Calculations Showing the Influence of Aerodynamic Damping on Binary Wing Flutter
The influence of damping is examined by comparing the flutter critical speeds and frequencies obtained using the complete equations of motion and those obtained when all the damping terms are omitted. The calculations are made for binary flexure-torsion flutter of a wing in incompressible flow and the comparisons extend over ranges of values of the principal parameters. When the ratio of air density to wing density is high, the damping terms are found to raise the flutter speed by a large amount. But when the ratio of air density to wing density is low, a condition often occurring in practice, it appears that, over a wide range of parameter variation, the flutter speed obtained in the absence of damping is reasonably close to that obtained from the complete equations. Further experience is obviously needed before any general conclusions can be re~¢hed, but the present results offer some hope of reducing either the extent of, or the accuracy needed in, the aerodynamic information used for wing flutter calculations. It is pointed out that with constant aerodynamic coefficients the flutter speed for an undamped system is independent of the wing density.
Approximate Formulae for Flutter Prediction
On the basis of certain simplifying assumptions a general equation can be developed that provides an estimate of the flutter speed of a binary system. The equation includes aerodynamic stiffness derivatives, and in the absence of reliable derivatives for oscillatory motion it is suggested that derivatives derived from steady flow measurements can be used. The equation is applied to derive specific formulae for main surface flexure‐torsion flutter. The effects of compressibility on the derivatives for this particular case is deduced, and the derivatives are then used to estimate certain general effects of compressibility on flutter. It appears that many of the generally accepted features of flutter in the transonic region can be established by this approach, but the application of the formula is limited by the lack of reliable data for aerodynamic stiffness derivatives. A concentrated effort to establish these derivative values is likely to be more rewarding in the long run than flutter tests on innumerable models to establish overall flutter trends of limited application.
On the Concept of Elastic Stability
Publisher Summary This chapter focuses on the concept of elastic stability. The examples show that the correct approach to the solution of a stability problem depends on the nature of the problem. Unless a problem is purely nongyroscopic, the easy static approaches usually fail and even the kinetic approach frequently is questionable if physical imperfections are neglected. The instances treated are concerned with columns and shafts belong to a relatively narrow field of applications. As most of the stability problems solved in these instances have so far been concerned with comparatively simple load systems of purely nongyroscopic type, the usual static approach has not led to serious troubles. An example that has been studied but abandoned because the static approaches did not supply a satisfactory solution is the problem of a column loaded tangentially over its whole length. Another instance, where the results obtained by the static approach are questionable in certain cases, as the load is not conservative, is the problem of a cylindrical shell subjected to torsion.