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

ISBN-10: 0792301854

ISBN-13: 9780792301851

ISBN-10: 9401578583

ISBN-13: 9789401578585

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**Additional resources for A modern course in aeroelasticity**

**Example text**

13). 13) may be written, c aa (Y2, TJ) = = = f' ~J r dYl- [ ' ~JdYl f' ~JdYl r ~J dYl for Y2> TJ for Y2

1 Typical seetion model of an airfoil Solving, we obtain the trivial solution a e == 0, as weil as To be physically meaningful a e must be areal number; hence the right hand side of the above equation must be a positive number for the non trivial solution a e -:j:. 0 to be possible. For simplicity let us first assume that e > O. , for eqS(iJCJiJa) > K a } are non trivial solutions possible. 6. For q < qD, a e == 0 as a consequence of setting ao == CMAC == o. Clearly for e > 0, a e == 0 when q < Cfu where Ka qD == eS aCL/ila Note that two (symmetricaI) equilibrium solutions are possible for q > qD.

21) All full matrices are of order N x N and row or column matrices of order N. 23) Now let us interpret this solution. 24) IDI=O and hence, {a}-+{oo}. 24) is a polynomial in q. , qDivergence' Rather than see king the roots of the polynomial we might more simply plot IDI versus q to determine the values of dynamic pressure for which the determinant is zero. 11. From the above results we may plot qD (the lowest positive q for which IDI = 0) vs. 12. The 'exact' value of ~ is obtained as N -+ 00. Usually reasonably accurate results can be obtained for small values of N, say 10 or so.

### A modern course in aeroelasticity 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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