By Sergey D. Algazin, Igor A. Kijko
Back-action of wind onto wings factors vibrations, endangering the full constitution. through cautious offerings of geometry, fabrics and damping, damaging results on wind engines, planes, generators and autos may be shunned.
This publication supplies an outline of aerodynamics and mechanics at the back of those difficulties and describes a number mechanical results. Numerical and analytical the right way to learn and examine them are constructed and supplemented by means of Fortran code
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Additional info for Aeroelastic vibrations and stability of plates and shells
5 Fig. 9. 7: shape of Re φ (φ is the amplitude) for θ = 0. 5 1 1,00 0 8 0, 0,00 0 4 0, 0 0,6 0 0,4 0 0 0, 0 0,2 00 –0, 0 ,4 –0 20 –0, 40 –0, 60 –0, 0 ,8 –0 Fig. 10. 1 (clamped boundary). velocity is higher. e. the shape of the eigen mode for the ellipse is qualitatively different for angles θ = 0 to π /8. Analysis of the calculation results shows that the qualitative behavior of flutter eigen modes for an elliptic plate is different for clamped and simply supported boundary conditions. The critical flutter velocity is higher in the case of a clamped plate, as compared to a simply supported plate.
1,0 0,5 −1,0 −0,5 0,0 0,5 1,0 −0,5 −1,0 Fig. 7. 0625. problem of the first kind was considered first. 2848. 458456). 6. The second calculation was carried out for θ = π /12. 2849. 458494). 2851. Thus, the last two calculations gave practically coinciding results, which confirms the reliability of the proposed approach. Then the boundary value problem of the second kind was considered on the same domain. 2291. 371835). 7. The next calculation on this domain was carried out for simply supported edges with θ = π /12.
2) lω . Ω= a0 On the edges y = 0 and y = 1, boundary conditions of simple support φ = 0, φ ???????? = 0 are posed. 2) consists of finding the eigenvalues Ω for a given function h(y), this can be solved numerically; however, in order to solve the optimization problem as well as reveal new mechanical effects, we obtain an approximate solution by the twoterm Bubnov–Galerkin method: φ = c1 sin π y + c2 sin 2π y. 3) 4 2 2 c1 (μ1 a11 + 4π α (1 − ????)b11 + A1 M sin θ + A2 c11 Ω2 ) 3 iα 1 2 2 + c2 (μ2 a02 + 8π α (1 − ????)b02 − A1 M cos θ + A1 Ω + A2 c02 Ω2 ) = 0.
Aeroelastic vibrations and stability of plates and shells by Sergey D. Algazin, Igor A. Kijko