Engineering Solutions for Flutter
It was noted in the preceding section that the presumption of simple harmonic motion in classical flutter analysis has both advantages and disadvantages. The prime argument for specification of simple harmonic time dependency is, of course, its correspondence to the stability boundary. Identification of the flight conditions along this boundary requires the execution of a tedious, iterative process such as the one outlined in Section 5.3. This type of solution can be attributed to Theodorsen (1934), who presented the first comprehensive flutter analysis with his development of the unsteady airloads on a two-dimensional wing in incompressible potential flow.
Although unsteady-aerodynamics analyses for simple harmonic motion are not simple to formulate and execute, they are far more tractable than those for oscillatory motions with varying amplitude. Since the work of Theodorsen, numerous unsteady – aerodynamic formulations have been developed for simple harmonic motion of lifting surfaces. These techniques have proven to be adequate for compressible flows in both the subsonic and supersonic regimes. They also have been developed for three-dimensional surfaces and, in some cases, with surface-to-surface interaction. This availability of relatively accurate unsteady-aerodynamic theories for simple harmonic motion was the stimulus for further development of flutter analyses beyond that of the classical flutter analysis described in Section 5.3.
There are two other important considerations of practicing engineers. The first is to obtain an understanding of the margin of stability at flight conditions in the vicinity of the flutter boundary. The second—and possibly the more important—is to obtain an understanding of the physical mechanism that causes the instability. With this information, engineers can propose design variations that may alleviate or even eliminate the instability. When a suitable unsteady-aerodynamic theory is available, the p method can address these considerations. In this section, we examine alternative ways that engineers have addressed these problems when unsteady – aerodynamic theories that assume simple harmonic motion must be used.