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AN INTEGRAL EQUATION IN AEROELASTICITY A. V. BALAKRISHNAN FSRC / UCLA

AN INTEGRAL EQUATION IN AEROELASTICITY A. V. BALAKRISHNAN FSRC / UCLA. MONS, BELGIUM AUGUST 2006. POSSIO INTEGRAL EQUATION. SPATIAL-FOURIER TRANSFORM Balakrishnan 2002. BALAKRISHNAN-LIN 2002. TO CONVERT TO VOLTERRA EQUATION. SPECIAL CASE k = 0. AIRFOIL EQUATION SOHNGEN

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AN INTEGRAL EQUATION IN AEROELASTICITY A. V. BALAKRISHNAN FSRC / UCLA

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  1. AN INTEGRAL EQUATION IN AEROELASTICITYA. V. BALAKRISHNANFSRC / UCLA MONS, BELGIUM AUGUST 2006

  2. POSSIO INTEGRAL EQUATION

  3. SPATIAL-FOURIER TRANSFORMBalakrishnan 2002

  4. BALAKRISHNAN-LIN 2002

  5. TO CONVERT TO VOLTERRA EQUATION

  6. SPECIAL CASE k = 0 AIRFOIL EQUATION SOHNGEN SOLUTION: TRICOMI OPERATOR T

  7. g(·) ЄLp, 1 < p < 4/3 (Tricomi) FORfЄC1(-b, b) (~ Lipschitz order α, 1/2 < α ≤ 1) g(·)ЄLp(-b, b), 1 < p < 2 ANDg (x) → 0 as x → b- SOLUTION IS UNIQUE WITH THIS LAST CONDITION

  8. VOLTERRA EQUATION

  9. A(t,x) → 0 as x → b- FOR UNIQUENESS OF SOLUTION

  10. M = 0

  11. M = 0 LAPLACE TRANSFORM SOLUTION

  12. SEARS 1940 : (1+k L(k, h(k)) never vanishes & INVERSE LAPLACE TRANSFORM OF 1/(1+k L(k, h(k)) =

  13. M≠ 0LAPLACE TRANSFORM

  14. VOLTERRA

  15. Approximation at Infinity

  16. Generalization: Non-Zero Angle of Attack TRANSONIC DIP As M→1, this → ∞ for α ≠ 0 → 0 for α = 0

  17. Generalization to 2 Dimensions

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