This dissertation describes the design, analysis and testing of an unconventional rotor featuring extremely flexible, retractable blades. These rotor blades are composed of a flexible matrix composite material; they are so flexible that they can be rolled up and stowed in the rotor hub. The motivation for this study is to equip the next generation of unmanned rotary-wing vehicles with morphing rotors that can change their diameter in flight, based on mission requirements. Due to their negligible structural stiffness, the static and dynamic behavior of these blades is dominated by centrifugal effects. Passive stabilization of the flexible blades is achieved by centrifugal stiffening in conjunction with an appropriate spanwise and chordwise mass distribution. In particular, such blades are susceptible to large deformations. For example, a combination of the trapeze effect and the tennis racquet effect induces a large negative twist that results in decreased efficiency. Additionally, the rotor blades are prone to aeroelastic instabilities due to their low rotating torsional frequency, and it is seen that without careful design the blades experience coupled pitch-flap limit cycle oscillations. The primary focus of this research is to develop analytical and experimental tools to predict and measure the deformations of an extremely flexible rotor blade with non-uniform mass distribution. A novel aeroelastic analysis tailored towards unconventional blades with negligible structural stiffness is developed. In contrast to conventional analyses developed for rigid rotor blades, the present analysis assumes very large elastic twist. The nonlinear coupled equations of motion for the flap bending, lead-lag bending and torsion of an elastic rotating blade are derived using Hamilton's principle. The virtual work associated with unsteady aerodynamic forces in hover is included in the analysis. An ordering scheme consistent with the relevant physical quantities is defined and terms up to second order are retained in the Hamiltonian. The equations of motion are solved using a nonlinear finite element analysis. The steady-state deformation of the rotor blade is obtained from the time invariant part of the solution. The rotating flap, lag and torsional frequencies are found by solving the eigenvalue problem associated with the homogeneous system of equations. Finally, stability boundaries are computed for various operating conditions and the influence of parameters such as rotational velocity and collective pitch angle is discussed. The analytical predictions are validated by experimental measurements of the blade deformation in hover. These measurements are obtained by a novel, non-contact optical technique called three-dimensional Digital Image Correlation (3D DIC). The use of this technique is demonstrated for the first time to obtain full-field deformation measurements of a rotating blade. In addition, stability boundaries are extracted from experimental observations and correlated with predictions. / text

Recent design trends in steam turbines strive for high aerodynamic loading and high aspect ratio to meet the demand of higher efficiency. These design trends together with the low structural frequency in last stage steam turbines increase the susceptibility of the turbine blades to flutter. Flutter is the self-excited and self-sustained aeroelastic instability phenomenon, which can result in rapid growth of blade vibration amplitude and eventually blade failure in a short period of time unless adequately damped. To prevent the occurrences of flutter before the operation of new steam turbines, a compromise between aeroelastic stability and stage efficiency has to be made in the steam turbine design process. Due to the high uncertainty in present flutter prediction methods, engineers use large safety margins in predicting flutter which can rule out designs with higher efficiency. The ability to predict flutter more accurately will allow engineers to push the design envelope with greater confidence and possibly create more efficient steam turbines. The present work aims to investigate the influence of tip clearance flow on the prediction of steam turbine flutter characteristics. Tip clearance flow effect is one of the critical factors in flutter analysis for the majority of aerodynamic work is done near the blade tip. Analysis of the impact of tip clearance flow on steam turbine flutter characteristics is therefore needed to formulate a more accurate aeroelastic stability prediction method in the design phase.Besides the tip leakage vortex, the induced vortices in the tip clearance flow can also influence blade flutter characteristics. However, the spatial distribution of the induced vortices cannot be resolved by URANS method for the limitation of turbulence models. The Detached-Eddy Simulation (DES) calculation is thus applied on a realistic-scale last stage steam turbine model to analyze the structure of induced vortices in the tip region. The influence of the tip leakage vortex and the induced vortices on flutter prediction are analyzed separately. The KTH Steam Turbine Flutter Test Case is used in the flutter analysis as a typical realistic-scale last stage steam turbine model. The energy method based on 3D unsteady CFD calculation is applied in the flutter analysis. Two CFD solvers, an in-house code LUFT and a commercial software ANSYS CFX, are used in the flutter analysis as verification of each other. The influence of tip leakage vortex on the steam turbine flutter prediction is analyzed by comparing the aeroelastic stability of two models: one with the tip gap and the other without the tip gap. Comparison between the flutter characteristics predicted by URANS and DES approaches is analyzed to investigate the influence of the induced vortices on blade flutter characteristics. The multiple induced vortices and their relative rotation around the tip leakage vortex in the KTH Steam Turbine Flutter Test Case are resolved by DES but not by URANS simulations. Both tip leakage vortex and induced vortices have an influence on blade loading on the rear half of the suction side near the blade tip. The flutter analysis results suggest that the tip clearance flow has a significant influence on blade aerodynamic damping at the least stable interblade phase angle (IBPA), while its influence on the overall shape of the damping curve is minor. At the least stable IBPA, the tip leakage vortex shows a stabilization effect on rotor aeroelastic stabilities while the induced vortices show a destabilization effect on it. Meanwhile, a non-linear unsteady flow behavior is observed due to the streamwise motion of induced vortices during blade oscillation, which phenomenon is only resolved in DES results.

This thesis describes the analysis, fabrication and testing of a rotor with extremely flexible blades, focusing on application to a micro-helicopter. The flexibility of the rotor blades is such that they can be rolled into a compact volume and stowed inside the rotor hub. Stiffening and stabilization of the rotor is enabled by centrifugal forces acting on a tip mass. Centrifugal effects such as bifilar and propeller moments are investigated and the torsional equation of motion for a blade with low torsional stiffness is derived. Criteria for the design of the tip mass are also derived and it is chosen that the center of gravity of each blade section must be located ahead of the aerodynamic center. This thesis presents the design of 18-inch diameter two-bladed rotors having untwisted circular arc airfoil profile with constant chord. A systematic experimental investigation of the effect of various blade parameters on the stability of the rotor is conducted in hover and forward flight. These parameters include blade flexibility in bending and torsion, blade planform and mass distribution. Accordingly, several sets of blades varying these parameters are constructed and tested. It is observed that rotational speed and collective pitch angles have a significant effect on rotor stability. In addition, forward flight velocity is found to increase the blade stability. Next, the performance of flexible rotors is measured. In particular, they are compared to the performance of a rotor with rigid blades having an identical planform and airfoil section. It is found that the flexible blades are highly twisted during operation, resulting in a decreased efficiency compared to the rigid rotor blades. This induced twist is attributed to an unfavorable combination of tip body design and the propeller moment acting on it. Consequently, the blade design is modified and three different approaches to passively tailor the spanwise twist distribution for improved efficiency are investigated. In a first approach, extension-torsion composite material coupling is analyzed and it is shown that the centrifugal force acting on the tip mass is not large enough to balance the nose-down twist due to the propeller moment. The second concept makes use of the propeller moment acting on the tip mass located at an index angle to produce an untwisted blade in hover. It is constructed and tested. The result is an untwisted 18-inch diameter rotor whose maximum Figure of Merit is equal to 0.51 at a blade loading of 0.14. Moreover, this rotor is found to be stable for any collective pitch angle greater than 11 degrees. Finally, in a third approach, addition of a trailing-edge flap at the tip of the flexible rotor blade is investigated. This design is found to have a lower maximum Figure of Merit than that of an identical flexible rotor without a flap. However, addition of this control surface resulted in a stable rotor for any value of collective pitch angle. Future plans for increasing the efficiency of the flexible rotor blades and for developing an analytical model are described. / text

Les roues aubagées sont des composants dont le comportement dynamique est très sensible au désaccordage involontaire causé par les tolérances de fabrication qui rendent les aubes légèrement différentes les unes des autres. Cette sensibilité se traduit généralement par une amplification des vibrations. L’objectif de ce travail de recherche est de proposer de nouvelles méthodologies permettant d’optimiser la conception en vibration des roues aubagées vis à vis du désaccordage involontaire. L’optimisation est faite pour la réponse forcée et sous une contrainte de marge à la stabilité aéroélastique. Dans ce contexte, le désaccordage intentionnel par modification géométrique des aubes est utilisé. Pour réduire les temps de calcul, une nouvelle méthode de réduction de modèles de roues aubagées désaccordées intentionnellement par modification géométrique est développée et validée. La modélisation des incertitudes incluant le désaccordage involontaire, est faite avec une approche probabiliste non paramétrique. Une application à l’optimisation de la conception en vibration d’une roue réelle a finalement été effectuée en deux phases : (1) une optimisation de la répartition des différentes aubes désaccordées intentionnellement sur la roue aubagée et (2) une optimisation du niveau de modification géométrique de ces aubes. Les résultats montrent qu’une conception robuste par désaccordage intentionnel de la roue aubagée a été effectuée / Bladed disks are components which dynamic behaviour are very sensitive to mistuning induced by the manufacturing process which makes blades differ from one another. This sensitivity increases in general the vibrations. The objective of this research is to propose new methods for optimizing design in vibration of bladed disks with respect to mistuning. Optimization is done for the forced response while keeping a sufficient aeroelastic stability margin. In this context, detuning by modifying geometrically the blades’ shapes is used. To reduce numerical computational costs, a new reduction method for geometrically detuned bladed disks is developed and validate. Uncertainties modeling including mistuning is done with a non-parametric probabilistic approach. An application by optimizing the design in vibration of a realistic bladed disk is finally done in two steps : (1) An optimization of the different detuned blades arrangements around the disk and (2) an optimization of the geometric modification level of blades. The results show that a robust design of the bladed disks has been done using geometric detuning

As características arquitetônicas e o desempenho estrutural de pontes suspensas, estaiadas ou pênseis, têm determinado a sua crescente utilização em obras de arte destinadas a vencer grandes vãos. Essa utilização crescente que ocorreu no mundo nas últimas décadas se repete agora nos últimos anos no país. Várias dessas obras estão em execução e em projeto. Um dos aspectos relevantes na análise estrutural das pontes suspensas é o de seu comportamento quando submetidas à ação do vento. Apresenta-se o sistema computacional ANA-PSp desenvolvido especialmente para o estudo do movimento de tabuleiros de pontes suspensas sujeitas a esforços aeroelásticos e aerodinâmicos. Esse sistema computacional formado por um conjunto de subsistemas, é elaborado para a análise aeroelástica de pontes suspensas sob a ação de vento e permite análises paramétricas extensas dos fenômenos de drapejamento (flutter) e de martelamento (buffeting). A discretização da estrutura é efetuada pelo método dos elementos finitos e a redução dos graus de liberdade é realizada por superposição modal com modos selecionados que melhor descrevem os movimentos do tabuleiro. Utiliza-se modelo matemático reduzido para a análise multimodal no domínio do tempo e da freqüência. A velocidade crítica ou velocidade de drapejamento é determinada por procedimento de autovalores complexos com a obtenção de freqüências e taxas de amortecimentos modais para várias velocidades do vento. Adicionalmente, o fenômeno do drapejamento é estudado por séries temporais de respostas de coordenadas generalizadas e de deslocamentos selecionados e por análise espectral dessas séries temporais, que permitem a verificação das características de vibração do tabuleiro da ponte no domínio da freqüência. O estudo do fenômeno de martelamento considera esforços aeroelásticos determinísticos e esforços aerodinâmicos estocásticos e apresentam-se resultados em espectros de potência de deslocamentos e em desvios padrão de deslocamentos ao longo do tabuleiro. Para validar o sistema ANA-PSp, apresentam-se estudos de caso para a ponte estaiada da Normandia, para a ponte pênsil colapsada de Tacoma Narrows e para a ponte estaiada projetada, mas não executada, sobre o Rio Tietê e localizada na extremidade do complexo viário Jacu-Pêssego. / The architectonic characteristics and the structural performance of suspension bridges and cable-stayed bridges have determined their growing use on large span bridges. This growing usage, which has occurred world-wide during the last decades, is now being repeated in Brazil during the last few years. Several such bridges are presently either undergoing construction or being designed. One of the outstanding aspects in the structural analysis of suspension bridges is their behavior under wind action. This paper presents the computer system ANA-PSp, specially developed for studying the movement of suspended bridge decks under aeroelastic and aerodynamic forces. This computer system is formed by a group of subsystems and is created for aeroelastic analysis of suspended bridges under wind action. It allows extended parametric analyses of the flutter and the buffeting phenomena. Structural discretization is done by the finite element method and the reduction of degrees of freedom is obtained by modal superposition of the selected modes which best describe the deck movements. A reduced mathematical model is used for the multimodal analysis in the time and frequency domains. Critical velocity or flutter velocity is determined by a procedure of complex eigenvalues which obtains frequencies and damping ratios for different wind speeds. Additionally, the flutter phenomenon is studied by temporal series of answers to generalized coordinate responses and of selected displacements by spectral analysis of such temporal series, which allow us to verify the characteristics of the vibrations of the bridge deck in the frequency domain. The study of the buffeting phenomenon considers deterministic aeroelastic and stochastic aerodynamic forces. The paper presents results in displacement power spectra and in the standard deviation of displacements along the deck. In order to validate system ANA-PSp, case studies are presented for the cable-stayed Ponte de Normandie in Le Havre (France), for the collapsed suspension bridge on Tacoma Narrows and for the cable-stayed bridge, already designed but not built, on Tietê River, located at one end of the highway complex Jacu-Pêssego (São Paulo, SP, Brazil).

Response of flexible structures — such as cable-supported bridges and aircraft wings — is associated with a number of uncertainties in structural and flow parameters. This thesis is aimed at efficient uncertainty quantification in a few such flow and flow-induced structural response problems. First, the uncertainty quantification in the lift force exerted on a submerged body in a potential flow is considered. To this end, a new method — termed here as semi-intrusive stochastic perturbation (SISP) — is proposed. A sensitivity analysis is also performed, where for the global sensitivity analysis (GSA) the Sobol’ indices are used. The polynomial chaos expansion (PCE) is used for estimating these indices. Next, two stability problems —divergence and flutter — in the aeroelasticity are studied in the context of reliability based design optimization (RBDO). Two modifications are proposed to an existing PCE-based metamodel to reduce the computational cost, where the chaos coefficients are estimated using Gauss quadrature to gain computational speed and GSA is used to create nonuniform grid to reduce the cost even further. The proposed method is applied on a rectangular unswept cantilever wing model. Next, reliability computation in limit cycle oscillations (LCOs) is considered. While the metamodel performs poorly in this case due to bimodality in the distribution, a new simulation-based scheme proposed to this end. Accordingly, first a reduced-order model (ROM) is used to identify the critical region in the random parameter space. Then the full-scale expensive model is run only over a this critical region. This is applied to the rectangular unswept cantilever wing with cubic and fifth order stiffness terms in its equation of motion. Next, the wind speed is modeled as a spatio-temporal process, and accordingly new representations of spatio-temporal random processes are proposed based on tensor decompositions of the covariance kernel. These are applied to three problems: a heat equation, a vibration, and a readily available covariance model for wind speed. Finally, to assimilate available field measurement data on wind speed and to predict based on this assimilation, a new framework based on the tensor decompositions is proposed. The framework is successfully applied to a set of measured data on wind speed in Ireland, where the prediction based on simulation is found to be consistent with the observed data.

As características arquitetônicas e o desempenho estrutural de pontes suspensas, estaiadas ou pênseis, têm determinado a sua crescente utilização em obras de arte destinadas a vencer grandes vãos. Essa utilização crescente que ocorreu no mundo nas últimas décadas se repete agora nos últimos anos no país. Várias dessas obras estão em execução e em projeto. Um dos aspectos relevantes na análise estrutural das pontes suspensas é o de seu comportamento quando submetidas à ação do vento. Apresenta-se o sistema computacional ANA-PSp desenvolvido especialmente para o estudo do movimento de tabuleiros de pontes suspensas sujeitas a esforços aeroelásticos e aerodinâmicos. Esse sistema computacional formado por um conjunto de subsistemas, é elaborado para a análise aeroelástica de pontes suspensas sob a ação de vento e permite análises paramétricas extensas dos fenômenos de drapejamento (flutter) e de martelamento (buffeting). A discretização da estrutura é efetuada pelo método dos elementos finitos e a redução dos graus de liberdade é realizada por superposição modal com modos selecionados que melhor descrevem os movimentos do tabuleiro. Utiliza-se modelo matemático reduzido para a análise multimodal no domínio do tempo e da freqüência. A velocidade crítica ou velocidade de drapejamento é determinada por procedimento de autovalores complexos com a obtenção de freqüências e taxas de amortecimentos modais para várias velocidades do vento. Adicionalmente, o fenômeno do drapejamento é estudado por séries temporais de respostas de coordenadas generalizadas e de deslocamentos selecionados e por análise espectral dessas séries temporais, que permitem a verificação das características de vibração do tabuleiro da ponte no domínio da freqüência. O estudo do fenômeno de martelamento considera esforços aeroelásticos determinísticos e esforços aerodinâmicos estocásticos e apresentam-se resultados em espectros de potência de deslocamentos e em desvios padrão de deslocamentos ao longo do tabuleiro. Para validar o sistema ANA-PSp, apresentam-se estudos de caso para a ponte estaiada da Normandia, para a ponte pênsil colapsada de Tacoma Narrows e para a ponte estaiada projetada, mas não executada, sobre o Rio Tietê e localizada na extremidade do complexo viário Jacu-Pêssego. / The architectonic characteristics and the structural performance of suspension bridges and cable-stayed bridges have determined their growing use on large span bridges. This growing usage, which has occurred world-wide during the last decades, is now being repeated in Brazil during the last few years. Several such bridges are presently either undergoing construction or being designed. One of the outstanding aspects in the structural analysis of suspension bridges is their behavior under wind action. This paper presents the computer system ANA-PSp, specially developed for studying the movement of suspended bridge decks under aeroelastic and aerodynamic forces. This computer system is formed by a group of subsystems and is created for aeroelastic analysis of suspended bridges under wind action. It allows extended parametric analyses of the flutter and the buffeting phenomena. Structural discretization is done by the finite element method and the reduction of degrees of freedom is obtained by modal superposition of the selected modes which best describe the deck movements. A reduced mathematical model is used for the multimodal analysis in the time and frequency domains. Critical velocity or flutter velocity is determined by a procedure of complex eigenvalues which obtains frequencies and damping ratios for different wind speeds. Additionally, the flutter phenomenon is studied by temporal series of answers to generalized coordinate responses and of selected displacements by spectral analysis of such temporal series, which allow us to verify the characteristics of the vibrations of the bridge deck in the frequency domain. The study of the buffeting phenomenon considers deterministic aeroelastic and stochastic aerodynamic forces. The paper presents results in displacement power spectra and in the standard deviation of displacements along the deck. In order to validate system ANA-PSp, case studies are presented for the cable-stayed Ponte de Normandie in Le Havre (France), for the collapsed suspension bridge on Tacoma Narrows and for the cable-stayed bridge, already designed but not built, on Tietê River, located at one end of the highway complex Jacu-Pêssego (São Paulo, SP, Brazil).