TABLE OF CONTENTS 



Page 

 ABSTRACT 



1 . INTRODUCTION 1 



2. HARMONIC END FORCING OF AN UNDAMPED UNIFORM BEAM WITH SHEAR 

 WARPING 3 



3. HARMONIC END FORCING OF AN UNDAMPED UNIFORM BEAM WITHOUT 



SHEAR WARPING 10 



h . HARMONIC FORCING AT AN INTERMEDIATE POINT 20 



5. HARMONIC END FORCING OF A UNIFORM BEA!^ HAVING EXTERNAL AND 

 INTERNAL DAMPING 2? 



6. FLUTTER OF A RIGID FOIL ATTACHED TO A UNIFORM BEAM I43 



6.1 DERIVATION OF EQUATIONS OF MOTION Ii3 



6 . 2 CRITICAL FLUTTER SPEED 50 



6.3 THE SINGULAR CASE: s^S2-a^2^21^1^2 "" °' HENCE D = 55 



6 . k DISCUSSION OF DAf^ING EFFECTS 58 



6 . 5 THREE SPECIAL CASES 60 



6.5.1 DAMPING DUE TO LIFT ONLY (c = c = O) 60 



6.5.2 FOIL RIGIDLY MOUNTED ON THE BEAM 60 



6.5.3 LOW- FREQUENCY APPROXIMATION 6I 



6.6 SIMILITUDE 6k 



T . TWO SIMPLE CASES OF FLUTTER 71 



7.1 FOIL ATTACHED ELASTICALLY WITH DAMPING TO AN IMMOBILE 



BASE 72 



7.2 FOIL ELASTICALLY MOUNTED WITH DAMPING ON A FREE RIGID 



BODY Bo 



8. SUMMARY 89 



9 . REFERENCES 92 



