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Analysis of influence of the incompessible flow unsteadyness on the bending-torshional aeroelastic vibrations of oc large elongation wing

Grishanina T.V., Russkikh N.M.

#### Abstract:

Forced harmonic bending-torsional vibrations of a straight large elongation wing in incompressible flow of ideal liquid (gas) is considered. Hypothesis of plane non-tear flow over thin wing the cross sections is used. The aerodynamic load acting on a thin vibrating airfoil in incompressible flow of ideal gas for small harmonic vibrations of the wing in determined exactly using unsteady linear theory and as well quasi-steady theory. A wing is considered as supported by longitudinal elements (spars, stringers) a thin-walled beam with a single-closed or multi-closed cross-section contour, which are considered to be non-deformable in their planes. Elastic displacements of the wing for bending-torsional vibrations are determined by the Ritz method in series of basic functions with unknown coefficients which are considered as generalized coordinates. The equations of the wing aeroelastic vibrations under action of transverse harmonic force with prescribed frequency are obtained as the Lagrange equations and solved in complex variables. The purpose of the work is the comparison of the calculation results for the amplitude-frequency characteristics of the forced bending-torshional vibrations of the wing obtained by use of the unsteady and quasi-steady aerodynamic theories. Calculations were made for a wing model of constant cross section, where one generalized coordinate represents the wing bending and the other – torsion. On the basis of the obtained results it was shown that for small reduced oscillation frequencies a simple (from the point of view of laboriousness of computations) quasi-steady theory makes it possible to obtain solutions with quite acceptable accuracy. The influence of the added air masses, which was taken into account in the unsteady theory, is very small.

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