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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Extra info for A modern course in aeroelasticity
21) by a m and J~ ... ]am! = Solving for Am! , 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.
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. 1). 24) * For a more detailed mathematical discussion of the above, see Hildebrand , pp. 224-234. This problem is one of a type known as 'Sturm-Liouville Problems'. 25) where GJ (GJ)ref 'Y=-- Let as before.
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. By systematically increasing the terms in the series, the convergence of the method can be assessed. , they are 'primitive functions' for a variable property wing even though eigenfunctions for a constant property wing.