The determination of the modal parameters of an airplane wing, such as damping and natural frequency, as well as the determination of the aircraft's flutter speed, is an important part of aircraft design and testing. The effect that a 'defect' can have on the system, such as a loose hinge or worn fastening, is also an important part of aircraft analysis. / In this study, a two-dimensional, symmetrical airfoil was mounted as part of a linear system in a wind tunnel, subject to steady, incompressible flow. Experimental data was collected using both free and forced vibrations of the airfoil, at different increments of airspeed. This data was then analyzed using conventional modal analysis techniques, extracting the damping factor and the natural frequency of the system, thus enabling a value for the flutter speed to be calculated. / A structural freeplay nonlinearity was then introduced into the system, mimicking the effects a loose hinge or worn fastening can have on the airfoil modal parameters. The same tests were performed, and the modal parameters were evaluated using special nonlinear parameter extraction techniques. The behaviour of the damping and natural frequency of the nonlinear system, obtained from all three methods of data collection, were then compared to those of the linear system.

A three-dimensional code has been developed for the simulation of tone noise generated by turbofan engine inlets using computational aeroacoustics. The governing equations are the linearized Euler equations, which are further simplified to a set of equations in terms of acoustic potential, using the irrotational flow assumption, and subsequently solved in the frequency domain. / Due to the special nature of acoustic wave propagation, the spatial discretization is performed using a spectral element method, where a tensor product of the nth-degree polynomials based on Chebyshev orthogonal functions is used to approximate variations within hexahedral elements. Non-reflecting boundary conditions are imposed at the far-field using a damping layer concept. This is done by augmenting the continuity equation with an additional term without modifying the governing equations as in PML methods. / Solution of the linear system of equations for the acoustic problem is based on the Schur complement method, which is a nonoverlapping domain decomposition technique. The Schur matrix is first solved using a matrix-free iterative method, whose convergence is accelerated with a novel local preconditioner. The solution in the entire domain is then obtained by finding solutions in smaller subdomains. / The 3D code also contains a mean flow solver based on the full potential equation in order to take into account the effects of flow variations around the nacelle on the scattering of the radiated sound field. / All aspects of numerical simulations, including building and assembling the coefficient matrices, implementation of the Schur complement method, and solution of the system of equations for both the acoustic and mean flow problems are performed on multiprocessors in parallel using the resources of the CLUMEQ Supercomputer Center. A large number of test cases are presented, ranging in size from 100 000-2 000 000 unknowns for which, depending on the size of the problem, between 8-48 CPU's are used. / The developed code is demonstrated to be robust and efficient in simulating acoustic propagation for a large number of problems, with an excellent parallel performance.

Computational Fluid Dynamics (CFD) is emerging as an integral part of engineering design and analysis. Traditionally, idealizations have been made to categorize flows as being either incompressible or compressible, with their respective numerical treatments being completely different. Incompressible flow solvers are completely incapable of capturing compressible flow phenomena, while compressible flow solvers are very inefficient in the limit of low compressibility. For situations in which there are regions of incompressible and compressible flows, or when there is no a priori knowledge of the level of compressibility, a general numerical treatment is no longer obvious. / The method proposed in this thesis has been formulated for efficient computation of mixed incompressible/compressible flows and is based on the SIMPLE algorithm of S. V. Patankar. It is capable of correctly modeling the elliptic/hyperbolic nature of the pressure perturbations and is well suited for calculating a wide range of engineering applications such as turbomachinery, aerodynamics, etc. / This thesis will describe the details of the compressible extension of the SIMPLE algorithm and provide numerical examples which demonstrate the ability of the solver to efficiently resolve mixed incompressible/compressible flows.

This thesis presents a new theoretical approach based on the concept of velocity singularities developed by Mateescu for airfoils in subsonic flows and for wing-body systems in supersonic regime. The present approach uses the velocity singularities in the Trefftz plane to derive the contributions of the wing incidence and chord changes in the solution of the circulation variation along the wing span. The new specific functions derived for these contributions contain both natural and forced symmetry and anti-symmetry terms, and represent the first correct mathematical modeling of the physical problem. The new forced symmetry and anti-symmetry terms and the new contributions of the incidence and chord distribution changes, which were missing from the previous methods, determine a high level of accuracy of the solution, which is free of spurious oscillations. (Abstract shortened by UMI.)

The resurgence of airships has created a need for dynamics models and simulation capabilities of these lighter-than-air vehicles. The focus of this thesis is a theoretical framework that integrates the flight dynamics, structural dynamics, aerostatics and aerodynamics of flexible airships. The study begins with a dynamics model based on a rigid-body assumption. A comprehensive computation of aerodynamic effects is presented, where the aerodynamic forces and moments are categorized into various terms based on different physical effects. A series of prediction approaches for different aerodynamic effects are unified and applied to airships. The numerical results of aerodynamic derivatives and the simulated responses to control surface deflection inputs are verified by comparing to existing wind-tunnel and flight test data. With the validated aerodynamics and rigid-body modeling, the equations of motion of an elastic airship are derived by the Lagrangian formulation. The airship is modeled as a free-free Euler-Bernoulli beam and the bending deformations are represented by shape functions chosen as the free-free normal modes. In order to capture the coupling between the aerodynamic forces and the structural elasticity, local velocity on the deformed vehicle is used in the computation of aerodynamic forces. Finally, with the inertial, gravity, aerostatic and control forces incorporated, the dynamics model of a flexible airship is represented by a single set of nonlinear ordinary differential equations. The proposed model is implemented as a dynamics simulation program to analyze the dynamics characteristics of the Skyship-500 airship. Simulation results are presented to demonstrate the influence of structural deformation on the aerodynamic forces and the dynamics behavior of the airship. The nonlinear equations of motion are linearized numerically for the purpose of frequency domain analysis and for aeroelastic stability analysis. The results from the latter for / L'intérêt renouvelé envers les dirigeables a créé un besoin de modèles dynamique et de simulations de ces véhicules plus légers que l'air. Cette thèse traite d'un cadre théorique qui intègre la dynamique de vol, la dynamique structurale, l'aérostatique et l'aérodynamique des dirigeables flexibles. La recherche débute par une étude d'un modèle dynamique fondé sur l'hypothèse d'un corps rigide. Une approche de calcul d'aérodynamique complète est présentée, où les forces et les moments aérodynamiques sont classés par catégories basées sur différents effets physiques. Une série d'approches de prédiction des différents effets aérodynamiques est unifiée et appliqué aux dirigeables. Les résultats numériques des dérivés aérodynamiques et des réponses simulées à des commandes spécifiés sont comparés à des résultats d'essais provenant d'autre œuvres. Une fois l'aérodynamique et le modèle de corps rigide validés, les équations de mouvement d'un dirigeable élastique sont dérivées avec une formulation Lagrangienne. Le dirigeable est modélisé comme poutre Euler-Bernoulli et les déformations sont représentées par des fonctions de forme choisies. Afin de prendre en considération la dépendance entre les forces aérodynamiques et l'élasticité structurale, la vitesse locale sur le véhicule déformé est employée dans le calcul des forces aérodynamiques. En conclusion, avec les forces d'inertie, de gravité, d'aérodynamique et de commande incorporées, le modèle dynamique d'un dirigeable flexible est exprimé sous la forme d'un ensemble d'équations différentielles ordinaires non-linéaires. Le modèle proposé est mis en pratique sous forme de simulation dynamique afin d'analyser les caractéristiques dynamiques du dirigeable Skyship-500. Des résultats de simulation sont présentés pour démontrer l'influence de la déformation structurale sur les forces aérodynamiques et le comportement dynamique du di

The method of sweep excitation is employed in the resonance testing of aircraft and other structures. The method allows resonant frequencies and corresponding modal damping parameters to be calculated from a limited amount of real time test data. The amount of test time required to obtain the system's frequency response characteristics is reduced by subjecting the structure to an entire range of frequencies within one test pattern, or "sweep", instead of repeating individual tests at a number of different frequencies. The "sweep-rate" is defined as the rate at which the frequency increases or decreases during the frequency sweep. This thesis studies the effect of sweep-rate and sweep-direction on the accuracy of estimated system parameters, as well as assessing two different methods used to reduce discrete time histories to frequency transfer data. The impact of introducing a structural nonlinearity into the aeroelastic system is also investigated. (Abstract shortened by UMI.)

ABSTRACT This thesis is concerned with the investigation of the influence of damping on the frequencies of plane frames in the presence of rotational joint damping. Usually damping is ignored in dynamic analysis of structures, or is taken into account using the simple concept of Rayleigh damping. However, damping is always present, and must be considered for a realistic analysis of structures, especially if a matching is desired with frequencies obtained from vibration testing of the structure. In the thesis, the view point is adopted that the damping is caused mainly by the relative slip of the joined parts at various joints of the structure. The slip may either be translational or rotational. However, it appears that purely translational slip is not as significant as that caused by relative rotation of members at a joint. The thesis considers frames in which joints are not perfectly rigid, and hence allow relative rotation of members meeting at the joint. The resistance to the relative rotation is modeled by (1) assigning rotational stiffness to the joints, and (2) by assigning rotational damping coefficients to the joints. The damping is considered to be of the viscous variety, so that the damping moments are proportional to the rotational velocities at the joint. The resulting problem for free vibrations is a complex-valued eigenvalue problem. The thesis investigates this problem analytically, experimentally and numerically. Exact free vibration analyses were performed for straight beams with translational and rotational dampers at the ends. Experiments were conducted on a simple frame to determine the effect of joint damping on its in-plane frequencies. A finite element program was constructed to determine frequencies of general plane frames in the presence of rotational joint damping. / RésuméCette thèse présente une recherche portant sur l'influence de l'amortissement sur les fréquences des cadres en présence d'amortissement de rotation aux joints. Normalement on ne tient pas compte des amortissements dans une analyse dynamique des structures, si ce n'est par le concept d'amortissement de Rayleigh. Toutefois, l'amortissement est toujours présent et doit être pris en considération pour une analyse réaliste des structures surtout si on souhaite obtenir un résultat correspondant aux fréquences obtenues lors des tests de vibration de la structure. Dans cette thèse on considère que l'amortissement provient surtout du glissement se produisant aux parties jointes à plusieurs joints de la structure. Il peut s'agir d'un glissement de translation ou encore de rotation. Il semble toutefois qu'un simple glissement de translation ne soit pas aussi important qu'un glissement de rotation des membres à un joint. Cette thèse porte sur les cadres dans lesquels les joints ne sont pas parfaitement rigides et permettent donc une certaine rotation des membres aux joints. On crée un modèle de résistance relative à la rotation en donnant (1) des rigidités de rotation et (2) des coefficients d'amortissement de rotation aux joints. L'amortissement est considéré de type visqueux afin que le moment de glissement soit proportionnel à la vélocité de rotation aux joints.Le problème résultant des vibrations libres est un problème de valeurs propres (eigen-value) Dans cette thèse on étudie le problème de façon analytique, expérimentale et numérique. Des analyses précises de vibration libre sont faites pour des poutres droites avec des amortisseurs de translation et de rotation aux extrémités. Des expériences ont été faites sur un cadre simple afin de déterminer l'effet de l'amortissement aux joints sur la fréquence dans le plan du cadre. Un programme d'éléments finis a ét

This thesis presents a new method of solution for the aerodynamics of finite-span wings, which overcomes the difficulties of the previous methods. The present method uses velocity singularities in the Trefftz plane (situated downstream at infinity) to derive the contributions in the solution of the circulation distribution caused by the changes in the spanwise variation of the wing chord and incidence. The new specific functions derived for these contributions contain both natural and forced symmetry and antisymmetry terms, and thus represent a correct mathematical modeling of the physical problem. The correct mathematical representation of these contributions leads to a highly accurate theoretical solution which is not the case in the previous methods. / The method has been validated in comparison with the results obtained by theoretical methods such as Rasmussen & Smith, and Carafoli for rectangular and tapered wings of uniform incidence, and with panel method (Katz & Plotkin) results. Accurate theoretical solutions have been derived for various wing geometries of aeronautical interest, such as wings with curved leading and trailing edges, and wings with asymmetric incidence variations caused by symmetric and antisymmetric deflection of flaps and ailerons (which are more difficult to model using the panel methods). / Furthermore, the present method of solution has been extended to solve the problem of swept wings. A procedure has been developed to specifically treat this problem.

The combustion of modern jet fuel, known as Jet A, in aero-derived gas turbine engines is a complicated process that is not fully understood. While many attempts have been made to produce numerical and chemical models of Jet A, the current lack of consensus within literature suggests that more work remains. This work will study three pure substances, which are representative of the chemical components that comprise typical jet fuels. n-Decane represents the alkanes present in Jet A, methylcyclohexane the cyclic hydrocarbons, and toluene the aromatics. All three compounds are used to stabilize flames in a stagnation flow burner, with their velocity profiles measured using particle image velocimetry. These velocity profiles are then compared so that the relative reactivity of these three compounds can be established. It was found that the most reactive substance was n-decane, followed by methylcyclohexane, with toluene being the least reactive. In addition, the predictions of an analytical hydrodynamic model are compared to experimental results. The analytical model was found to be in good agreement under stoichiometric and fuel rich conditions, but diverges as the flames become increasingly fuel lean. This result can be explained either by issues which remain in the experimental apparatus, or by inaccuracies within data collected from literature, and this warrants further investigation. The experience gained in assembling the apparatus will be used to continue its development to facilitate future studies. / La combustion du carburant d'aviation, connu sous le nom de Jet A, dans les turbines à gaz aro-drives est un processus complexe qui n'est pas entièrement compris. Bien que de nombreuse études on été faites pour produire des modèles num ́eriques et chimiques du Jet A, l'absence de consensus dans la littérature montre qu'il reste encore du travail. Ce travail est une étude de trois substances pures, qui sont représentatifs de la composition chimique qui constituent les carburants d'aviation. Le n-décane représente les alcanes présents dans le Jet A, le méthylcyclohexane les hydrocarbures cycliques, et le toluène les aromatiques. Les trois composés sont utilisés pour stabiliser les flammes dans un brûleur à écoulement stagné, avec les profils de vitesse mesurés à l'aide de la technique de vélocimétrie par images de particules. Ces profils de vitesse sont ensuite comparés de telle sorte que la réactivité relative de ces trois composés peut être déduite. Il a été constat que la substance la plus réactive est le n-décane, suivie par le méthylcyclohexane et le toluène étant le moins réactif. Aussi, les prédictions d'un modèle analytique hydrodynamique sont comparèes aux résultats expérimentaux. Le modèle analytique a donné un bon accord sous les conditions stœchiomtrique et riche mais diverge dans les conditions de flammes pauvres. Ce résultat peut s'expliquer soit par des problèmes qui restent dans le dispositif expérimental, ou par l'inexactitude des données collectées dans la littérature, ce qui justifie plus d'investigations. L'expérience acquise dans le montage de l'appareil sera utilisé pour continuer son développement afin de faciliter les études futures.

In this thesis, dynamics and control of multi-body tethered satellite systems are investigated. First a dynamical model is developed that takes into account the three dimensional librational motion of the system as well as the nonlinear vibrations of the tethers, both in longitudinal and transverse directions. The assumed modes method is used to discretize the continuous tethers. Using Lagrange's equations, splitting the vector of generalized coordinates to a set of subvectors, where each subvector corresponds to a specific tether, a set of nonlinear ordinary differential equations governing the motion of the system is obtained in the explicit analytical form. A fourth order strain energy expression is used in the formulation to allow the possibility of moderately large deformation of the tethers. The equations are applicable whether the length of the tethers are constant (station-keeping phase) or changing with time (deployment and retrieval phases). They are transformed into vector form for simulation purposes. / Among the external forces, the aerodynamic forces and their effects on the dynamics and stability of the system are given more attention. The free molecular flow model is used to calculate the aerodynamic forces resulting from the material damping of the tethers are considered in this investigation. These forces, which are very difficult to model accurately, are modelled using a viscous damping model. / Equilibrium configurations of the system, as special solutions of the equations of motion, in the absence or presence of the aerodynamic forces, are studied in more detail. A closed form solution to the static equilibrium equations is obtained when there is no external force acting on the system other than the gravitational force. The set of nonlinear equations of motion is then linearized analytically about a particular equilibrium configuration for stability and eigenvalue analysis. The natural frequencies of some single-tether as well as multi-tether systems are calculated using these linearized equations. / Stability of a single-tether system in low orbit missions is investigated, ignoring the aerodynamic forces on the main-satellite as well as on the tether. Assuming a particular geometrical configuration for the subsatellite and using the linearized equations, the effect of the aerodynamic forces, particularly aerodynamic lift, on the stability of the system as well as the equilibrium configuration of the system is examined through the eigenvalue analysis. This analysis is then extended to multi-body systems. / Finally the problem of controlling the nonlinear system through the application of Lyapunov's stability theory is examined for multi-body tethered systems, ignoring the transverse oscillations of the tethers. Initially, based on the Hamiltonian of the system, a Lyapunov function is introduced for a system with massless and rigid tethers. It leads to a linear tension control law. When the mass of the tethers is taken into account the Lyapunov function is modified and a new tension control law is developed which is no longer linear. With the assumption that the longitudinal oscillations of the tethers are small compared to the length of the tethers, a Lyapunov functions is constructed for systems with elastic tethers. At the end, a hybrid control law is examined to improve the performance of the controlled system.