STRUCTURAL FLUID 



DAMPING EXCITATION AND DAMPING 



+ 2 ^j y = fj. -^^ (Q sin <j> — Cr sin <^i). 



(E.1.4b) 



A decomposition of the system such as this allows the fluid and structural force contributions to be 

 separated completely. The various fluid forces then can be measured individually or derived from the 

 total measured force. 



Using a different approach Sarpkaya (E4, E5) has expressed the measured total fluid force on a 

 resonantly vibrating cylinder as the sum of two components 



F 



Ct 



= C„/, sin ar — Q/, cos a?. 



(E.1.5) 



'TOTAL ,/^^ y2j^ 



where C^f, is an "inertia" force and Q/, is a "drag" force. These components are related to Sarpkaya's 

 "generalized force coefficients" Q/ and C„i (E5), see Figs. 2.3 to 2.6, by 



2 



and 



^'' ~ 37 ^'" 



TT^C 



1 ^ 



^""-D 



Iv 



D 



2ttV V 



where V. is the "reduced velocity" Fj. = =- or —r-r-. 



oj„D f„D 



(E.1.6a) 



(E.1.6b) 



In this case the equation of motion for the cylinder becomes 



y + 2C,s y + y = IJ' —^ iC„i, sin ar — Cjf, cos ar) . (E.1.7) 



The force component Q/, is negative when energy is transferred to the cylinder, as is the case for 

 resonant, vortex-excited oscillations. If a steady-state response is assumed, then 



y = y sin (ar — e) , 

 where e is an undefined phase angle. This form of the equation of motion separates into 



sin ot:— a^ Y cos e -I- 2 ^j K sin e -I- Y cos e —jx 



C/, = 



(E.l.Sa) 



163 



