TABLE OF CONTENTS 



Page 



ABSTRACT 1 



ADMINISTRATIVE INFORMATION • *■ 



1. INTRODUCTION 



2. REFLECTION OF WAVES FROM DISCONTINUITIES 



ON A STRING 



3. SOLUTION OF THE W-H EQUATION 13 



4. INVERSION OF THE FOURIER 



INTEGRALS ........ 20 



5. DIFFE'AENT CONDITIONS AT x - 23 



6. WAVES ON BEAMS • 



7. GENERALIZED W-H EQUATIONS: THREE-PART 32 



BOUNDARY V^LUE PROBLEMS 



8. 



.UO-DIMENSI0NAL KALF-PLANE PROBLEMS 50 



9. HALF-PLANE PROBLEMS V/ITH MEAN FLOW: 



WAKES AND KUTTA CONDITION 



10 CONSTRUCTION OF W-H SPLIT FUNCTIONS 71 



REFERENCES 



LIST OF FIGURES 



1 - Reflection and Transmission from a Simple 



Discontinuity in String Density. ...... 



2 - Complex S-Plane with Overlapping Upper and 



Lower Half-Planes R + , R_ and Strip of 



Analyticity D 7 83 



3 - Singularities Associated with Reflection 



Ftea Discontinuities on Beams 



4 - Common Choices for Location of the Branch 



Cuts for the Square Root Function >. . . . 



iii 



C2 



84 



f:5 



