# Browsing by Subject "nonlinear"

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Item A Conformal Mapping Grid Generation Method for Modeling High-Fidelity Aeroelastic Simulations(2010-07-14) Worley, GregoryShow more This work presents a method for building a three-dimensional mesh from two- dimensional topologically identical layers, for use in aeroelastic simulations. The method allows modeling of large deformations of the wing in both the span direction and deformations in the cord of the wing. In addition, the method allows for the modeling of wings attached to fuselages. The mesh created is a hybrid mesh, which allows cell clustering in the viscous region. The generated mesh is high quality and allows capturing of nonlinear uid structure interactions in the form of limit cycle oscillation.Show more Item A thermodynamic approach for compaction of asphaltic composites(2009-05-15) Koneru, SaradhiShow more 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.Show more Item Analysis of WACSIS data using a directional hybrid wave model(Texas A&M University, 2007-04-25) Zhang, ShaosongShow more This study focuses on the analysis of measured directional seas using a nonlinear model, named Directional Hybrid Wave Model (DHWM). The model has the capability of decomposing the directional wave field into its free wave components with different frequency, amplitude, direction and initial phase based on three or more time series of measured wave properties. With the information of free waves, the DHWM can predict wave properties accurately up to the second order in wave steepness. In this study, the DHWM is applied to the analyses of the data of Wave Crest Sensor Inter-comparison Study (WACSIS). The consistency between the measurements collected by different sensors in the WACSIS project was examined to ensure the data quality. The wave characteristics at the locations of selected sensors were predicted in time domain and were compared with those recorded at the same location. The degree of agreement between the predictions and the related measurements is an indicator of the consistency among different sensors. To analyze the directional seas in the presence of strong current, the original DHWM was extended to consider the Doppler effects of steady and uniform currents on the directional wave field. The advantage of extended DHWM originates from the use of the intrinsic frequency instead of the apparent frequency to determine the corresponding wavenumber and transfer functions relating wave pressure and velocities to elevation. Furthermore, a new approach is proposed to render the accurate and consistent estimates of the energy spreading parameter and mean wave direction of directional seas based on a cosine-2s model. In this approach, a Maximum Likelihood Method (MLM) is employed. Because it is more tolerant of errors in the estimated cross spectrum than a Directional Fourier Transfer (DFT) used in the conventional approach, the proposed approach is able to estimate the directional spreading parameters more accurately and consistently, which is confirmed by applying the proposed and conventional approach, respectively, to the time series generated by numerical simulation and recorded during the WACSIS project.Show more Item Circular sensor array and nonlinear analysis of homopolar magnetic bearings(Texas A&M University, 2007-04-25) Wiesenborn, Robert KyleShow more Magnetic bearings use variable attractive forces generated by electromagnetic control coils to support rotating shafts with low friction and no material wear while providing variable stiffness and damping. Rotor deflections are stabilized by position feedback control along two axes using non-contacting displacement sensors. These sensor signals contain sensor runout error which can be represented by a Fourier series composed of harmonics of the spin frequency. While many methods have been proposed to compensate for these runout harmonics, most are computationally intensive and can destabilize the feedback loop. One attractive alternative is to increase the number of displacement sensors and map individual probe voltages to the two independent control signals. This approach is implemented using a circular sensor array and single weighting gain matrix in the present work. Analysis and simulations show that this method eliminates runout harmonics from 2 to n-2 when all sensors in an ideal n-sensor array are operational. Sensor failures result in reduced synchronous amplitude and increased harmonic amplitudes after failure. These amplitudes are predicted using derived expressions and synchronous measurement error can be corrected using an adjustment factor for single failures. A prototype 8-sensor array shows substantial runout reduction and bandwidth and sensitivity comparable to commercial systems. Nonlinear behavior in homopolar magnetic bearings is caused primarily by the quadratic relationship between coil currents and magnetic support forces. Governing equations for a permanent magnet biased homopolar magnetic bearing are derived using magnetic circuit equations and linearized using voltage and position stiffness terms. Nonlinear hardening and softening spring behavior is achieved by varying proportional control gain and frequency response is determined for one case using numerical integration and a shooting algorithm. Maximum amplitudes and phase reversal for this nonlinear system occur at lower frequencies than the linearized system. Rotor oscillations exhibit amplitude jumps by cyclic fold bifurcations, creating a region of hysteresis where multiple stable equilibrium states exist. One of these equilibrium states contains subharmonic frequency components resulting in quasiperiodic rotor motion. This nonlinear analysis shows how nonlinear rotor oscillations can be avoided for a wide range of operation by careful selection of design parameters and operating conditions.Show more Item Development of the Ultrashort Pulse Nonlinear Optical Microscopy Spectral Imaging System(2012-10-19) Lee, Anthony Chien-derShow more Nonlinear Optical Microscopy (NLOM) has been shown to be a valuable tool for noninvasive imaging of complex biological systems. An effective approach for multicolor molecular microscopy is simultaneous excitation of multiple fluorophores by broadband sub-10-fs pulses. This dissertation will discuss the development of two spectral imaging systems using the principles of nonlinear optical microscopy for pixel-by-pixel spectral segmentation of multiple fluorescent spectra. The first spectral system is reliant on a fiber-optic cable to transmit fluorescent signal to a spectrometer, while the second is based on a spectrometer with an aberration-corrected concave grating that is directly coupled to the microscope. A photon-counting, 16-channel multianode photomultiplier tube (PMT) is used for both systems. Custom software developed in LabVIEW controls multiple counter cards as well as a field-programmable gate array (FPGA) for 1 Hz acquisition of 256x256x16 spectral images. Biological specimen consisting of multicolor endothelial cells and zebrafish will be used for experimental verification. Results indicate successful spectral segmentation of multiple fluorophores with a decrease in signal-to-noise ratio in the FPGA-based imaging system.Show more Item Operator Ideals in Lipschitz and Operator Spaces Categories(2012-10-19) Chavez Dominguez, JavierShow more We study analogues, in the Lipschitz and Operator Spaces categories, of several classical ideals of operators between Banach spaces. We introduce the concept of a Banach-space-valued molecule, which is used to develop a duality theory for several nonlinear ideals of operators including the ideal of Lipschitz p-summing operators and the ideal of factorization through a subset of a Hilbert space. We prove metric characterizations of p-convex operators, and also of those with Rademacher type and cotype. Lipschitz versions of p-convex and p-concave operators are also considered. We introduce the ideal of Lipschitz (q,p)-mixing operators, of which we prove several characterizations and give applications. Finally the ideal of completely (q,p)-mixing maps between operator spaces is studied, and several characterizations are given. They are used to prove an operator space version of Pietsch's composition theorem for p-summing operators.Show more Item The nonlinear dynamics of the sea breeze(Texas A&M University, 2004-11-15) Walter, Kevin RobertShow more The response of the land and sea breeze circulation to two highly simplified dynamical models is presented. The first dynamical model is the explicit specification of an oscillating interior heat source analogous to that from Rotunno (1983). Emphasis is placed on the variation of the response with heating amplitude and latitude. In addition, a weakly nonlinear analysis focuses on the dynamic forcing of nonlinear features such as a semi-diurnal gravity wave, fronts, and asymmetry in the magnitude of onshore and offshore flow. One surprising result is the identification of a cycle-mean surface divergence pattern at both 0? and 45?. At 45?, this divergence pattern is accompanied by a cycle mean shore-parallel response due to the Earth's rotation. The second dynamical model is the explicit specification of an oscillating surface heat flux. Again, comparison is made between simulations at different heating amplitudes, and between simulations at different latitudes. To address changes in the solution due to the heating method itself, comparison is made between solutions from the surface heating method and solutions from the interior heating method. Finally, solutions across the planetary continuum are explored for critical latitude dependence in high-amplitude simulations.Show more