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AEROELASTICITY
By Raymond L. Bisplinghoff, Holt Ashley, Robert L. Halfman Dover Publications, Inc.
Copyright © 1983 Raymond L. Bisplinghoff, Holt Ashley and Robert L. Halfman
All rights reserved.
ISBN: 978-0-486-13243-3
CHAPTER 1
INTRODUCTION TO AEROELASTICITY
1–1 Definitions. The term aeroelasticity has been applied by aeronautical engineers to an important class of problems in airplane design. It is often defined as a science which studies the mutual interaction between aerodynamic forces and elastic forces, and the influence of this interaction on airplane design. Aeroelastic problems would not exist if airplane structures were perfectly rigid. Modern airplane structures are very flexible, and this flexibility is fundamentally responsible for the various types of aeroelastic phenomena. Structural flexibility itself may not be objectionable; however, aeroelastic phenomena arise when structural deformations induce additional aerodynamic forces. These additional aerodynamic forces may produce additional structural deformations which will induce still greater aerodynamic forces. Such interactions may tend to become smaller and smaller until a condition of stable equilibrium is reached, or they may tend to diverge and destroy the structure.
The term aeroelasticity, however, is not completely descriptive, since many important aeroelastic phenomena involve inertial forces as well as aerodynamic and elastic forces. We shall apply a definition in which the term aeroelasticity includes phenomena involving interactions among inertial, aerodynamic, and elastic forces, and other phenomena involving interactions between aerodynamic and elastic forces. The former will be referred to as dynamic and the latter as static aeroelastic phenomena.
Collar has ingeniously classified problems in aeroelasticity by means of a triangle of forces. Referring to Fig. 1–1, the three types of forces, aerodynamic, elastic, and inertial, represented by the symbols A, E, and I, respectively, are placed at the vertices of a triangle. Each aeroelastic phenomenon can be located on the diagram according to its relation to the three vertices. For example, dynamic aeroelastic phenomena such as flutter, F, lie within the triangle, since they involve all three types of forces and must be bonded to all three vertices. Static aeroelastic phenomena such as wing divergence, D, lie outside the triangle on the upper left side, since they involve only aerodynamic and elastic forces. Although it is difficult to define precise limits on the field of aeroelasticity, the classes of problems connected by solid lines to the vertices in Fig. 1–1 are usually accepted as the principal ones. Of course, other borderline fields can be placed on the diagram. For example, the fields of mechanical vibrations, F, and rigid-body aerodynamic stability, DS, are connected to the vertices by dotted lines. It is very likely that in certain cases the dynamic stability problem is influenced by airplane flexibility and it would therefore be moved within the triangle to correspond with DSA, where it would be regarded as a dynamic aeroelastic problem.
It will be convenient to state concise definitions of each aeroelastic phenomenon which appears on the diagram in Fig. 1–1.
Flutter, F. A dynamic instability occurring in an aircraft in flight, at a speed called the flutter speed, where the elasticity of the structure plays an essential part in the instability.
Buffeting, B. Transient vibrations of aircraft structural components due to aerodynamic impulses produced by the wake behind wings, nacelles, fuselage pods, or other components of the airplane.
Dynamic response, Z. Transient response of aircraft structural components produced by rapidly applied loads due to gusts, landing, gun reactions, abrupt control motions, moving shock waves, or other dynamic loads.
Aeroelastic effects on stability, SA. Influence of elastic deformations of the structure on dynamic and static airplane stability.
Load distribution, L. Influence of elastic deformations of the structure on the distribution of aerodynamic pressures over the structure.
Divergence, D. A static instability of a lifting surface of an aircraft in flight, at a speed called the divergence speed, where the elasticity of the lifting surface plays an essential role in the instability.
Control effectiveness, C. Influence of elastic deformations of the structure on the controllability of an airplane.
Control system reversal, R. A condition occurring in flight, at a speed called the control reversal speed, at which the intended effects of displacing a given component of the control system are completely nullified by elastic deformations of the structure.
1–2 Historical background. Problems in aeroelasticity did not attain the prominent role that they now play until the early stages of World War II. Prior to that time, airplane speeds were relatively low and the load requirements placed on aircraft structures by design criteria specifications produced a structure sufficiently rigid to preclude most aeroelastic phenomena. As speeds increased, however, with little or no increase in load requirements, and in the absence of rational stiffness criteria for design, aircraft designers encountered a wide variety of problems which we now classify as aeroelastic problems.
Although aeroelastic problems have occupied their current prominent position for a relatively short period, they have had some influence on airplane design since the beginning of powered flight. Perhaps the first designer to be affected was Professor Samuel P. Langley of the Smithsonian Institution. In the light of modern knowledge, it seems likely that the unfortunate wing failure which wrecked Langley's machine on the Potomac River houseboat in 1903 could be described as wing torsional divergence. In going over the arguments put forward at the time, the best explanation of what happened was given by Griffith Brewer, one time president of the Royal Aeronautical Society. Brewer described the phenomenon which wrecked the Langley monoplane in the same way as we describe wing torsional divergence today. Langley's misfortune occurred shortly before the Wright Brothers made the first sustained heavier-than-air flight.
Perhaps the success of the Wright biplane and the failure of the Langley monoplane was the original reason for the strong predilection for biplanes in the early days of airplane design. The technical arguments of biplane versus monoplane, which were prevalent for so many years, were undoubtedly influenced by the lack of a rational torsional stiffness criterion for monoplane wings. Although a number of externally braced monoplanes were constructed by the French and Germans prior to World War I, the monoplane as a military machine ceased to exist in 1917, and it was not until the mid-thirties that designers ventured to build high-performance monoplane military aircraft.
The most widespread early aeroelastic problem in the days when military aircraft were almost exclusively biplanes was the tail flutter problem. One of the first documented cases of flutter occurred on the horizontal tail of the twin-engined Handley Page 0/400 bomber, shown by Fig. 1–2, at the beginning of World War I. Lanchester and Bairstow were asked to investigate the cause of violent oscillations of the fuselage and tail surfaces. They discovered that the fuselage and tail had two principal low-frequency modes of vibration. In one mode, the left and right elevators oscillated about their hinges 180° out of phase. This was possible because the elevators were not attached to the same torque tube, but were connected by a relatively weak spring provided by the long control cables through which each individual elevator was connected to the stick. In the second mode, the fuselage oscillated in torsion. The possibility of a self-excited oscillation involving coupling between the modes was diagnosed as the cause of the vibrations. One of the proposed remedial measures was that of connecting both elevators to the same torque tube. A second epidemic of tail flutter due to the same cause was experienced by the DH-9 airplane in 1917, and a number of lives were lost before it was cured. The cure was identical to that applied to the Handley Page airplane, and a torsionally stiff connection between elevators has been a design feature in airplanes ever since.
Aeroelastic wing problems appeared when designers abandoned biplane construction with its interplane bracing and relatively high torsional rigidity, in favor of monoplane types. The latter often had insufficient torsional rigidity, and flutter, loss of aileron effectiveness, and deformation effects on load distribution resulted. An early example of this kind arose during World War I in the development of the Fokker D-8 airplane shown in Fig. 1–3. In the initial design of this airplane, which was a high-wing cantilever monoplane, the torsional stiffness was determined by a criterion which had been applied to biplanes. The D-8 was put into production because of its superior performance, and was not in combat more than a few days before wing failures repeatedly occurred in high-speed dives. Since the best pilots and squadrons were receiving them first, it appeared possible that the flower of the German Air Corps would be wiped out. After a period in which the Army engineers and the Fokker Company each tried to place the responsibility on the other, the Army conducted static strength tests on half a dozen wings and found them sufficiently strong to support the required ultimate factor of 6. This produced a serious dilemma, and it was clearly up to Anthony Fokker to discover the cause or cease production on the D-8. Static tests were undertaken by the Fokker Company, and this time, deflections were carefully measured from tip to tip. In Fokker's words, the following conclusions were drawn: "I discovered that with increasing load, the angle of incidence at the wing tips increased perceptibly. It suddenly dawned on me that this increasing angle of incidence was the cause of the wing's collapse, as logically the load resulting from the air pressure in a steep dive would increase faster at the wing tips than at the middle. The resulting torsion caused the wings to collapse under the strain of combat maneuvers." This seems to be the first documented case where static aeroelastic effects at a fairly high speed produced a redistribution in airload such that failure resulted.
In later experience with the D-8, subsequent to the war, U. S. Army Air Corps engineers at McCook Field, Dayton, Ohio, observed a violent but nondestructive case of wing bending-aileron flutter. This was cured by statically balancing the ailerons about the hinge line, a technique which seems to have been pointed out first by Baumhauer and Koning in 1922. Several of the monoplane racers of the 1920's and 1930's experienced forms of wing-aileron flutter, and mass balancing was a commonly applied cure and preventive measure.
The period of development of the cantilever monoplane seems to have been the period in which serious research in aeroelasticity commenced. In the earliest days of monoplane design, aeroelastic problems were overcome by cut-and-try methods. A theory of wing-load distribution and wing divergence was first presented in 1926 by Hans Reissner. A theory of loss of lateral control and aileron reversal was published six years later by Roxbee Cox and Pugsley in 1932. The mechanism of potential flow flutter was understood sufficiently well for design use by 1935, largely through the early efforts of Glauert, Frazer and Duncan, Küssner, and Theodorsen. However, few designers were able to comprehend the theories in the early papers and the majority were reluctant to trust mathematicians to compute sizes of structural members to preclude aeroelastic effects.
1–3 Influence of aeroelastic phenomena on design. Aeroelastic phenomena in modern high-speed aircraft have profound effects upon the design of structural members and somewhat lesser but nonetheless important effects upon mass distribution, lifting surface planforms, and control system design.
Flutter. Flutter has perhaps the most far-reaching effects of all aeroelastic phenomena on the design of high-speed aircraft. Modern aircraft are subject to many kinds of flutter phenomena. The classical type of flutter is associated with potential flow and usually, but not necessarily, involves the coupling of two or more degrees of freedom. The nonclassical type of flutter, which has so far been difficult to analyze on a purely theoretical basis, may involve separated flow, periodic breakaway and reattachment of the flow, stalling conditions, and various time-lag effects between the aerodynamic forces and the motion. Preventive measures and cures usually involve either increased stiffness or decreased coupling by adjustments in mass distribution, or a combination of both. The most important stiffness parameter affected by flutter considerations is wing torsional stiffness. It is not uncommon for the flutter condition to control the selection of wing skin thickness. Of course, wing structural design is controlled by either a strength or a stiffness criterion. For example, if the torsion carrying structure of a wing is designed by a stiffness requirement, the wing would probably consist of a structure which carries its normal stresses in the wing skin with a minimum of stringers and flanges. This type of wing structure would require several spanwise webs in order to stabilize the heavily loaded cover skin. For a wing designed initially by strength considerations to carry a given load factor, it is obvious that a higher torsional stiffness and hence a higher flutter speed will result if the ratio of stiffener area to skin area is reduced to a minimum. In addition, the use of higher strength alloys, which have no corresponding increase in modulus of elasticity, tends to make flutter more critical for wings designed for strength only.
Heavy mass items in the wing are often located by considerations of optimum conditions for flutter prevention. For example, a given mass distribution may require higher wing stiffness and hence higher wing structural weight to prevent flutter than some other mass distribution. For this reason, analytical and model studies are often made in the design stages in order to determine the optimum mass distribution for flutter prevention.
Wing planform and aspect ratio also have significant effects on flutter characteristics. Decreases in wing aspect ratio and increases in sweep tend to raise flutter speeds, whereas increases in aspect ratio and decreases in sweep, including sweep forward, reduce flutter speeds.
Flutter considerations may affect control surface design in the determination of aerodynamic and mass balance, hinge location, and the degree of irreversibility required in the actuating system.
Buffeting. A serious buffeting phenomenon confronting designers is encountered by fighter aircraft during pull-ups to CLmax at high speed. This often results in rugged transient vibrations in the tail due to aerodynamic impulses from the wing wake. The principal problems are those of reducing the severity of these vibrations, and the provision of adequate strength. Designing for strength is very difficult. The problem of predicting dynamic stresses due to a given buffeting condition is still unsolved analytically. The principal obstacle has been a lack of knowledge of the properties of the wake behind a stalled wing. Designers have alleviated their buffeting problems up to the present time largely by proper positioning of the tail assembly and by clean aerodynamic design.
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Excerpted from AEROELASTICITY by Raymond L. Bisplinghoff, Holt Ashley, Robert L. Halfman. Copyright © 1983 Raymond L. Bisplinghoff, Holt Ashley and Robert L. Halfman. Excerpted by permission of Dover Publications, Inc..
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