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

By Sergey D. Algazin, Igor A. Kijko

Back-action of wind onto wings reasons vibrations, endangering the entire constitution. by way of cautious offerings of geometry, fabrics and damping, damaging results on wind engines, planes, generators and automobiles may be kept away from.

This e-book provides an outline of aerodynamics and mechanics in the back of those difficulties and describes a number mechanical results. Numerical and analytical the way to research and examine them are constructed and supplemented through Fortran code

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Aeroelastic vibrations and stability of plates and shells

Back-action of wind onto wings factors vibrations, endangering the full constitution. by way of cautious offerings of geometry, fabrics and damping, dangerous results on wind engines, planes, generators and vehicles could be kept away from. This booklet supplies an summary of aerodynamics and mechanics at the back of those difficulties and describes various mechanical results.

Additional info for Aeroelastic vibrations and stability of plates and shells

Example text

In this section we consider the computational experiments in which the dependence of the critical flutter velocity on the plate thickness is studied. The following approach is taken. 001. Then the critical velocities obtained are fitted by an analytical formula v = v(h). The calculations were carried out for the same parameters of the plate as were used in the previous section. 1476(1). Here the number in parentheses denotes the number of the eigenvalue by which stability was determined. Interestingly, for a thin plate the stability is determined by the eigenvalue other than the first one (compare with calculations for problem 4).

Therefore, D(α 2 + β 2 )2 v2 = ≡ v02 . e. that the corresponding eigenvalue is located beyond the stability parabola. Therefore, the perturbed motion is unstable for any velocity v ≠ 0, which means that the critical flutter velocity is equal to zero. 2. Infinitely long strip. Consider an elastic strip occupying on anxy-plane a domain Γ : {|x| < ∞, 0 ≤ y ≤ l}; consider also the case of longitudinal flow V = {vx , 0}; the strip sides are assumed to be simply supported. The system of equations takes the (nondimensional) form y = 0, ????φ = λφ , ghω 2 + ????ω + λ = 0 ????x ????2 φ ????2 φ = 0; y = 1, φ = 0, = 0.

The Bubnov–Galerkin method gives satisfactory estimates for the values of vcr if the number of terms in the formula for φ is not less than N ∼ 4a/b (two “halfwaves” along the smaller side and 2a/b “half-waves” along the larger side). 2. Upon the determination of the dependence λ = λ (v, θ ) and, consequently, the vibration modes, the Bubnov–Galerkin method gives an error that increases with the increase in the flow velocity and leads to the deterioration of qualitative results. These conclusions are not final; investigation for plates of different geometries and different combinations of boundary conditions is required.

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