Beach and Liu 



accurate, when three-dimensional loading modifications are included. 

 Despite the theoretically improved loading expression, the flutter 

 speed predicted for the new mode is a highly nonconservative 147 

 knots. Mode 3 is unstable over the entire speed range, except at low 

 speeds where inclusion of structural damping would produce a positive 

 damping ratio. Both unstable modes have a first bending mode shape 

 in the vicinity of the experimental flutter speed. The frequency of 

 mode 3 now decreases rapidly with speed, but nevertheless does not 

 decrease sufficiently to agree with experiment at 81 knots . On the 

 other hand, the frequency of the new mode shows fairly good agree- 

 ment with experiment at 81 knots . In this case and in general, 

 frequencies of hydroelastic modes are predicted more accurately than 

 damping characteristics, and are less sensitive to variation in hydro- 

 dynamic loading. It is concluded that flutter occurred experimentally 

 in the new mode, and that mode 3 is not unstable below 81 knots . 



Each of the loading modification parameters was varied inde- 

 pendently to determine its effect on predicted flutter instabilities. 

 Equal loading was used at all spanwise positions. The resulting flutter 

 speeds for the new mode and mode 3 are shown in Figure 10. Mode 3 

 becomes unstable when any of the three modification parameters is 

 changed sufficiently from two-dimensional values. A three-dimensional 

 value of lift slope produces greater instability in mode 3 than three- 

 dimensional values of the other parameters. Interactions among para- 

 meters and variations in strut configuration also affect the stability of 

 mode 3. The behavior of hydroelastic modes 1 and 2 was not signifi- 

 cantly affected by the variation of applied loading. 



The nature of the oscillations experienced by Model 2 at flutter 

 was further investigated in order to determine whether the oscillations 

 consisted of standing or travelling waves. Calculations by Dugundji, 

 et al.Q8j and Prasad, et al. [J9jhad indicated a bending flutter con- 

 dition occurring in the form of travelling waves for low mass ratio 

 wings. The present complex eigenvalue calculation restricted oscil- 

 lations to a series of standing waves in which nodal lines remained 

 stationary and all displacements in each mode maintained their rela- 

 tive distributions at all times. Travelling waves are characterized 

 by nodal lines which traverse the entire surface of the strut during a 

 cycle of oscillation. 



A direct solution to the equations of motion was attempted, 

 using a finite difference technique in the time domain |_20 J . The method 

 of solution yields a time history of the transient motion following an 

 initial excitation of finite duration. Flutter inception occurs when os- 

 cillations change from decreasing to increasing amplitude. Neutral 

 stability should occur at the same speed using either method of solution. 



356 



