Besch and Liu 



All struts exhibit a fundamental (lowest frequency) vibration 

 mode shape resembling first bending. Struts show a marked differ- 

 ence in their second modes, however, permitting struts to be divided 

 into two groups. The second mode of any strut will consist of a second 

 bending mode coupled with a first torsion mode, with one usually pre- 

 dominating. Predominance is determined by the relative linear dis- 

 placements produced by bending and torsion, which provide an indicat- 

 ion of nodal line characteristics. If the second vibration mode is pre- 

 dominantly second bending, the strut is a bending -type strut. If the 

 second vibration mode is predominantly first torsion, the strut is a 

 torsion-type strut. 



Struts having little or no tip weighting are usually bending -type 

 struts. Struts having relatively heavy pods are usually torsion-type 

 struts. A transition region exists in which the second vibration mode 

 of a strut is equally due to a second bending mode shape and a first 

 torsion mode shape, with neither predominating. Struts in this tranr- 

 sition region have moderately weighted pods or medium to large foils. 

 The effect of foils in coupling second bending and first torsion is very 

 pronounced when the foils are submerged due to the large rotary iner- 

 tia effect at the tip of the strut. When such strong coupling occurs, it 

 is impossible to classify the strut as bending-type or torsion-type. 



In most cases the third vibration modes of bending-type struts 

 are first torsion, while torsion-type struts have a third vibration 

 mode resembling second bending. This observation indicates that a 

 change in strut type usually involves a reversal in the order of the 

 second and third mode shapes. 



Most struts have the same mode order in air and in water. If 

 there is a difference, the mode order in water should be used for 

 classifying a strut. Either measurement or calculation can be used 

 to determine the required mode shapes. 



II. 2. Flutter Mode Shapes 



The flutter mode shapes of bending-type struts are radically 

 different from those of torsion-type struts. Bending-type struts under- 

 go flutter in a predominantly first bending mode shape, while torsion- 

 type struts undergo flutter in a predominantly first torsion mode 

 shape. In accordance with the flutter mode shapes, flutter of bending- 

 type hydrofoils will be referred to as bending flutter, and flutter of 

 torsion-type hydrofoils will be referred to as torsional flutter. 



The two types of flutter mode shapes have not been quantita- 

 tively measured, but were discovered because the very striking dif- 



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