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By Sergey D. Algazin, Igor A. Kijko

Back-action of wind onto wings motives vibrations, endangering the full constitution. via cautious offerings of geometry, fabrics and damping, unsafe results on wind engines, planes, generators and autos will be refrained from.

This ebook offers an summary of aerodynamics and mechanics in the back of those difficulties and describes a number mechanical results. Numerical and analytical the right way to examine and examine them are built and supplemented by means of Fortran code

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8) we obtain af1/4 2 ter simple transformations: αcr = π (1 + 36C0 /7π 4 ) , C0 = (8A1 tan θ /(3√3A2 π )) . Evidently, with high accuracy αcr = π . 8), we obtain 2 = Mcr = 1 z ( 2) 2 A2 cos θ α cr 8A1 tan θ 2 4π 2 4 ???? (1 ) . 9) The solution depends on the linear functional a????20 ; we formulate the optimization problem in the following way. 10) ∗ where c is some constant. We write a functional 1 2 I(f ) = ∫ [f (y) sin2 π y + λ1 f (y) + λ2 (f ???? (y)) ] dy. 0 From its stationary condition, after normalization, we obtain the solution f (y) = cos2 π y + k1 + k2 y + k3 y2 .

7. The angle between the flow velocity vector and x-axis takes the values θ = 0, π /8, π /4, 3π /8, and π /2. Calculations were carried out on 9 × 15 and 15 × 31 grids using standard parameters (see problem 3). On both grids, close results were obtained. 4505. 2798, see problem 3) higher critical velocities are obtained. The critical velocity increases with the increase in the flow vector angle from 0 to π /2. 8. This surface is featured by a distinct “hump” elongated in the flow direction. When the flow velocity angle varies, this hump is rotating along with the flow velocity vector, but the qualitative shape of the eigen mode remains the same.

16) in the matrix form λ 1 −1 GZ (aD(r) + bD(θ ) ) φ = Gφ + R̄ + δ D D 1 δ = GZ −1 (aδ (r) + bδ (θ ) ) . 17) 1 −1 GZ (aD(r) + bD(θ ) ) . 17) the matrix A, we finally obtain φ= λ −1 A Gφ + R∗ , D R∗ = A−1 (R̄ + δ ). 18) Neglecting the discretization error R∗ , we obtain an approximate eigenvalue problem, which will be studied below. 5 Test problems In this section, we first consider relatively simple flutter problems for an infinite plate and a strip; these results are mainly of methodological value, though the new mechanical effects obtained are also observed in the general case.

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