipated that the present work will aid in the development of better constitutive equations which in turn will accurately model asphalt compaction both in laboratory and in field. Distinct numerical approaches have been used to demonstrate the applicability of the theoretical framework to model material response of asphalt.

The leading cause of death in patients who survive subarachnoid hemorrhage (SAH) is stroke as a result of cerebral arterial vasospasm1. Such vasospasms involve a vasoactive response, but they remain enigmatic and no clinical treatment has proven effective in prevention or reduction2. Arteries remodel in response to diverse mechanical loads and chemical factors. Following SAH, the surrounding vasculature is exposed to a radically altered chemo-mechanical environment. It is our hypothesis that chemical stimuli associated with the formation of an extravascular blood clot dominates the maladaptive growth and remodeling response early on, thus leading to important structural changes. However, it is not clear which of the many chemical factors are key players in the production of vasospasm. Before an accurate picture of the etiology of vasospasm can be produced, it is imperative to gain a better understanding of the non-pathogenic cerebral vasculature. In particular, the rabbit basilar artery is a well established model for vasospasm. However, surprisingly little is known about the mechanical properties of the rabbit basilar artery. Using an in vitro custom organ culture and mechanical testing device, acute and cultured basilar arteries from male White New Zealand specific pathogen free rabbits underwent cyclic pressurization tests at in vivo conditions and controlled levels of myogenic tone. Sections of basilar arteries were imaged for collagen fiber orientation at 0, 40 and 80 mmHg at in vivo stretch conditions using nonlinear optical microscopy. The nonlinear stress-strain curves provide baseline characteristics for acute and short-term culture basilar arteries. The active and passive testing creates a framework for interpreting the basal tone of arteries in our culture system. Nonlinear optical microscopy second harmonic generation provides unique microstructural information and allows imaging of live, intact arteries while maintaining in vivo geometries and conditions. Collagen fibers were found to be widely distributed about the axial direction in the adventitial layer and narrowly distributed about the circumferential direction in the adventitial layer. The quantified collagen fiber angles within the artery wall further support the development of accurate mathematical models.

Input¬output approximation of spacecraft motion is convenient and necessary in many situations. For a rigid¬body spacecraft, this process is simple because the system is governed by a set of equations that is linear in the system parameters. However, the combination of a flexible appendage and a rigid hub adds complexity by increasing the degrees of freedom and by introducing nonlinear coupling between the hub and appendage. Assumed Modes is one technique for modeling flexible body motion. Traditional Assumed Modes uses a set of linear assumed modes, but when dealing with rotating flexible systems, a modification of this method allows for the use of quadratic assumed modes. The quadratic assumed model provides an increased level of sophistication, but the derivation still neglects a set of higher¬order terms. This work develops the nonlinear equations of motion that arise from retaining these nonlinear, higher¬order terms. Simulation results reveal that the inclusion of these terms noticeably changes the motion of the system. Once the equations of motion have been developed, focus turns to the input¬output mapping of a system that is simulated using this set of equations. Approxi¬mating linear systems is straightforward, and many methods exist that can success¬fully perform this function. On the other hand, few approximation methods exist for nonlinear systems. Researchers at Texas A&M University recently developed one such method that obtains a linear estimation and then uses an adaptive polynomial estimation method to compensate for the disparity between that estimate and the true measurements. This research includes an in¬depth investigation of this nonlinear approximation technique. Finally, these two major research thrusts are combined, and input¬output approx¬imation is performed on the nonlinear rotational spacecraft model developed herein. The results of this simulation show that the nonlinear method holds a significant advantage over a traditional linear method in certain situations. Specifically, the nonlinear algorithm provides superior approximation for systems with nonzero natu¬ral frequencies. For the algorithm to be successful when rigid¬body modes are present, the system motion must be persistently exciting. This research is an important first step toward developing a nonlinear parameter identification algorithm.

Tool chatter in longitudinal turning is addressed with a new perspective using a complex machining model describing the coupled tool-workpiece dynamics subject to nonlinear regenerative cutting forces, instantaneous depth-of-cut (DOC) and workpiece whirling due to material imbalance. The workpiece is modeled as a system of three rotors: unmachined, being machined and machined, connected by a flexible shaft. The model enables workpiece motions relative to the tool and tool motions relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous DOC, rate of material removal and whirling. Excluding workpiece vibrations from the cutting model is found improper. A rich set of nonlinear behaviors of both the tool and the workpiece including period-doubling bifurcation and chaos signifying the extent of machining instability at various DOCs is observed. Presented numerical results agree favorably with physical experiments reported in the literature. It is found that whirling is non-negligible if the fundamental characteristics of machining dynamics are to be fully understood. The 3D model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Numerical simulations reveal diverse behaviors for the 3D coupled and 1D uncoupled equations of motion for the tool. Most notably, observations made with regard to the inconsistency in describing stability limits raise the concern for using 1D models to obtain stability charts. The nonlinear 3D model is linearized to investigate the implications of applying linear models to the understanding of machining dynamics. Taylor series expansion about the operating point where optimal machining conditions are desired is applied to linearize the model equations of motion. Modifications are also made to the nonlinear tool stiffness term to minimize linearization errors. Numerical experiments demonstrate inadmissible results for the linear model and good agreement with available physical data in describing machining stability and chatter for the nonlinear model. Effects of tool geometry, feed rate, and spindle speed on cutting dynamics are also explored. It is observed that critical DOC increases with increasing spindle speed and small DOCs can induce cutting instability -- two of the results that agree qualitatively well with published experimental data.

The ability to perceive the dynamics of nature is ultimately limited by the temporal resolution of the instruments available. With the help of the ultrashort optical pulse, people now are able to observe and steer the electronic dynamics on the atomic scale. Meanwhile, high power attainable in such short time scale helps to boost the study of nonlinear physics. Most commercial femtosecond lasers are based on Ti:sapphire, but such systems can only be tuned in a spectral range around 800 nm. Few applications need only a single wavelength in this spectral region and pulses tunable from the UV to the IR are highly desirable. Based on the soliton characteristics of ultrashort laser pulses, we are the first ones who propose to make use of resonant dispersive waves, which are phase-matched non-solitonic linear waves, to extend the spectral tuning range of ultrashort laser without involving complicated amplifiers. Experimentally, we achieve the tuning of dispersive wave wavelengths by changing the dispersion parameters of the laser cavity, and confirm dispersive waves are ultrashort pulses under appropriate conditions. We successfully apply such a system into a multi-wavelength operation Ti:sapphire laser. The proposed idea is general, and can be applied to systems where solitons dominate, for example fiber lasers. Thanks to the newly developed novel fiber -photonic crystal fiber- we obtain widely tunable and gap-free femtosecond pulse by extending this mechanism to waveguides. This is the largest reported tuning range for efficient nonlinear optical frequency conversion obtained with such a simple and low energy laser. We apply such a Ti:sapphire laser to Raman micro-spectroscopy. Because of the different temporal behaviors of the Raman process and other parametric processes, we can efficiently separate the coherent Raman signal from the unwanted background, and obtain a high chemical contrast and high resolution image. This high repetition rate and low energy laser oscillator makes it very suitable for biological Raman micro-spectroscopy, especially living samples for which damage is a big concern.

By using Lyapunov stability theorem, a quasi-optimal model reference adaptive control (QOMRAC) scheme is presented in this thesis to stabilize a class of uncertain systems with input nonlinearity. This control scheme contains two main types of controllers. The first type is a linear feedback controller, which is an optimal controller if the controlled systems do not have any perturbations. The second type is an adaptive controller, which is used for adapting the unknown upper bound of perturbation or perturbation estimation error. The property of uniformly ultimately boundness is guaranteed when employing the proposed control scheme, and the effects of each design parameter on the dynamic performance are also analyzed. An example is demonstrated for showing the feasibility of the proposed control scheme.