Hot section components of land-based gas turbines are subject to extremely harsh, high temperature environments and require the use of advanced materials. Directionally solidified Ni-base superalloys are often chosen as materials for these hot section components due to their excellent creep resistance and fatigue properties at high temperatures. These blades undergo complex thermomechanical loading conditions throughout their service life, and the influences of blade geometry and variable operation can make life prediction difficult. Accurate predictions of material response under thermomechanical loading conditions is essential for life prediction of these components. Complex crystal viscoplasticity models are often used to capture the behavior of Ni-base superalloys. While accurate, these models are computationally expensive and are not suitable for all phases of design. This work involves the calibration of a previously developed reduced-order, macroscale transversely isotropic viscoplasticity model to a directionally solidified Ni-base superalloy. The unified model is capable of capturing isothermal and thermomechanical responses in addition to secondary creep behavior. An extreme reduced order microstructure-sensitive constitutive model is also developed using an artificial neural network to provide a rapid first-order approximation of material response under various temperatures, rates of loading, and material orientation from the axis of solidification.

This dissertation proposes a modular fast direct (MFD) analysis method for a class of problems involving a large fixed platform region and a smaller, variable design region. A modular solution algorithm is obtained by first decomposing the problem geometry into platform and design regions. The two regions are effectively detached from one another using basic equivalence concepts. Equivalence principles allow the total system model to be constructed in terms of independent interaction modules associated with the platform and design regions. These modules include interactions with the equivalent surface that bounds the design region. This dissertation discusses how to analyze (fill and factor) each of these modules separately and how to subsequently compose the solution to the original system using the separately analyzed modules. The focus of this effort is on surface integral equation formulations of electromagnetic scattering from conductors and dielectrics. In order to treat large problems, it is necessary to work with sparse representations of the underlying system matrix and other, related matrices. Fortunately, a number of such representations are available. In the following, we will primarily use the adaptive cross approximation (ACA) to fill the multilevel simply sparse method (MLSSM) representation of the system matrix. The MLSSM provides a sparse representation that is similar to the multilevel fast multipole method. Solutions to the linear systems obtained using the modular analysis strategies described above are obtained using direct methods based on the local-global solution (LOGOS) method. In particular, the LOGOS factorization provides a data sparse factorization of the MLSSM representation of the system matrix. In addition, the LOGOS solver also provides an approximate sparse factorization of the inverse of the system matrix. The availability of the inverse eases the development of the MFD method. Because the behavior of the LOGOS factorization is critical to the development of the proposed MFD method, a significant part of this dissertation is devoted to providing additional analyses, improvements, and characterizations of LOGOS-based direct solution methods. These further developments of the LOGOS factorization algorithms and their application to the development of the MFD method comprise the most significant contributions of this dissertation.

On considère un écoulement compressible bidimensionnel, autour d'une cavité ouverte. Des d'instabilité, auto-entretenues par l'effet de rétroaction de l'écrasement de la couche de cisaillement sur le bord aval de la cavité, génèrent des émissions acoustiques qu'il faut réduire. Des simulations numériques directes (DNS) permettent d'obtenir, avec ou sans actionnement, un modèle précis de l'écoulement. A partir des champs issus de la simulation, des décompositions orthogonales de modes propres (POD) sont proposées pour bâtir, par projection de Galerkin sur les équations isentropiques, des modèles d'ordre réduit non linéaires en prenant en compte l'actionnement (le contrôle). Pour éviter la divergence temporelle, les coefficients du système dynamique non forcé sont calibrés par diverses approches originales dont une basée sur la sensiblité modale. A partir du système dynamique forcé par un actionnement multifréquentiel (présent aussi dans les DNS), un contrôle en boucle fermée linéaire quadratique gaussien est proposé sur un système linéarisé. La reconstruction de l'état est basée sur une estimation stochastique linéaire sur 6 points de pression. Le contrôle optimal obtenu s'avère être périodique à la fréquence du second mode de Rossiter, qui est exactement celles des instabilits auto-entretenues dans la cavité. Par introduction de ce contrôle dans les simulations numériques directes, nous avons obtenu une réduction du bruit (faible) sur la fréquence du contrôle. / We consider a two dimensional compressible flow around an open cavity. The Flow around a cavity is characterised by a self-sustained mechanism in which the shear layer impinges on the downstream edge of the cavity resulting in an acoustic feedback mechanism which must be reduced. Direct Numerical Simulations (DNS) of the flow at a representative Reynolds number has been carried to obtain pressure and velocity fields, both for the case of unactuated and multi frequency actuation. These fields are then used to extract energy ranked coherent structures also called as the Proper Orthogonal Decomposition (POD) modes. A Reduced Order Model is constructed by a Galerkin projections of the isentropic compressible equations. The model is then extended to include the effect of control. To avoid the divergence of the model while integrating in time various calibration techniques has been utillized. A new method of calibration which minimizes a linear functional of error, based on modal sensitivity is proposed. The calibrated low order model is used to design a feedback control of the Linear Quadratic Gaussian (LQG) type, coupled with an observer. For the experimental implementation of the controller, a state estimate based on the observed pressure measurements at 6 different locations, is obtained through a Linear Stochastic Estimation (LSE). The optimal control obtained is periodic with a frequency corresponding to the second Rossiter mode of the cavity. Finally the control obtained is introduced into the DNS to obtain a decrease in spectra of the cavity acoustic mode.

<p>Asymptotic Modal Analysis (AMA) is a computationally efficient and accurate method for studying the response of dynamical systems experiencing banded, random harmonic excitation at high frequencies when the number of responding modes is large. In this work, AMA has been extended to systems of coupled continuous components as well as nonlinear systems. Several prototypical cases are considered to advance the technique from the current state-of-the-art. The nonlinear problem is considered in two steps. First, a method for solving problems involving nonlinear continuous multi-mode components, called Iterative Modal Analysis (IMA), is outlined. Secondly, the behavior of a plate carrying a nonlinear spring-mass system is studied, showing how nonlinear effects on system natural frequencies may be accounted for in AMA. The final chapters of this work consider the coupling of continuous systems. For example, two parallel plates coupled at a point are studied. The principal novel element of the two-plate investigation reduces transfer function sums of the coupled system to an analytic form in the AMA approximation. Secondly, a stack of three parallel plates where adjacent plates are coupled at a point are examined. The three-plate investigation refines the reduction of transfer function sums, studies spatial intensification in greater detail, and offers insight into the diminishing response amplitudes in networks of continuous components excited at one location. These chapters open the door for future work in networks of vibrating components responding to banded, high-frequency, random harmonic excitation in the linear and nonlinear regimes.</p> / Dissertation

Les microsystèmes, qui sont réalisés à partir de technologies micro-électroniques, connaissent un essor scientifique et technologique important grâce à leurs applications qui sont de plus en plus présentes dans la vie courante. Un des microsystèmes très en vogue est le transducteur ultrasonore capacitif micro-usiné, couramment appelé CMUT. Il est utilisé pour transmettre ou réceptionner des ondes ultrasonores et son domaine d’application est très vaste puisqu’on le trouve dans des sondes d’imagerie médicale, dans des hauts parleurs ultra directifs, pour le contrôle non destructif de matériaux… Dans la plupart des applications la puissance acoustique émise par le CMUT doit être très élevée ce qui implique que le CMUT va être utilisé en régime non-linéaire. En outre, même en utilisant des procédés de fabrication avancés, la microplaque mobile constituant le CMUT possède une déformation géométrique dans son état de repos. Il faudra par conséquent tenir compte des non-linéarités et des imperfections géométriques lors de l’analyse statique et dynamique du CMUT.Dans ce travail le modèle multiphysique d’un CMUT est développé en tenant compte des non-linéarités géométriques et électrostatiques ainsi que de la déflexion initiale de la microplaque. Les équations différentielles du mouvement de la microplaque, issues de la théorie des plaques de von Kármán, sont discrétisées spatialement en utilisant la méthode différentielle quadratique. La réponse statique d’un CMUT a été analysée à partir de simulations numériques et d’essais expérimentaux, en considérant des plaques planes et des plaques courbes et on montre qu’une déflexion initiale de la plaque conduit à une augmentation de la tension de pull-in. Le comportement dynamique non-linéaire du CMUT est analysé en discrétisant la variable temporelle et en utilisant la méthode des différences finies. En utilisant la technique de continuation arclength, nous déterminons la réponse en fréquence non-linéaire du CMUT. Suivant la valeur de la tension DC, le CMUT aura un comportement raidissant ou assouplissant. Une validation expérimentale du modèle numérique est réalisée en utilisant des microplaques planes et des microplaques courbes. En particulier nous montrons que l’utilisation de microplaques courbes, dues aux imperfections géométriques, change la réponse en fréquence du CMUT, passant d’un comportement raidissant à un comportement assouplissant, augmente le domaine de bi-stabilité et modifie la topologie de bifurcation.Le modèle numérique est par la suite étendu afin d’analyser les effets du film d’air sur le comportement dynamique de la microplaque en couplant les équations mécaniques du CMUT avec les équations de Reynolds du fluide. Les fréquences de résonance du problème multiphysique sont obtenues par résolution d'un système linéaire amorti. La validation expérimentale et numérique du modèle est effectuée en déterminant les fréquences de résonance du CMUT à des pressions différentes. Nous montrons que l’air comprimé change la réponse dynamique du CMUT par l’ajout d’une raideur et d’un amortissement. La diminution de la pression conduit à une diminution de la fréquence de résonance du système couplé et tend vers la fréquence de résonance de la microplaque. D'autre part la réponse en fréquence du système devient non-linéaire due à la diminution du coefficient d'amortissement. A la pression atmosphérique, on montre que le CMUT a un comportement non-linéaire de type assouplissant lorsque les excitations sont élevées. Le modèle numérique développé est un outil efficace pour analyser les CMUTs et augmenter leurs performanaces. / Micro Electro Mechanical Systems (MEMS) have attracted the interest of scientists and engineers thanks to the variety of their applications and their significant roles in our real life. One of the most important microsystems is the capacitive micromachined ultrasonic transducer (CMUT), which is used for transmitting ultrasonic waves, for instance in medical imaging and therapy. In such applications, a high-transmitted acoustic power is needed which implies driving the CMUT in the nonlinear regime. Moreover, from a manufacturing point of view, the fabrication of a CMUT with a flat surface is extremely difficult even with the recent advances in the fabrication process. Modeling this type of microsystem while including the main sources of nonlinearities and geometric imperfections is a challenging step in understanding its static and dynamic behavior.In this thesis, a multiphysics model of imperfect CMUTs is developed taking into account the geometric and electrostatic nonlinearities. The governing equations of motions are derived from the von Kármán plate theory and spatially discretized using the Differential Quadrature Method (DQM). For the static response, numerical simulations and experimental characterizations have been conducted on flat and curved CMUTs, showing that a positive initial deflection leads to an increase in the pull-in voltage. The nonlinear dynamic behavior of a CMUT is studied by discretizing the time variable using the Finite Difference Method (FDM). The nonlinear frequency and force responses have been determined by combining FDM with the arclength continuation technique. It is shown that the CMUT can exhibit a hardening or softening behavior depending on the DC voltage. An experimental validation of the numerical model is performed for the case of flat and curved microplates. We demonstrate that the geometric imperfection modifies the nonlinear frequency response of a CMUT from hardening to softening, increases its bistability domain and permits the tuning of its bifurcation topology.The numerical model is extended to investigate the effect of an air film on the dynamic behavior of the microplate by coupling the nonlinear mechanical equations with the Reynolds equation. The complex resonance frequencies of the multi-physical problem are determined by solving the damped linear system. An experimental and numerical validation of the model is performed by determining the resonance frequencies at several static pressures. We demonstrate that the air film is able to modify the dynamic response of the CMUT by adding stiffness and damping. By decreasing the static pressure, the resonance frequency of the coupled problem decreases and becomes closer to the natural resonance frequency of the microplate. Moreover, the frequency response of the system becomes nonlinear due the decrease in the damping coefficient. At atmospheric pressure, the softening type behavior of the CMUT is obtained by applying high excitation levels. The presented numerical model is a very efficient tool to understand the nonlinear dynamic behavior CMUTs and to enhance their performances.

abstract: This investigation focuses on the development of uncertainty modeling methods applicable to both the structural and thermal models of heated structures as part of an effort to enable the design under uncertainty of hypersonic vehicles. The maximum entropy-based nonparametric stochastic modeling approach is used within the context of coupled structural-thermal Reduced Order Models (ROMs). Not only does this strategy allow for a computationally efficient generation of samples of the structural and thermal responses but the maximum entropy approach allows to introduce both aleatoric and some epistemic uncertainty into the system. While the nonparametric approach has a long history of applications to structural models, the present investigation was the first one to consider it for the heat conduction problem. In this process, it was recognized that the nonparametric approach had to be modified to maintain the localization of the temperature near the heat source, which was successfully achieved. The introduction of uncertainty in coupled structural-thermal ROMs of heated structures was addressed next. It was first recognized that the structural stiffness coefficients (linear, quadratic, and cubic) and the parameters quantifying the effects of the temperature distribution on the structural response can be regrouped into a matrix that is symmetric and positive definite. The nonparametric approach was then applied to this matrix allowing the assessment of the effects of uncertainty on the resulting temperature distributions and structural response. The third part of this document focuses on introducing uncertainty using the Maximum Entropy Method at the level of finite element by randomizing elemental matrices, for instance, elemental stiffness, mass and conductance matrices. This approach brings some epistemic uncertainty not present in the parametric approach (e.g., by randomizing the elasticity tensor) while retaining more local character than the operation in ROM level. The last part of this document focuses on the development of “reduced ROMs” (RROMs) which are reduced order models with small bases constructed in a data-driven process from a “full” ROM with a much larger basis. The development of the RROM methodology is motivated by the desire to optimally reduce the computational cost especially in multi-physics situations where a lack of prior understanding/knowledge of the solution typically leads to the selection of ROM bases that are excessively broad to ensure the necessary accuracy in representing the response. It is additionally emphasized that the ROM reduction process can be carried out adaptively, i.e., differently over different ranges of loading conditions. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2019

This work presents a number of the practical aspects of developing reduced- order models (ROMs) based on proper orthogonal decomposition (POD). ROMS are derived and implemented for multiphase flow, quasi-2D nozzle flow and 2D inviscid channel flow. Results are presented verifying the ROMs against existing full-order models (FOM). POD is a method for separating snapshots of a flow field that varies in both time and space into spatial basis functions and time coefficients. The partial differential equations that govern fluid flow can then be pro jected onto these basis functions, generating a system of ordinary differential equations where the unknowns are the time coefficients. This results in the reduction of the number of equations to be solved from hundreds of thousands or more to hundreds or less. A ROM is implemented for three-dimensional and non-isothermal multiphase flows. The derivation of the ROM is presented. Results are compared against the FOM and show that the ROM agrees with the FOM. While implementing the ROM for multiphase flow, moving discontinuities were found to be a ma jor challenge when they appeared in the void fraction around gas bubbles. A point-mode POD approach is proposed and shown to have promise. A simple test case for moving discontinuities, the first order wave equation, is used to test an augmentation method for capturing the discontinuity exactly. This approach is shown to remove the unphysical oscillations that appear around the discontinuityin traditional approaches. A ROM for quasi-2D inviscid nozzle flow is constructed and the results are com- pared to a FOM. This ROM is used to test two approaches, POD-Analytical and POD-Discretized. The stability of each approach is assessed and the results are used in the implementation of a ROM for the Navier-Stokes equations. A ROM for a Navier-Stokes solver is derived and implemented using the results of the nozzle flow case. Results are compared to the FOM for channel flow with a bump. The computational speed-up of the ROM is discussed. Two studies are presented with practical aspects of the implementation of POD- based ROMs. The first shows the effect of the snapshot sampling on the accuracy of the POD basis functions. The second shows that for multiphase flow, the cross- coupling between field variables should not be included when computing the POD basis functions.

<p>A new method of stabilizing low-order, proper orthogonal decomposition based reduced-order models of the Navier Stokes equations is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in that, in addition to optimally representing the solution, the new proposed basis functions also provide stable reduced-order models. The proposed approach is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer.</p> / Dissertation

High-flying unmanned reconnaissance and surveillance systems are now being used extensively in the United States military. Current development programs are producing demonstrations of next-generation unmanned flight systems that are designed to perform combat missions. Their use in first-strike combat operations will dictate operations in densely cluttered environments that include unknown obstacles and threats, and will require the use of terrain for masking. The demand for autonomy of operations in such environments dictates the need for advanced trajectory optimization capabilities. In addition, the ability to coordinate the movements of more than one aircraft in the same area is an emerging challenge. This thesis examines using an analytical reduced order formulation for trajectory generation for minimum time and terrain masking cases. First, pseudo-3D constant velocity equations of motion are used for path planning for a single vehicle. In addition, the inclusion of winds, moving targets and moving threats is considered. Then, this formulation is increased to using 3D equations of motion, both with a constant velocity and with a simplified varying velocity model. Next, the constant velocity equations of motion are expanded to include the simultaneous path planning of an unspecified number of vehicles, for both aircraft avoidance situations and formation flight cases.

Interactions between the aerodynamics and dynamics of bluff bodies are important in many engineering applications, including suspension bridges, tall buildings, oil platforms, wind turbine towers, air drops, and construction with cranes. In the rotorcraft field, bluff bodies are commonly suspended underneath the vehicle by tethers. This approach is often the only practical way to deliver a payload in a reasonable amount of time in disaster relief efforts, search-and-rescue operations, and military operations. However, currently a fundamental understanding of the aerodynamics of these bluff bodies is lacking, and accurate dynamic simulation models for predicting the safe flying speed are not available. In order to address these shortcomings, two main advancements are presented in this thesis. The aerodynamics of several three-dimensional canonical bluff bodies are examined over a range of Reynolds numbers representative of wind-tunnel-scale to full-scale models. Numerical experiments are utilized, with a focus on uncertainty analysis and validation of the computations. Mean and unsteady forces and moments for these bluff bodies have been evaluated, and empirical models of the shear layer characteristics have been extracted to quantify the behaviors and provide predictive capability. In addition, a physics-based reduced-order simulation model has been developed for bluff bodies. The physics-based approach is necessary to ensure that the predicted behavior of new configurations is accurate, and it is made possible by the breakthroughs in three-dimensional bluff body aerodynamics presented in this thesis. The integrated aerodynamic forces and moments and dynamic behavior predicted by model are extensively validated with data from wind tunnels, flight tests, and high-fidelity computations. Furthermore, successful stability predictions for tethered loads are demonstrated. The model is applicable to the simulation of any generic bluff body configuration, is readily extensible, and has low computational cost.