# Flutter stability polynomial calculation of a short wing

### Аuthors

Blagodyreva O. V.

Tactical Missile Corporation, 7, Lenin str., Korolev, Moscow region, 105005, Russia

e-mail: OksanaBlag@yandex.ru

### Abstract

Ritz polynomial calculation of short wing flutter stability is considered by the example of a rudder bar in subsonic flow. Eigen frequencies and forms of the first two oscillation tones are identified. A flutter stability boundary is determined in accordance with relative density of air.
Deformation of a short wing is representing as deformation of its middle surface in relation to the straight normal hypothesis. Ritz polynomial calculation allows to describe a deformation function in the form of coordinates polynomial series in direction of flow and wingspread. Mathematical powers of the polynom depend on boundary conditions of a short wing and number of freedom degrees, which is necessary for finding the predetermined number of oscillation tones. A short wing is modeled with the help of specific units allowing to increase the precision of output.
Calculation of flutter stability considered by the example of a rudder bar in subsonic flow has shown a good convergence with the experimental results. This fact confirms the highest precision of methodology. Simplicity of the mathematical model, quickness of data preparation and computation speed give the base for calculation efficiency of a flutter stability boundary.
Ritz polynomial calculation can be applied for flutter stability computation of both single aircraft unit and whole aircraft. If initial data is initialized exactly or if they can be corrected on the basis of results of ground frequency test, then it is possible to get calculation accuracy within 1-5% diapason.
Ritz polynomial calculation is realized as independent engineering software showing high accuracy of calculation. The important feature is application of the straight normal hypothesis. This approach is applicable for construction, which assumes realization of this hypothesis, only.

### Keywords:

flutter, method of polynomials, modeling of the aircraft, subsonic flow

### References

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