The earliest study of flutter seems to have been made by Lanchester,5,29 Bairstow, and Fage5,4 in 1916 in connection with the antisymmetrical (fuselage torsion-elevator torsion) flutter of a Handley Page bomber. Blasius,5,8 in 1918, made some calculations after the failure of the lower wing of the Albatross D3 biplane. But the real development of flutter analysis had to wait for the development of the nonstationary airfoil theory, the foundation of which was laid by Kutta and Joukowsky in the period 1902 to 1906. The first numerical calculation of the aerodynamic force on a harmonically oscillating flat plate in a two-dimensional flow was given twenty years later in 1922 by Birnbaum in his thesis at Gottingen. It is well known that PrandtL’s theory of bound vortices was completed in 1918, and was applied by Ackermann to compute the lift of a stationary airfoil. At the suggestion of Prandtl, Birnbaum extended Ackermann’s concept to nonstationary airfoils.13 2’13-3 He obtained numerical results up to a reduced frequency к — 0.12.
About the same time, Wagner15,30 investigated the aerodynamic forces acting on a body that moves suddenly from a stationary configuration to a constant velocity U. The sudden change of angle of attack was also treated.
The next landmark was recorded in 1929. In that year, Glauert15,23,13,14 published data on the force and moment acting on a cylindrical body due to an arbitrary motion, and aerodynamic coefficients of an oscillating wing up to к = 0.5. The calculation was based on Wagner’s method. In the same year, K ussner5,28 extended the method of Birnbaum to obtain the aerodynamic coefficients up to к = 1.5.
In 1934, Theodorsen’s exact solution of a harmonically oscillating wing with a flap was published;13,32 the range of к is then unlimited. Much additional work on aerodynamics appeared since then. It will be reviewed in Chapters 12-15.
Up to 1934, only a few cases of flutter were recorded. In those days, only airplane wings showed flutter. Aileron mass unbalance and low torsional stiffness of the wing were responsible for most of these accidents.
As early as 1929, the theory of flutter was clarified by KUssner5,28 with respect to many fundamental details—elimination of the time coordinate, substitution of the wing structure by a simple beam, iterative solution of the resulting system, of differential equations, representation of the internal damping by a phase lag in the elastic restoring force, etc. On the other hand, Duncan and Frazer measured5,21,5,25 (1928) flutter derivatives in a wind tunnel and introduced the concept of semirigidity and the methods of matrices. Simple rules of flutter prevention were derived from statistical studies both in Germany (by KUssner) and in England (by Roxbee Cox).5,12
From 1934 to 1937, the development of new types of airplane was lively, owing to the arms race of the great powers. Numerous cases of flutter occurred, not only with wings, but also with tail surfaces. The experience of accidents demonstrated the decisive effect of the mass unbalance of the control surfaces, and dynamic mass-balance requirements were generally incorporated into design specifications. In this period, intensive research on flutter was reflected by numerous publications. Many methods of analysis were discussed, and details of aerodynamic forces for control surfaces were published. The two-dimensional problem of airfoil flutter with two degrees of freedom no longer involved any difficulty. Quick solutions (for example, Kassner and Fingado’s graphical method6,15) became available. Two-dimensional problems with three degrees of
freedom—airfoils with flap—were treated satisfactorily. For a three – dimensional wing, Galerkin’s method was applied together with the “strip theory” of aerodynamics. Above all, the theory was confirmed by flutter model tests in wind tunnels.
On the engineering side, ground-vibration tests of an airplane became a routine. The stiffness criteria were generally accepted and proved satisfactory from the point of view of safety.
It was supposed before 1938 that the solution of the flutter problem could be found in flight testing. Unfortunately, in February 1938, during a carefully planned flight test, a four-engined Junkers plane Ju 90 VI crashed, killing all scientists aboard. Since this accident it has been recognized that the inherent difficulties and uncertainties of flight-flutter testing are great. It is only one of many means of investigation, and is justified only if the flutter characteristics are investigated before the test and the dangerous points to be observed are approximately known.
This picture led to an emphasis on theoretical research. With the development of multi-engined wings, twin rudders, auxiliary control surfaces, etc., the two-dimensional analysis had to concede to more complicated three-dimensional analyses. Flutter analysis became more and more a specialized field.
In the period 1937 to 1939, the most frequent cause of flutter accidents was the control-surface tabs. Investigation of the aerodynamically balanced flaps became a central problem. Wind-tunnel tests in this period indicated that, aerodynamically, the “strip theory” gives reasonable accuracy for calculating the critical speed, at least in the incompressible range and for wings of moderate aspect ratio.
In the early part of World War II, most wing flutter cases were due to insufficient aileron mass balance and most tail-surface flutter cases were due to control-surface tabs. Toward the latter part of World War II, airplane speed increased toward the transonic range, and supersonic missiles appeared. Sweptback wings and delta wings attracted the attention of research workers. Steady-state instabilities, especially the control – surface effectiveness of large airplanes, became a real problem. Buffeting, another aeroelastic phenomenon, emerged with new threats because of the shock stall. On the other hand, airplane dynamics, which so far was regarded as a distant relative to aeroelasticity, now strengthened its tie to flutter and other aeroelastic problems.
At present, transonic flight is a daily event, and supersonic flight is a reality. Aeroelastic analysis becomes an organic part of the design. Many problems still await the solution.