Rozprawy doktorskie na temat „Flutter Stability”

Flutter analyses and tests are the major items in flight certification efforts required when a new air vehicle is developed or when a new external store is developed for an existing aircraft. The flight envelope of a new aircraft as well as the influence of aircraft modifications on an existing flight envelope can be safely determined only by flutter tests. In such tests, the aircraft is instrumented by accelerometers and exciters. Vibrations of the aircraft at specific dynamic pressures are measured and transmitted to a ground station via telemetry systems during flutter tests. These vibration data are analyzed online by using a flutter test software with various methods implemented in order to predict the safety margin with respect to flutter. Tests are performed at incrementally increasing dynamic pressures and safety regions of the flight envelope are determined step by step. Since flutter is a very destructive instability, tests are performed without getting too close to the flutter speed and estimations are performed by extrapolation. In this study, pretest analyses and flutter prediction methods that can be used in various flight conditions are investigated. Existing methods are improved and their applications are demonstrated with experiments. A novel method to predict limit cycle oscillations that are encountered in some modern fighter aircraft is developed. The prediction method developed in this study can effectively be used in cases where the nonlinearities in aircraft dynamics and air flow reduce the applicability of the classical prediction methods. Some further methods to reduce the adverse effects of these nonlinearities on the predictions are also developed.

With the advent of smart materials it is becoming possible to alter the structural characteristics of turbomachine airfoils. This change in structural characteristics can include, but is not limited to, changes in the shape (morphing) of the airfoil. Through changes in the airfoil shape, aerodynamic performance can be improved. Moreover, this technique has the potential to act as a flutter suppressant. In this investigation changes in the airfoil front camber while maintaining the airfoil thickness distribution are made to increase airfoil stability. The airfoil section is representative of current low aspect ratio fan blade tip sections. To assess the influence of the change in airfoil shape on stability the work-per-cycle was evaluated for torsion mode oscillations around the mid-chord at an inlet Mach number of 0.5 with an interblade phase angle of 180 degree Cchordal incidence angles of both 0 degree and 10 degree, and a reduced frequency of 0.4.

Thanks to the increasing slenderness and lightness allowed by new construction techniques and materials, the effects of wind on structures became in the last decades a research field of great importance in Civil Engineering. Thanks to the advances in computers power, the numerical simulation of wind tunnel tests has became a valid complementary activity and an attractive alternative for the future. Due to its flexibility, during the last years, the computational approach gained importance with respect to the traditional experimental investigation. However, still today, the computational approach to fluid-structure interaction problems is not as widely adopted as it could be expected. The main reason for this lies in the difficulties encountered in the numerical simulation of the turbulent, unsteady flow conditions generally encountered around bluff bodies. This thesis aims at providing a guide to the numerical simulation of bridge deck aerodynamic and aeroelastic behaviour describing in detail the simulation strategies and setting guidelines useful for the interpretation of the results.

Thanks to the increasing slenderness and lightness allowed by new construction techniques and materials, the effects of wind on structures became in the last decades a research field of great importance in Civil Engineering. Thanks to the advances in computers power, the numerical simulation of wind tunnel tests has became a valid complementary activity and an attractive alternative for the future. Due to its flexibility, during the last years, the computational approach gained importance with respect to the traditional experimental investigation. However, still today, the computational approach to fluid-structure interaction problems is not as widely adopted as it could be expected. The main reason for this lies in the difficulties encountered in the numerical simulation of the turbulent, unsteady flow conditions generally encountered around bluff bodies. This thesis aims at providing a guide to the numerical simulation of bridge deck aerodynamic and aeroelastic behaviour describing in detail the simulation strategies and setting guidelines useful for the interpretation of the results.

In recent years, combat aircraft with external stores have experienced a decrease in their mission capabilities due to lack of robustness of the current passive wing/store flutter suppression system to both structured as well as unstructured uncertainties. The research program proposed here is to investigate the feasibility of using a piezoceramic wafer actuator for active control of store flutter with the goal of producing a robust feedback system that demonstrates increased performance as well as robustness to modeling errors. This approach treats the actuator as an active soft-decoupling tie between the wing and store, thus isolating the wing from store pitch inertia effects. Advanced control techniques are used to assess the nominal performance and robustness of wing/store system to flutter critical uncertainties. NOTE: (10/2009) An updated copy of this ETD was added after there were patron reports of problems with the file.
Ph. D.

Labyrinth seals are widely used in rotating machinery and have been shown to experience aeroelastic instabilities. The rapid development of computational fluid dynamics now provides a high fidelity approach for predicting the aeroelastic behavior of labyrinth seals in three dimension and exhibits great potential within industrial application, especially during the detailed design stages. In the current publication a time-marching unsteady Reynolds- averaged Navier-Stokes solver was employed to study the various historically identified parameters that have essential influence on the stability of labyrinth seals. Advances in understanding of the related aeroelastic (flutter) phenomenon were achieved based on extensive yet economical numerical analysis of a simplified seal model. Further, application of the same methodology to several realistic gas turbine labyrinth seal designs confirmed the perceived knowledge and received agreements from experimental indications. Abbott’s criteria in describing the labyrinth seal aeroelastic behaviors were reaffirmed and further developed.

The present work is a study of the aeroelastic stability limit of the Hålogaland Bridge. The state-of-the-art theory concerning determination of flutter stability limits in modern bridge design is presented. The self-excited loads are modeled using aerodynamic derivatives obtained in a free vibration wind tunnel test of a section model. The bimodal flutter limit of all relevant mode pairs are evaluated, by considering frequency separation and mode shape similarity of the respective modes. The findings of the bimodal analysis are used as a starting point in the assessment of the multimodal flutter limit. The governing flutter mechanism of the Hålogaland Bridge is three-mode flutter, where the fundamental symmetric torsion mode couple with the first and second symmetric vertical modes. The critical mean wind velocity is found to 68.1 m/s, which is above the design requirement of 60.2m/s. The critical oscillation frequency is found to 2.03 rad/s. The development of the total damping in the system with respect to increasing mean wind velocity is evaluated. Horizontal mode influence is investigated by applying quasi-static theory and aerodynamic derivatives obtained in the discrete vortex shedding software DVMFLOW. The results indicate that horizontal modes do not have influence on the flutter limit. Modeling uncertainty in the prediction of flutter limits is discussed. A proposed probabilistic flutter analysis utilizing Monte Carlo simulations is used to evaluate the effect of parameter uncertainty. The sensitivity with respect to parameter uncertainty of flutter derivatives and structural damping is assessed by considering the probability distribution of the flutter limit. Including uncertainties of the flutter derivatives due to different interpretation of scatter in the wind tunnel test series is found to have a significant influence on the flutter limit.Large scatter resulted in wide distributions. Choice of structural damping ratio is seen to have little influence. The distribution of critical flutter velocity maybe modeled by an extreme value distribution, where a 99 % confidence interval ranges from 63.5 m/s to 78.6 m/s. The results indicate that the proposed probabilisticflutter analysis provides extended information concerning the accuracy in the prediction of flutter limits.

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.

L'instabilité de flottement a été le sujet de nombreuses études depuis le milieu du vingtième siècle à cause de ses applications critiques en aéronautique. Elle est classiquement décrite comme un instabilité linéaire en écoulement potentiel, mais les effets visqueux et nonlinéaires du fluide peuvent avoir un impact crucial.La première partie de cette thèse est consacrée au développement de méthodes théoriques et numériques pour l'analyse linéaire et nonlinéaire de la dynamique d'une ``section typique aéroélastique'' --- une plaque montée sur des ressorts de flexion et torsion --- plongée dans un écoulement laminaire bidimensionnel modélisé par les équations de Navier--Stokes incompressibles.D'abord, on développe une analyse faiblement nonlinéaire pour étudier le régime basse amplitude, puis, une approche d'équilibrage harmonique, connue comme la Méthode Spectrale en Temps (TSM), de façon à capturer des solutions de flottement plus fortement nonlinéaires. Le défi de la résolution numérique des équations TSM est relevé grâce au développement d'une approche parallèle en temps de type Newton--Krylov, combinée à un préconditionneur spécialement développé, dit ``bloc-circulant''.La seconde partie de la thèse est dédiée à l'étude physique de la bifurcation de flottement. On commence par revisiter le problème de stabilité linéaire en mettant en lumière, en particulier, les effets de viscosité.On poursuit avec l'étude des effets nonlinéaires fluides: les structures légères et les hauts nombres de Reynolds favorisent des bifurcations sous-critiques.On achève cette partie en étudiant l'apparition de modulations de basse fréquence sur des solutions périodiques de flottement. On explique ce comportement par une instabilité linéaire (Floquet) de cycle limite.La dernière partie de la thèse vise à initier l'extension des différentes méthodes évoquées précédemment pour le cas de configurations tridimensionnelles à grande échelle. En guise de premier pas vers cet objectif à long terme, on développe un outil open-source massivement parallèle capable de réaliser l'analyse de stabilité linéaire hydrodynamique (structure figée) d'écoulements tridimensionnels possédant plusieurs dizaines de millions de degrés de liberté
The flutter instability has been the focus of numerous works since the middle of the twentieth century, due to its critical application in aeronautics. Flutter is classically described as a linear instability using potential flow models, but viscous and nonlinear fluid effects may both crucially impact this aeroelastic phenomenon.The first part of this thesis is devoted to the development of theoretical and numerical methods for analyzing the linear and nonlinear dynamics of a ``typical aeroelastic section'' --- a heaving and pitching spring-mounted plate --- immersed in a two-dimensional laminar flow modeled by the incompressible Navier--Stokes equations.First, we develop a semi-analytical weakly nonlinear analysis to efficiently study the small amplitude regime. Second, we develop a harmonic balance-type method, known as the Time Spectral Method (TSM), in order to tackle highly-nonlinear periodic flutter solutions. The challenging task of solving the TSM equations is tackled via a time-parallel Newton--Krylov approach in combination with a new, so-called block-circulant preconditioner.The second part of the thesis focuses on the physical investigation of the flutter bifurcation. We start by revisiting the linear stability problem using a Navier--Stokes fluid model allowing to highlight, in particular, the effect of viscosity.We continue our route on the flutter bifurcation by investigating the effect of fluid nonlinearities: low solid-to-fluid mass ratios and increasing Reynolds numbers foster subcritical bifurcations.We conclude our study by investigating the appearance of low-frequency amplitude modulations on top of a previously established periodic flutter solution. We explain this behavior by a (Floquet) linear instability of periodic solutions.The last part of the thesis aims at initiating the extension of the different methods previously evoked to large-scale three-dimensional configurations. As a first step towards this long-term goal, we develop an open-source massively parallel tool, able to perform hydrodynamic (the structure is fixed) linear stability analysis of three-dimensional flows possessing several tens of millions of degrees of freedom

The first part of this Thesis deals with the analysis of piecewise-smooth mechanical systems and the definition of special stability criteria in presence of non-conservative follower forces. To illustrate the peculiar stability properties of this kind of dynamical system, a reference 2 d.o.f. structure has been considered, composed of a rigid bar, with one and constrained to slide, without friction, along a curved profile, whereas the other and is subject to a follower force. In particular, the curved constraint is assumed to be composed of two circular profiles, with different and opposite curvatures, defining two separated subsystems. Due to this jump in the curvature, located at the junction point between the curved profiles, the entire mechanical structure can be modelled by discontinuous equations of motion, the differential equations valid in each subsystem can be combined, leading to the definition of a piecewise-smooth dynamical system. When a follower force acts on the structure, an unexpected and counterintuitive behaviour may occur: although the two subsystems are stable when analysed separately, the composed structure is unstable and exhibits flutter-like exponentially-growing oscillations. This special form of instability, previously known only from a mathematical point of view, has been analysed in depth from an engineering perspective, thus finding a mechanical interpretation based on the concept of non-conservative follower load. Moreover, the goal of this work is also the definition of some stability criteria that may help the design of these mechanical piecewise-smooth systems, since classical theorems cannot be used for the investigation of equilibrium configurations located at the discontinuity. In the literature, this unusual behaviour has been explained, from a mathematical perspective, through the existence of a discontinuous invariant cone in the phase space. For this reason, starting from the mechanical system described above, the existence of invariant cones in 2 d.o.f. mechanical systems is investigated through Poincaré maps. A complete theoretical analysis on piecewise-smooth dynamical systems is presented and special mathematical properties have been discovered, valid for generic 2~d.o.f. piecewise-smooth mechanical systems, which are useful for the characterisation of the stability of the equilibrium configurations. Numerical tools are implemented for the analysis of a 2~d.o.f. piecewise-smooth mechanical system, valid for piecewise-linear cases and extendible to the nonlinear ones. A numerical code has been developed, with the aim of predicting the stability of a piecewise-linear dynamical system a priori, varying the mechanical parameters. Moreover, “design maps” are produced for a given subset of the parameters space, so that a system with a desired stable or unstable behaviour can easily be designed. The aforementioned results can find applications in soft actuation or energy harvesting. In particular, in systems devoted to exploiting the flutter-like instability, the range of design parameters can be extended by using piecewise-smooth instead of smooth structures, since unstable flutter-like behaviour is possible also when each subsystem is actually stable. The second part of this Thesis deals with the numerical analysis of an elastic cloak for transient flexural waves in Kirchhoff-Love plates and the design of special metamaterials for this goal. In the literature, relevant applications of transformation elastodynamics have revealed that flexural waves in thin elastic plates can be diverted and channelled, with the aim of shielding a given region of the ambient space. However, the theoretical transformations which define the elastic properties of this “invisibility cloak” lead to the presence of a strong compressive prestress, which may be unfeasible for real applications. Moreover, this theoretical cloak must present, at the same time, high bending stiffness and a null twisting rigidity. In this Thesis, an orthotropic meta-structural plate is proposed as an approximated elastic cloak and the presence of the prestress has been neglected in order to be closer to a realistic design. With the aim of estimating the performance of this approximated cloak, a Finite Element code is implemented, based on a sub-parametric technique. The tool allows the investigation of the sensitivity of specific stiffness parameters that may be difficult to match in a real cloak design. Moreover, the Finite Element code is extended to investigate a meta-plate interacting with a Winkler foundation, to analyse how the substrate modulus transforms in the cloak region. This second topic of the Thesis may find applications in the realization of approximated invisibility cloaks, which can be employed to reduce the destructive effects of earthquakes on civil structures or to shield mechanical components from unwanted vibrations.

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).

Demonstration of utter stability over the design envelope and identi fication of safe ight envelope is a prerequisite for operational clearance of any new aircraft design. An important step involved in flight flutter testing is the proper use of flutter prediction techniques to accurately predict flutter. This study focuses on flutter estimation techniques given flight test data. We review various flutter prediction techniques by simulating them on a three-degree-of-freedom aeroelastic system. We show that flutter margin and an auto-regressive model based approach are robust and reasonably accurate in predicting flutter onset. Using these two techniques, flutter margins are computed at flight test points obtained from flight test data of flexible aircraft. Throughout, we have predicted flutter dynamic pressure at constant Mach number. One of the contributions of this work is in predicting flutter dynamic pressure at transonic Mach numbers. A critical issue in flutter prediction is the lack of information on the flutter instability mode and thereby the number of modes to include in a model. In a novel application of tools from statistical signal processing, we determine the optimum model order to construct an auto-regressive model using the flight flutter test time response data. From this auto-regressive model the frequency and damping values are estimated which in turn is used to estimate aeroelastic stability parameters. High resolution property of auto-regressive technique even with short data records is demonstrated in this thesis. This will provide a quick evaluation of spectral estimate and stability parameter using the same auto-regressive model, facilitating a quick envelope expansion. Aeroelastic stability during wake penetration is an essential part of operational clearance of new aircraft. In this thesis, and perhaps one of the first such study, wake flight test response data is used to assess the stability of the aircraft during wake penetration by modeling the wake response data in an auto-regressive framework. We have compared analytical predictions of incremental load factor based on simulations with flight tests on wake interactions. Estimates for safe wake encounter distance that do not exceed structural limit load factors have been determined.

There is a growing interest in extracting more power per turbine by increasing the rotor size in offshore wind turbines. As a result, the turbine blades will become longer and therefore more flexible and a flexible blade is susceptible to flow-induced instabilities, such as classical flutter. In order to design and build stable large wind turbine blades, the onset of instability should be considered in the design process. To observe flow-induced instabilities in wind turbine blades, a small-scale flexible blade was built based on NREL 5MW reference wind turbine blade. The blade was placed in the test section of a wind tunnel and its tip displacement was measured using a non-contacting displacement measurement device. The blade was non-rotating and was subjected to uniform incoming flow. For a range of blade angles of attack, instability was observed beyond a critical wind speed. The amplitude of oscillations increases for wind speeds higher than the critical speed, and the frequency of oscillations remains constant. Flow visualizations and force measurements are conducted and the influence of various system parameters including the angle of attack and the blade twist was examined.

This dissertation explores the stability of beams, plates and membranes due to subsonic aerodynamic flows or solar radiation forces. Beams, plates and membranes are simple structures that may act as building blocks for more complex systems. In this dissertation we explore the stability of these simple structures so that one can predict instabilities in more complex structures. The theoretical models include both linear and nonlinear energy based models for the structural dynamics of the featureless rectangular structures. The structural models are coupled to a vortex lattice model for subsonic fluid flows or an optical reflection model for solar radiation forces. Combinations of these theoretical models are used to analyze the dynamics and stability of aeroelastic and solarelastic systems. The dissertation contains aeroelastic analysis of a cantilevered beam and a plate / membrane system with multiple boundary conditions. The dissertation includes analysis of the transition from flag-like to wing-like flutter for a cantilevered beam and experiments to quantify the post flutter fluid and structure response of the flapping flag. For the plate / membrane analysis, we show that the boundary conditions in the flow direction determine the type of instability for the system while the complete set of boundary conditions is required to accurately predict the flutter velocity and frequency. The dissertation also contains analysis of solarelastic stability of membranes for solar sail applications. For a fully restrained membrane we show that a flutter instability is possible, however the post flutter response amplitude is small. The dissertation also includes analysis of a membrane hanging in gravity. This systems is an analog to a spinning solar sail and is used to validate the structural dynamics of thin membranes on earth. A linear beam structural model is able to accurately capture the natural frequencies and mode shapes. Finally, the dissertation explores the stability of a spinning membrane. The analysis shows that a nonlinear model is needed to produce a conservative estimate of the stability boundary.

Dissertation

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.
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