Besch and Liu 



^generalized 



This expression reduces to the mass ratio traditionally used in flutter 

 analysis when pure bending motion of uniform amplitude is assumed. 

 A similar simplification occurs when pure torsional motion is assum- 

 ed. These assumed motions provide suitable approximations to the 

 mode shapes of bending and torsional flutter. Exact flutter mode 

 shapes are of course not available. Therefore simplified expressions 

 for mass ratio were used in analyzing experimental flutter results. 



It was found that bending flutter occurs at low values of mass 

 ratio, and that torsional flutter occurs at high values of mass ratio. 

 Other than this generalization, comparisons involving mass ratio will 

 not be made between struts having different flutter modes. Such com- 

 parisons would require extensive calculations involving exact flutter 

 mode shapes, which are not available. Calculations presented later 

 indicate that bending flutter and torsional flutter involve entirely dif- 

 ferent vibration modes and do not represent different mass ratio 

 ranges of the same mode. Mass ratio will be used as a parameter for 

 comparing flutter results of similar mode. Each flutter region will be 

 discussed separately. 



Bending Flutter Region 



In the bending flutter region, generalized mass ratio can be 

 approximated by dividing total strut mass by the mass of a cylinder 

 of water circumscribing the strut. The cylinder of water should have 

 a diameter equal to the strut chord and a length equal to the submerg- 

 ed span of the strut. This cylinder of water approximates the added 

 mass of the strut for the first bending mode shape associated with 

 bending flutter. Bending mass ratio may be written symbolically as 



mL + M 



pod 



^bending 2/, * 



Trpb l+M pod 



Flutter speeds obtained from bending -type struts are plotted 

 as a function of bending mass ratio in Figure 4. Values of bending 

 mass ratio range from 0.1 to 0. 66. The flutter speeds fall into two 



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