By AV Balakrishnan
Introduction.- Dynamics of Wing Structure.- The ventilation Model.- The regular nation HStatic L answer of the Aeroelastic Equation.- Linear Aeroelasticity thought The Possio indispensable Equation.- NonLinear Aeroelasticity thought in 2 D Aerodynamics Flutter As LCO.- Viscous stream Theory.-Optimal keep watch over conception : Flutter Suppression.- Aeroelastic Gust reaction
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Extra info for Aeroelasticity : the continuum theory
One point mass with s1 D `=2. Here d. A. A. 51) which can be expressed: F1 . ; /sin `; where F1 . 1 C cosh EI Ã! 1 C i / ` sinh : 2 . 1 C cosh ` cos `/ ` cos `/ 40 2 Dynamics of Wing Structures As we expect, the mass at the center does not affect the torsion modes. Hence we call the roots of F1 . ; / D 0 the bending modes which now depend on as well. Obviously we get back the beam modes for large mass m1 . 2. Several Point Masses. This result readily generalizes to the case of several point masses, but none at the end points.
K; 0/ and the main thing to note is that Re. k C k / < 0I ! 0 as k ! 37) The modes are damped, and the mode shapes are now coupled. The bending modeshape vector now has a nonzero torsion component proportional to S 2 , and similarly for the torsion-mode shape there is a bending component. But the extra components being small, we continue to identify them as bending or torsion modes. Calculating these would take us too far from our main interest. 5 Robust Feedback Control Theory: Stability Enhancement We have seen in Sect.
15) 2 IÂ Â Note that this is “no more” than taking Laplace transforms of the time domain equations, familiar in engineering. Thus k is of the form: Â Ã Â Ã hk 0 or 0 Âk and we can distinguish between the “bending” modes and the “torsion” modes. k then are pure bending modes. As may be expected, this is a classical result already found in Timoshenko, 1928  and in textbooks . k y/; 0 < y < `: For more see [32, 34]. 19) An obvious comment here is that the modes decrease linearly in magnitude as the span length increases.