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To the calculation of a straight high aspect-ratio wing in an incompressible flow using a nonstationary aerodynamic theory

Grishanina T.V., Rybkina N.M.

#### Abstract:

Bending-torsional vibrations of a straight high aspect-ratio wing in an incompressible flow of an ideal gas are considered. Linear aerodynamic loads (lift and torque) are determined by non-stationary and quasi-stationary theories of cross sections flat flow. The displacements and twisting angles of the wing console cross sections during bending-torsional vibrations are represented by the Ritz method as an expansion for given functions with unknown coefficients, which are considered as generalized coordinates. The equations of aeroelastic wing oscillations are composed as Lagrange equations and written in matrix form as first-order differential equations. The problem of determining eigenvalues is solved on the basis of the obtained equations. The main purpose of this work is to compare calculations for determining the dynamic stability boundary (flutter) obtained using non-stationary and quasi-stationary aerodynamic theories. Calculations are performed for a wing model with constant cross-section characteristics. As the set functions eigenmodes of bending and torsional vibrations of a cantilever beam of constant cross-section were used. Calculations are performed to determine the flutter boundary for a different number of approximating functions. The results obtained allow us to conclude that when using the quasi-stationary and refined quasi-stationary theories for determining aerodynamic loads, the values of the critical flutter velocity are obtained less than when calculating using the non-stationary theory. This makes it possible to use a simpler (from the point of view of labor intensity) quasi-stationary theory to determine flutter boundaries. It is also found that the influence of the attached air masses, which is taken into account in the non-stationary and refined quasi-stationary theories, is very small.

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