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By Earl H. Dowell, Howard C. Curtiss Jr. (auth.), Earl H. Dowell, Howard C. Curtiss Jr., Robert H. Scanlan, Fernando Sisto (eds.)

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25) where GJ (GJ)ref 'Y=-- Let as before. 25), multiplying by a m and J~ ... 26) The first and se co nd terms cannot be simplified further unless the eigenfunctions or 'modes' employed are eigenfunctions for the variable property wing. Hence, an is not as simply related to An as in the constant property wing example. 26) represents a system of equations for the an. 29) which is a polynomial in A2. , are infinite systems of equations (in an infinite number of unknowns). In practice, some large but finite number of equations is used to obtain an accurate approximation.

16) .. y u -py~-py t GEOMETRY .. 10 27 2 Statie aeroelasticity where a(~ts-l'A'-r,~ and Physical Interpretation of A La and A La: A La is the lift coefficient at y due to unit angle of attack at TI. A La is the lift coefficient at y due to unit rotation of control surface at TI. Physical Interpretation of aCJa(pl/U) and aCJaaR : aCJa(pl/U) is the Hft coefficient at y due to unit rolling velocity, pl/U. ) at y due to control surface rotation. Note aCMAdaaT=O by definition of the aerodynamic center.

Note that wand p are taken as positive in the same direction. , we may retrieve our beam-rod result. 3) may be thought of as polynomial (Taylor Series) expansions of deftections. " lie along an elastic axis, then C"M = caF = O. 5b) is OUT previous result. 5a). 5b) may be solved to determine h if desired. 5a) has no effect on divergence or control surface reversal, of course, and hence we were justified in neglecting it in our previous discussion. Two dimensional aerodynamic surfaees-integral representation In a similar manner (for simplicity we only include deformation dependent aerodynamic forces to illustrate the method), p(~ y) = JJ APw·(x, y;~, TJ) ~; (~, TJ) ~:d,TJ where A pw.

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