and 



cos aT. a^Y sine + 2 Cs ^ cos e — K sin e + /u, 

 when the coefficients of sin ar and cos ar are again grouped appropriately 



Upon rearranging, these equations reduce to 



C;, = 



(E.l.Sb) 



STRUCTURAL 

 INERTIA STIFFNESS 



-a^Y + Y 



STRUCTURAL 

 DAMPING 



2a Cs Y 



FLUID 

 FORCE TERMS 



[Q/, sin e - C„,, cos e] 



FLUID 

 FORCE TERMS 



[-Cm, cos e + Cm/, sin e]. 



(E.1.9a) 



(E.1.9b) 



which are of the same form as those derived above. The two approaches are in fact identical when 



Ci sin </) = — Q/, cos e , 



Q cos </) = Cdt, sin e , 



Ck sin 1 = — Q,/, sin e , 



Cr cos (f) 1 = C^i, cos e , 



EXCITATION 



FLUID INERTIA 



(E. 1.10a) 



(E. 1.1 Ob) 



FLUID REACTION (DAMPING) (E. 1 . 1 Oc) 



ADDED MASS 



(E.l.lOd) 



These relations can be used to compare recent measurements of the various force components. Blevins 

 (E6) also has proposed the use of a force decomposition such as that given by equations (E.1.4b) and 

 (E.1.9b). 



These equations are discussed further in Reference E2. 



164 



