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The purpose of this dissertation is to develop a methodology for designing active control laws in a computational aeroelasticity environment. The methodology involves employing a systems identification technique to develop an explicit state-space model for control law design from the output of a computational aeroelasticity code. The particular computational aeroelasticity code employed in this dissertation solves the transonic small disturbance equation using a time-accurate, finite-difference scheme. Linear structural dynamics equations are integrated simultaneously with the computational fluid dynamics equations to determine the time responses of the structural outputs. These structural outputs are employed as the input to a modern systems identification technique that determines the Markov parameters of an "equivalent linear system". The eigensystem realization algorithm is then employed to develop an explicit state-space model of the equivalent linear system. Although there are many control law design techniques available, the standard Linear Quadratic Guassian technique is employed in this dissertation. The computational aeroelasticity code is modified to accept control laws and perform closed-loop simulations. Flutter control of a rectangular wing model is chosen to demonstrate the methodology. Various cases are used to illustrate the usefulness of the methodology as the nonlinearity of the computational fluid dynamics system is increased through increased angle-of-attack changes. / Ph. D.

Design for prevention of aeroelastic instability (that is, the critical speeds leading to aeroelastic instability lie outside the operating range) is an integral part of the wing design process. Availability of the sensitivity derivatives of the various critical speeds with respect to shape parameters of the wing could be very useful to a designer in the initial design phase, when several design changes are made and the shape of the final configuration is not yet frozen. These derivatives are also indispensable for a gradient-based optimization with aeroelastic constraints. In this study, flutter characteristic of a typical section in subsonic compressible flow is examined using a state-space unsteady aerodynamic representation. The sensitivity of the flutter speed of the typical section with respect to its mass and stiffness parameters, namely, mass ratio, static unbalance, radius of gyration, bending frequency and torsional frequency is calculated analytically. A strip-theory formulation is newly developed to represent the unsteady aerodynamic forces on a wing. This is coupled with an equivalent plate structural model based on a Rayleigh-Ritz formulation and the aeroelastic equations are solved as an eigenvalue problem to determine the critical speed of the wing. The sensitivity of divergence and flutter speeds to shape parameters, namely, aspect ratio, area, taper ratio and sweep angle are computed analytically. The aeroelastic equations are also integrated with respect to time using the Wilson-θ method at different values of freest ream speed, to observe the aeroelastic phenomena in real time. of divergence and flutter speeds to shape parameters, namely, aspect ratio, area, taper ratio and sweep angle are computed analytically. The aeroelastic equations are also integrated with respect to time using the Wilson-B method at different values of freest ream speed, to observe the aeroelastic phenomena in real time. Flutter analysis of the wing is also carried out using a lifting-surface subsonic kernel function aerodynamic theory (FAST) and an equivalent plate structural model The flutter speed is obtained using a <i>V-g</i> type of solution. The novel method of automatic differentiation using ADIFOR is implemented to generate exact derivatives of the flutter speed with respect to shape and modal parameters of the wing. Finite element modeling of the wing is done using NASTRAN so that wing structures made of spars and ribs and top and bottom wing skins could be analyzed. The free vibration modes of the wing obtained from NASTRAN are input into FAST to compute the flutter speed. The derivatives of flutter speed with respect to shape parameters are computed using a combination of central difference scheme and ADIFOR and the sensitivity to modal parameters is calculated using ADIFOR. An equivalent plate model which incorporates first-order shear deformation theory is then examined so it can be used to model thick wings, where shear deformations are important. The sensitivity of natural frequencies to changes in shape parameters is obtained using ADIFOR. A simple optimization effort is made towards obtaining a minimum weight design of the wing, subject to flutter constraints, lift requirement constraints for level flight and side constraints on the planform parameters of the wing using the IMSL subroutine NCONG, which uses successive quadratic programming. / Ph. D.

A method for predicting the unsteady, subsonic, aeroservoelastic response of a wing has been developed. The air, wing, and control surface are considered to be a single dynamical system. All equations are solved simultaneously in the time domain by a predictor-corrector method. The scheme allows nonlinear aerodynamic and structural models to be used and subcritical, critical, and supercritical aeroelastic behavior may be modeled without restrictions to small disturbances or periodic motions. A vortex-lattice method is used to model the aerodynamics. This method accounts for nonlinear effects associated with high angles of attack, unsteady behavior, and deformations of the wing. The vortex-lattice method is valid as long as separation or vortex bursting does not occur. Two structural models have been employed: a linear model and a nonlinear model which accounts for large curvature. Both models consider the flexural-torsional motion of an inextensional wing. / Master of Science

The design of modern high-performance aircraft is toward increased aerodynamic efficiency, decreased structural weight, and higher flight speeds. Preliminary designs often exhibit a flutter instability within the desired operating envelope of the aircraft. Passive methods which have been used to solve the flutter problem include added structural stiffness, mass balancing, and speed restrictions. These methods may result in significant weight penalties. Studies by Boeing (ref. 1) show that weight penalties as high as 2 to 4% of the total structural weight may be required to solve the flutter problem passively by increasing the structural stiffness. Therefore, there is considerable interest in alternative methods of increasing the flutter speed beyond the original unaided value. / Master of Science

Panel flutter is an important design consideration for vehicles traveling at supersonic speeds. Most theoretical analyses of panel flutter consider the motion of the panel to be described adequately by classical thin plate theory. In such a theory, transverse shear deformations are neglected which is a reasonable assumption for solid plates. For a sandwich panel, neglect of transverse shear deformations may not be a good assumption in flutter analysis inasmuch as studies have indicated that the vibration and buckling behavior of such panels can be affected significantly by shear deformations. An analysis which considers transverse shear deformations is presented in order to determine the effect of finite transverse shear stiffness on the flutter behavior of sandwich plates. The sandwich theory used is due to Libove and Batdorf. The essential feature of this theory is that straight line elements perpendicular to the undeformed middle surface remain straight and of the same length but are not necessarily perpendicular to the deformed middle surface. The aerodynamic loading on the panel is given by two-dimensional static aerodynamics. The adequacy of such an approximation has been demonstrated for panels rigid in shear and the mathematical simplicity allows closed-form solutions to be found. The analysis proceeds from consideration of the equilibrium of an infinitesimal element. If equations are written in terms of the deflection and two shear deformations for equilibrium of forces in the z direction and equilibrium. of moments about the x and y axis, three differential equations involving the three unknown displacements are obtained. This system of equations is of sixth order with constant coefficients, but for simple support boundary conditions on the streamwise edges an exact solution can be obtained. The associated characteristics equation can be factored into a fourth degree equation and a second degree equation; thus an analytical expression can be obtained for the characteristic roots. The solution just described is a general solution for the motion of a sandwich panel simply supported along streamwise edges and subject to inertia loading and aerodynamic forces given by two-dimensional static aerodynamics. Any combination of boundary conditions consistent with the sandwich plate theory used can be applied at the leading and trailing edges. Two cases are considered: simply supported leading and trailing edges and clamped leading and trailing edges. With the use of either set of boundary condition, a transcendental equation is obtained which is satisfied by various combinations of frequency and dynamic pressure. The dynamic pressure necessary to cause the frequency to become complex corresponds to divergent oscillatory motion or flutter. Values of the flutter dynamic pressure have been calculated as a function of length-width ratio for a large range of shear stiffness. For infinite shear stiffness the results agree with those established by previous investigators. As shear stiffness decreases, the flutter dynamic pressure usually decreases also. An unusual result of the analysis is that at low length-width ratios, a clamped panel has a lower flutter dynamic pressure than a simply supported panel even though the vibration frequencies are higher for the clamped panel. Results are not presented for panels with normal inplane loadings but they can be obtained from the equations given. The analysis shows that flutter is independent of normal inplane loadings perpendicular to the flow direction just as was found for panels rigid in shear. An approximate two-mode Galerkin solution to the problem has been obtained by a previous investigator. Comparison of the exact solution to the approximate solution shows the approximate analysis to be in increasing error as length-width ratio increases or shear stiffness decreases. / Ph. D.

Os novos materiais utilizados nas estruturas de aeronaves, mais leves e flexíveis, tornam estas estruturas mais sujeitas a fenômenos aeroelásticos, sendo que o mais sério deles é o flutter, que deve ser cuidadosamente investigado com uma boa campanha de ensaios em vôo durante o desenvolvimento e certificação da aeronave. Este trabalho propõe um projeto conceitual de um excitador de flutter que atenda às necessidades dos ensaios, tentando resolver problemas encontrados nos modelos utilizados comumente. Para isso, é feita uma revisão da literatura pertinente, apresentando conceitos de ensaios em vôo e do fenômeno em questão, além de apresentar um histórico dos ensaios e modelos de excitadores utilizados ao longo da história. Em seguida, são apresentados alguns conceitos de excitadores, que são dimensionados e analisados segundo suas vantagens e desvantagens para finalmente escolher o modelo mais pertinente visando no futuro um projeto detalhado, construção e testes em túnel de vento. / The ultimate materials used in aircraft structures, lighter and more flexibles, make these structures more susceptible to aeroelastic phenomena including flutter, the most dangerous of all. This kind of phenomena must be carefully investigated with satisfactory flight test campaigns during the aircraft development and certification. This work proposes a flutter exciter conceptual design that attends the test necessities, trying to solve problems found in the models used actually. So, a bibliographic revision is done, presenting flight test concepts and the studied phenomena, regarding a flight test history and the exciter models used through the years. Finally, some exciter concepts are presented, dimensioned and analyzed considering their advantages and disadvantages in order to choose the most pertinent model, considering, in a near future, the detailed design, manufacturing and wind tunnel tests.

Na Indústria Aeronáutica, é de extrema importância a qualidade e o desempenho de seus produtos, que estão diretamente relacionados ao projeto e ao desenvolvimento de estruturas adequadas, pois além de seu caráter funcional deve-se também garantir a sua integridade nas mais diversas condições de operação. O comportamento dinâmico destas estruturas é um dos seus principais aspectos, principalmente devido à demanda contínua para estruturas mais leves e consequentemente mais flexíveis. Tradicionalmente, as estruturas aeroespaciais devem ser submetidas a alguma forma de verificação antes do voo, de forma a assegurar que a aeronave esteja livre de qualquer fenômeno de instabilidade aeroelástica, que pode ocorrer provocando problemas de fadiga ou falhas estruturais. Um dos fenômenos de instabilidade mais importantes é denominado flutter. As técnicas de ensaio em voo para identificação de flutter são de extrema importância para o conhecimento dos limites de voo seguro. Um dos elementos essenciais para a realização de ensaios de flutter em voo é o processo de identificação dos parâmetros modais estruturais da aeronave sob teste. A identificação precisa e rápida dos parâmetros modais permite determinar com antecedência e segurança as condições de voo em que o fenômeno de flutter irá ocorrer. Atualmente as pesquisas nesta área apontam na direção do desenvolvimento de tecnologia que permita a identificação em tempo real dos parâmetros modais associados ao flutter. Neste trabalho foi realizado o estudo de um método de identificação de parâmetros modais para ser aplicado em tempo real. O método de identificação utilizado para este estudo é o EERA - Extended Eigensystem Realization Algorithm, um método de identificação no domínio do tempo considerado eficiente e poderoso, pois é capaz de identificar o comportamento dinâmico complexo em estruturas. O algoritmo foi validado através de um ensaio experimental num modelo de asa no túnel de vento, onde foram determinados os parâmetros modais envolvidos no flutter. Também foi realizado um ensaio experimental numa placa de alumínio, onde foram identificados os seus parâmetros modais, frequências naturais e fatores de amortecimento. Após sua validação, o método EERA foi adaptado e programado no equipamento de aquisição e processamento de sinais dSPACE®, que é destinado a realizar identificação em tempo real. Por último foi realizado um ensaio experimental em tempo real na placa de alumínio utilizada anteriormente, onde os parâmetros modais identificados on-line foram comparados com os identificados off-line, comprovando assim a eficiência do método na identificação em tempo real. / In the Aeronautical Industry, the quality and the performance of its products, that are directly related to the project and the development of adequate structures, are of extreme importance, since, beyond their functional characteristics, their integrity, in the most diverse operation conditions, must also be guaranteed. The dynamic behavior of these structures is one of its main aspects, mainly due to continuous demand for lighter and consequently more flexible structures. Traditionally, the aerospace structures must be submitted to some form of verification before the flight, to assure that the aircraft is free of any aeroelastic instability phenomenon, which when occurring will provoke structural fatigue problems or failure. One of the more important instability phenomena is called flutter. The techniques of flight test for identification of flutter are of extreme importance for the knowledge of the limits of safe flight. One of the essential elements for the accomplishment of flutter tests in flight is the process of identification of the structural modal parameters of the aircraft under test. The accurate and fast identification of the modal parameters allows determining, with antecedence and security, the flight conditions where the phenomenon of flutter will occur. Currently the research in this area points in the direction of developing the technology that allows the identification in real time of the modal parameters associated to flutter. In this work the study of a method of identification of modal parameters was carried through to be applied in real time. The method of identification used for this study is the EERA - Extended Eigensystem Realization Algorithm, a method of identification in the time domain considered efficient and powerful, since it is capable to identifying complex dynamic behavior in structures. The algorithm was validated with an experimental test in a model of wing in the wind tunnel, where the involved modal parameters in flutter had been determined. Also an experimental test was carried out with an aluminum plate, where its modal parameters, natural frequencies and damping factors, had been identified. After its validation, the method EERA was adapted and programmed in the dSPACE® signals acquisition and processing equipment, which is used for carrying out identification in real time. Finally an experimental test, in real time, with the previously used aluminum plate was carried out, when the modal parameters identified on-line were compared with those identified off-line, thus proving the efficiency of the method for identification in real time.

A identificação de mecanismos modais é uma tarefa que requer um grande esforço ao se considerar geometrias complexas. O uso de materiais inteligentes como tecnologia nesse tipo de identificação vem sendo bastante difundido, principalmente o uso de sensores piezelétricos, como o piezo-fiber composite (PFC). Esse tipo de aplicação pode se tornar uma ferramenta bastante prática no estudo de instabilidades aeroelásticas, em especial o mecanismo modal de flutter. A proposta desse trabalho é criar uma metodologia de análise de flutter simulando o desempenho de materiais piezelétricos, aderidos em laminados compósitos, como sensores modais. Inicialmente, é realizada uma análise aeroelástica da estrutura para se identificar o mecanismo e os modos dominantes para o surgimento do flutter. Em seguida, os modos identificados são detectados pelos sensores com uma determinada potência de sinal. A sensibilidade desse sinal é avaliada de acordo com a posição e configuração do laminado embebido no sensor. Para realizar essa simulação, um modelo de asa é gerado e suas frequências naturais e modos são determinados pelo método dos elementos finitos (MEF). Com esses dados, é possível caracterizar o modelo nas equações de movimento aeroelásticas. O carregamento aerodinâmico dessas equações é obtido utilizando o método dos anéis de vórtice, do inglês: vortex lattice method (VLM). A simulação é realizada em cada velocidade de fluxo e a resposta dos sensores piezelétricos é obtida no domínio do tempo e domínio da freqüência para se analisar a potência do sinal. Foi realizada uma prévia análise de um modelo de asa representado por uma placa e as configurações de maior potência de sinal são identificadas. A posição dos sensores se demonstrou mais sensível do que a configuração do laminado e a utilização de apenas um sensor foi suficiente para identificação do mecanismo modal, o que pode tornar essa tecnologia viável em ensaios de flutter em estruturas de material compósito. / For complex aeronautical structures, modal mechanism identification requires a great deal of effort. The use of smart materials has been developed in this application, mainly the sensor application with piezo-fiber composites (PFC). It can become a useful tool in aeroelastic instabilities studies, especially on flutter modal mechanism. This work intends to develop a methodology of flutter analysis evaluating the piezoelectric materials performance, using composites impregnation effects, and working as a modal sensor. First, one aeroelastic analysis is done to identify the flutter mechanism and its dominant modes. Then, it modes is detected by sensors with some specific power of electric signal, whose sensitivity is evaluated according with position and embeeded laminate configuration. This simulation uses a plate model representing a wing, whose natural frequencies and modes are determined by finite element method (FEM). So, given this data, is possible to define the wing model using an equation of motion, whose aerodynamic load is obtained by vortex lattice method (VLM). That equation is solved step by step, for each airspeed considered, then, the PFC response is obtained both in the frequency and time domain. The analysis was done using a metric that qualifies the best configuration according with the power of signal. The sensor position was more significant than the laminate configuration; however, the use of only one sensor is sufficient to identify the modal mechanism, which becomes this technology feasible in flutter test of composite structures.

A aeroelasticidade é a ciência que estuda os fenômenos provenientes das interações entre forças aerodinâmicas, elásticas e inerciais. Estes fenômenos podem ser classificados como estáticos ou dinâmicos e estes divididos em problemas de estabilidade ou de resposta. Destaca-se aqui o flutter, um fenômeno aeroelástico dinâmico de estabilidade. A velocidade crítica de flutter é a fronteira entre a estabilidade e instabilidade de um sistema aeroelástico. Em velocidades menores que a crítica qualquer oscilação é amortecida ao longo do tempo. Na velocidade crítica o sistema aeroelástico apresenta oscilações auto excitadas com amplitude e frequência constantes. Acima da velocidade crítica verificam-se oscilações instáveis que resultam na falha de uma estrutura. Este trabalho apresenta o projeto, fabricação e testes de um modelo experimental para testes de flutter em túnel de vento. O modelo experimental é composto por uma asa rígida conectada a uma suspensão elástica que atribui dois graus de liberdade ao experimento. As características inerciais e elásticas do modelo experimental são determinadas e utilizadas em um modelo aeroelástico computacional. Este modelo utiliza as equações de movimento para uma seção típica combinadas com o modelo aerodinâmico não estacionário de Theodorsen. O método V-g é utilizado para a solução do problema de flutter, ou seja, determinação da velocidade crítica de flutter. Esta solução é confrontada com a velocidade crítica medida em ensaios em túnel de vento. A evolução aeroelástica do modelo experimental é medida e apresentada como respostas no domínio do tempo e da frequência. / Aeroelasticity is the science which studies the interaction among inertial, elastic, and aerodynamic forces. Aeroelastic phenomena can be divided in static and dynamic problems and these studied as problems of stability or response. Flutter is a dynamic aeroelastic problem of stability and one of the most representative topics of aeroelasticity. The critical flutter speed can be defined as the frontier between stability and instability. Below the critical speed vibrations are damped out as time proceeds. At the critical flutter speed the system presents a self-sustained oscillatory behavior with constant frequency and amplitude. Unstable oscillations are observed for speeds above the critical one leading to structural failure. The design, fabrication and tests of an experimental model for flutter tests in wind tunnels are presented in this work. The experimental model has a rigid wing connected to a flexible suspension that allows vibrations in two degrees of freedom. The elastic and inertial parameters of the experimental system are used in a computational aeroelastic model. The equations of motion for a typical aeroelastic section and an unsteady aerodynamic model given by Theodorsen are combined and the resulting aeroelastic equations are solved using the V-g method. The computational results are compared with the experimental critical flutter speed measured in wind tunnel tests. The experimental aeroelastic behavior with increasing airflow speed is given in time and frequency domain.