Besoh and Liu 



foils was represented only by adding their added mass and moment of 

 inertia to the structural components. 



The effects of the pod and foils on the vibration mode shapes of 

 the submerged strut are shown in Figure 15. It was necessary to use 

 67 percent of the published values for bending and torsional stiffness 

 to achieve agreement with measured in-air frequencies. These stiff- 

 ness values were used for in -water frequency calculations and hydro - 

 elastic mode calculations as well. The strut alone is a bending -type 

 strut, and the strut with pod is a torsion-type strut. The second and 

 third modes of the strut with pod and foils each exhibit both first tor- 

 sion and second bending oscillations. Strong couplings due to the foils 

 has also produced similar frequencies for these modes. The strut- 

 foil model must be classified in the transition region. The effect of 

 the foils is particularly striking because the pod-foil combination has 

 the same mass as the pod used on the strut-pod model. 



Flutter was found experimentally to depend on the angle of at- 

 tack of the foil. Two flutter conditions were obtained : at 1 6. 6 knots 

 with an angle of attack of -4 deg , and at 18. 1 knots with an angle of 

 attack of -2 deg . Testing was halted prior to flutter at higher angles 

 of attack because divergent deflections of the strut began to occur. 

 Flutter mode shapes were described as equally large bending and tor- 

 sional deflections. The bending deflections were seen to change from 

 second bending to first bending, while the torsional deflections were 

 consistently first torsion. Structural damping was not determined ex- 

 perimentally. 



Calculated hydroelastic modes for the strut-foil model are 

 shown in Figures 16 and 17. Both two-dimensional and three-dimen- 

 sional loading yield a flutter instability in mode 2. The predicted 

 flutter speed is overconservative at approximately 6 knots in both 

 cases. An additional unstable mode is found which is different for the 

 two types of loading. Two-dimensional loading yields an instability in 

 the new mode, while three-dimensional loading yields an instability in 

 mode 3. The frequencies predicted using three-dimensional loading 

 for mode 2 at the observed flutter speeds agree well with the experi- 

 mental frequencies, while those predicted for mode 3 do not agree 

 well. On the basis of the usually reliable frequency calculation of 

 three-dimensional loading, it is concluded that flutter occurred ex- 

 perimentally in mode 2. Additional damping data for individual modes 

 is needed to confirm this conclusion. 



Predicted mode shapes do not agree with observations. Mode 2 

 consisted of both second bending and first torsion oscillations at low 



362 



