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A Simple Approach to the Wing Flutter Problem

Published online by Cambridge University Press:  28 July 2016

B. Lockspeiser
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Extract

Let us first consider the oscillations, in still air, of a monoplane wing whose aileron is supposed locked to the wing in such a way that it behaves as though it were an integral part of the wing structure. When the wing is displaced from its position of equilibrium and released it will, in general, vibrate both in flexure and torsion. The initial displacement may be purely flexural, but if the inertial forces called into play, over any wing section, produce a twisting moment about the centre of twist (i.e., the centre about which the wing section twists on the application of a pure torque at that section) torsional as well as flexural oscillations will be set up. Inertia, in general, robs the two kinds of oscillation of their independence, and, when they are interdependent, we may conveniently speak of “inertial couplings” between the two motions. In still air these vibrations must, of necessity, die down. One part of the wing may gain energy at the expense of another, but the store of elastic energy given to the wing by the initial displacement must grow progressively less as the wing does work against the viscous air damping and structural hysteresis forces.

Type
Research Article
Information
The Aeronautical Journal , Volume 37 , Issue 273 , September 1933 , pp. 783 - 792
Copyright
Copyright © Royal Aeronautical Society 1933

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References

1 For some cross-sections the centre of twist coincides with the flexural centre, i.e., the point at which the application of a force displaces the section flexurally without twist, and the single term “flexural centre” is often used in reference to either centre. There is no justification for a general assumption of the coincidence of the centres in the case of wing sections, and, in this paper, the nomenclature appropriate to each centre will be used.

2 In still air m must be corrected for virtual mass.

3 i.e., distorts so that straight lines in the direction of the span remain straight, flexure occurring only at the root. See “The Flutter of Aeroplane Wings,” Frazer and Duncan. R. & M. 1155, p, 19.

4 In the case of a biplane the approximate nodal chord replaces the wing root chord as an axis of reference.

5 See footnote 1.

6 For a discussion of the conditions under which aileron spring control may reduce flutter speed, see R. & M. 1155, p. 142.

7 Following Frazer and Duncan, R. & M. 1155.

8 Frazer and Duncan (R. & M. 1155, p. 16) recommend “aileron definitely underbalanced aerodynamically.” See also p. 174 for a summary of the theoretical considerations governing the position of the aileron hinge.

Wind tunnel tests indicate that, with mass balanced ailerons, the most favourable position of the hinge axis for the avoidance of flutter is that of close aerodynamic balance. See “Wind Tunnel Tests of Recommendations for Prevention of Wing Flutter,” Lockspeiser and Callen, R. & M, 1464, pp. 21-24; also Appendix, p. 31, para. 4.

9 In the case of a biplane the approximate nodal chord replaces the wing root chord as an axis of reference.