A modern course in aeroelasticity by Earl H. Dowell, Howard C. Curtiss Jr. (auth.), Earl H.

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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Are not constants but vary with spanwise location. One way to do this is to first determine the eigenfunction expansion tor the variable property wing as done above for the constant property wing. The determination of such eigenfunctions may itself be fairly complicated, however. An alternative procedure can be employed which expands the solution for the variable property wing in terms of the eigenfunctions of the constant property wing. This is the last of the reasons previously cited for examining the eigenfunctions.

16 Fluid flow over a flexible wall. as weil as in the (uniform) beam-rod wing model, iJCL q(lc)eiJa GI (Low speed) fluid flow over a flexible wall A mathematically similar problem arises when a flexible plate is embedded in an otherwise rigid surface. 16. This is a simplified model of a physical situation which arises in nuclear reactor he at exchangers, for example. Aeronautical applications may be found in the local skin deformations on aircraft and missiles. * For a one dimensional (beam) structural representation of the wall, the equation of equilibrium is, as in our previous example, El iJ4w4 = L iJx Also, as a rough approximation, it has been shown that the aerodynamic loading may be writtent iJ2 w L-pU2 - - iJx 2 Hence using this aerodynamic model, there is a formal mathematical analogy to the previous example and the aeroelastic calculation is the same.

2 _1_ [CWP][APw. 11) For divergence IDI=O which permits the determination of qD. * For· definiteness eonsider a reetangular wing divided up into small (reetangular) finite differenee boxes. The weighting matrix [(W)) is for a given spanwise loeation and various ehordwise boxes. The elements in the matriees, {ilw/ile} and {w}, are ordered aeeording to fixed spanwise loeation and then over all ehordwise loeations. This numerieal seheme is only illustrative and not neeessarily thatwhieh one might ehoose to use in praetiee.

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