Aeroelastic vibrations and stability of plates and shells by Sergey D. Algazin, Igor A. Kijko

By Sergey D. Algazin, Igor A. Kijko

Back-action of wind onto wings reasons vibrations, endangering the full constitution. through cautious offerings of geometry, fabrics and damping, unsafe results on wind engines, planes, generators and vehicles could be refrained from.

This publication offers an summary of aerodynamics and mechanics in the back of those difficulties and describes a number mechanical results. Numerical and analytical easy methods to learn and examine them are constructed and supplemented by means of Fortran code

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Represent H in the form H = (H + H ???? )/2 + (H − H ???? )/2, and include the nonsymmetric part into the discretization error. A relevant perturbation introduced into the eigenvalue of matrix H depends on how close the resolvents of matrices H and (H + H ???? )/2 are in the part of the complex plane which is of interest for the flow stability analysis. This perturbation can be theoretically evaluated by the approach presented in Chapter 22 of Part III; here, numerical evaluation was undertaken. 3961.

Therefore, the most “dangerous” perturbations, from the possible vibration instability point of view, will be perturbations of the form φ = sin π y exp(−iπ x). In the case V = {vx , vy }, an approximate solution of the problem can be obtained by different methods; for example, by reduction to the Volterra integral equation, or 22 | 5 Test problems by the Bubnov–Galerkin method. We make use of the latter, because the qualitative results (which are of primary interest to us at the moment) will be the same; the accuracy of the Bubnov–Galerkin method will be discussed later for the rectangular plate problem.

7) are satisfied. Denote by L the differential operator on the left-hand side of the boundary condition. 13), we obtain 2n ∑ L(Hi (ξ ))zi Hij fj − ∑ L (Hi (ξ )) zi ∑ Hj01 (ζi )wj1 + LRn,M (ξ ; f , R, S) = Lφ (ξ ). i,j i j1 =0 Introduce now a new notation: ???? L (Hi (ξ ))????????????ξ =eiθj2 = H̄ i,j2 , j2 = 0, 1, . . , 2n, ∑ H̄ i,j2 zi Hij fj = Rj2 i,j ∑ H̄ i,j2 zi Hj01 (ζi ) = B̄ j2 ,j1 i ???? δj2 = LRn,M (ξ ; f , R, S)????????????ξ =eiθj2 . For the vector w = (w0 , w1 , . . , w2n )T we then have a system of linear equations: 2n ∑ B̄ j2 ,j1 wj1 = Rj2 + δj2 .

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