8 , SUMMARY 



A theory has been advanced for determining the vibrations , including 

 flutter, of a hydrofoil craft. In general, the craft is treated as a 

 rigid foil flexibly attached to a uniform mass-elastic free-free beam 

 immersed in a fliiid moving with uniform velocity. The hydrodynamic force 

 and moment on the foil are represented by two-dimensional quasi-steady 

 expressions. The sequence of steps undertaken in devising this theory is 

 summarized as follows: 



1. In Introduction the background and objective of this report is 

 discussed. 



2. In Section 2 influence and inertia coefficients are derived for 

 a uniform beam that is maintained in harmonic vibration with two degrees 

 of freedom by a transverse force F and a moment or couple G acting at one 

 end of the beam and in the same principal plane of the beam. Shear 

 warping of the beam is included but rotary inertia and damping are not. 

 These coefficients are useful in treating the vibrations of a system 

 composed of a \miform beam attached at one end to another structure 

 (e.g. , a foil). 



3. In Section 3, for convenience of analysis, the formulation for 

 these coefficients is simplified by neglecting shear warping. Various 

 interesting cases are discussed, in the order of increasing frequency, for 

 the vibrations of a forced, undamped, uniform beam without shear warping 

 and rotary inertia. 



1+. In Section U, the analysis is extended to provide formulas for 

 these coefficients in the case where the external force F and the moment 



