Aircraft Flutter Research Articles

Complex Notation in Flutter Analysis

Flutter analysis in aircraft or bridge engineering has to include motion-induced aerodynamic forces. These forces are mathematically described in two equivalent ways, namely, by real number or complex number expressions. Accordingly, flutter analysis can be performed using either real or complex arithmetic. At first glance, the use of either kind of notation seems to be more a question of personal preference, as both lead to the same numerical results. Nevertheless, this paper attempts to advocate the use of complex notation both in aircraft and bridge flutter analysis. Real-number and complex-number descriptions of the same mechanical phenomena are compared. It is shown that, apart from computational advantages, complex notation leads to mathematically more compact and more elegant expressions, which is of significance particularly from an educational standpoint.

Optimal Excitation for Aircraft Flutter Testing

The choice of excitation signal for flutter testing of a full-scale aircraft or wind tunnel model is crucial if the flutter test clearance is to be performed quickly and with confidence. The use of chirps (that is, sinusoidal signals with varying frequency) is commonplace but has limitations. In this paper the idea of a simple chirp is extended to the development of a multi-sectional variable amplitude/variable power chirp in which the relative signal amplitude and power between sections may be specified over the frequency range of interest. An optimal chirp for a particular application may thus be designed. Sample results from a wind tunnel model flutter test are presented. In addition, the practice of sweeping up and then down in frequency is shown to be inadvisable under certain circumstances.

Identification of system, observer, and controller from closed-loop experimental data

This paper considers the identification problem of a system operating in a closed loop with an existing feedback controller. The closed-loop system is excited by a known excitation signal, and the resulting time histories of the closed-loop system response and the feedback signal are measured. From the time history data, the algorithm computes the Markov parameters of a closed-loop observer, from which the Markov parameters of the individual open-loop plant, observer, and controller are recovered. A state-space model of the open-loop plant and the gain matrices for the controller and the observer are then realized. The results of the paper are demonstrated by an example using wind tunnel aircraft flutter test data.

Identification of State Space Models Using a Stochastic Realization Algorithm with Application to Modal Identification of Flexible Aerospace Structures

Abstract Accurate Control of Large Space Structures (LSS) for pointing and tracking applications requires accurate knowledge of the vibrational characteristics of the LSS. Since it is not practical to duplicate the space environment during ground vibration tests, accurate models of LSS can only be obtained via System Identification algorithms applied to real data collected from the LSS after deployment in orbit. A similar problem arises in Aircraft Flutter Testing, which is done to verify that the flight envelop does not contain any aeroelastic or aeroservoelastic instabilities. In this paper, we show that System Identification car be done with high accuracy using State Space Models and a Stochastic Realization Algorithm (SRA) It is shown that the Stochastic Realization Algorithm (SRA) outperforms other available techniques and produces excellent results for the AFAL Flexible GRID test data and the X-29 Aircraft Flutter data under natural turbulence conditions. SRA also produces robust estimates of frequencies, dampings and mode shapes for repeated frequency modes of an elastic membrane even under conditions of 300% multiplicative noise. SRA identifies a multi-input multi-output stochastic state space model for the data using a noniterative technique based on Singular Value Decomposition of a Hankel matrix.

Optimal control applied to aircraft flutter suppression

Optimal control applied to aircraft flutter suppression

Historical Development of Aircraft Flutter

Introduction A EROELASTICITY, and in particular flutter, has influenced the evolution of aircraft since the earliest days of flight. This paper presents a glimpse of problems arising in these areas and how they were attacked by aviation's pioneers and their successors up to about the mid-1950s. The emphasis is on tracing some conceptual developments relating to the understanding and prevention of flutter including some lessons learned along the way. Because it must be light, an airplane necessarily deforms appreciably under load. Such deformations change the distribution of the aerodynamic load, which in turn changes the deformations; the interacting feedback process may lead to flutter, a self-excited oscillation, often destructive, wherein energy is absorbed from the airstream. Flutter is a complex phenomenon that must in general be completely eliminated by design or prevented from occurring within the flight envelope. The initiation of flutter depends directly on the stiffness, and only indirectly on the strength of an airplane, analogous to depending on the slope of the lift curve rather than on the maximum lift. This implies that the airplane must be treated not as a rigid body but as an elastic structure. Despite the fact that the subject is an old one, this requires for a modern airplane a large effort in many areas, including ground vibration testing, use of dynamically scaled wind-tunnel models, theoretical analysis, and flight flutter testing. The aim of this paper is to give a short history of aircraft flutter, with emphasis on the conceptual developments, from the early days of flight to about the mid-1950s. Work in flutter has been (and is being) pursued in many countries. As in nearly all fields, new ideas and developments in flutter have occurred similarly and almost simultaneously in diverse places in the world, so that exact assignment of priorities is often in doubt. Moreover, a definitive historical account would require several volumes; yet we hope to survey some of the main developments in a proper historical light, and in a way that the lessons learned may be currently useful. It is recognized that detailed documentation of flutter troubles has nearly always been hampered by proprietary conditions and by a reluctance of manufacturers to expose such problems. From our present perspective, flutter is included in the broader term aeroelasticity, the study of the static and dynamic response of an elastic airplane. Since flutter involves the problems of interaction of aerodynamics and structural deformation, including inertial effects, at subcritical as well as at critical speeds, it really involves all aspects of aeroelasticity. In a broad sense, aeroelasticity is at work in natural phenomena such as in the motion of insects, fish, and birds (biofluid-dynamics). In man's handiwork, aeroelastic problems of windmills were solved empirically four centuries ago in Holland with the moving of the front spars of the blades from about the midchord to the quarter-chord position (see the article by Jan Drees in list of Survey Papers). We now recognize that some 19th century bridges were torsionally weak and collapsed from aeroelastic effects, as did the Tacoma Narrows Bridge in spectacular fashion in 1940. Other aeroelastic wind-structure interaction pervades civil

Some Recent Trends in Aircraft Flutter Research

Some Recent Trends in Aircraft Flutter Research

Solution of the matrix Riccati equation in optimal control

This paper is concerned with the solution of the finite-time Riccati equation. The solution to the Riccati equation is given in terms of the partition of the transition matrix. Matrix differential equations for the partition of the transition matrix are derived and are solved using methods developed in the fields of free vibration theory and aircraft flutter analysis. Simple examples illustrating the method are presented.

Instrumental variables algorithm for modal parameter identification in flutter testing

The paper is concerned with the task of estimating modal parameters from system response measurement in aircraft flutter testing. A frequency-domain derivation of an instrumental-variables algorithm is presented for a linear time-invariant dynamic system of order n. Basically, this algorithm fits a set of poles and zeros to the measured transfer function. An illustrative example is provided regarding the application of the algorithm to aeroelasticity testing. It is shown that the algorithm can be implemented for on-line data reduction with a microcomputer-based analysis system. By using instrumental variables the sensitivity of the modal parameter estimates to noise in the system-response measurements is reduced greatly. The algorithm is expected to be a powerful and valuable tool for on-line estimation of modal parameters in flutter testing and should be useful in control system and structural dynamics tests.

Literature Review : Some Recent Trends in Aircraft Flutter Research

Literature Review : Some Recent Trends in Aircraft Flutter Research

Modern Methods of Investigating Flutter and Vibration

SummaryThe past several years have seen a steady advance in the techniques employed in flutter and vibration analysis. At the same time aircraft performance has been improved on every front and margins have had to be reduced: it is only by making full use of these modern methods that the accepted margins of safety have been preserved.The paper reviews the processes which are currently used in the prediction and prevention of aircraft flutter in contrast to those of a few years back. The more recent types of flutter which have had to be considered are discussed briefly in relation to the methods which have been developed to deal with them. Ground and Flight testing methods are reviewed together with the use to which the results are put.Finally there is a discussion of the increasing need to predict sub-critical response. The methods employed are discussed in relation to the more important problems.

Some applications of the Newton—Raphson method to non-linear matrix problems

If D (A) is a A-matrix the latent roots are defined as the roots, A i , of the equation | D (A) | = 0, and the eigenvalues are defined as the roots, uj (A), of | D — uI | = 0. It is shown that u j (A) = 0 for some j if and only if A is a latent root, and it is shown th at the Newton—Itaphson method can be employed to find the zeros of the functions /q j (A) and hence the latent roots. In contrast to the solution of scalar equations, it is shown that, under certain conditions, the method is valid for multiple latent roots It is also shown that the method may be applied to stability problems of the kind arising in the study of aircraft flutter problems, and a numerical example is given.

Measurement of the Aerodynamic Forces on Oscillating Aerofoils

AT the present time it is a general practice to make extensive investigations of the flutter and oscillatory stability characteristics of all prototype aircraft at an early stage in the design. So far as theoretical investigations of these characteristics are concerned there is often considerable uncertainty as to the values of the aerodynamic coefficients to be used, for there is evidence that measured and theoretical coefficients may differ considerably. Measured values of the coefficients are therefore required both for direct use in calculations and as a check on the theoretical coefficients, and also to provide a guide in the development of more precise theories. Unfortunately the wide variations in wing plan forms and the rapid increase in flight speeds which have occurred in recent years have meant that experimental work in this particular field has not kept pace with development and the designer is faced with the problem of ensuring the safety and operational efficiency of his aircraft using theoretical coefficients whose values may be unreliable.

The Flutter of Servo-Controlled Aircraft

The Flutter of Servo-Controlled Aircraft