CALCULATE VIBRATIONAL PROPERTIES 

 OF STRUCTURE 



A. IN-SITU NATURAL FREQUENCIES i„ 



B. NORMAL MODES i/- i (S) 



C. MODAL SCALING FACTORS 



l. = lL^^ds/jLV'fds 



D. EQUIVALENT MASS mo 



CALCULATE CRITICAL CROSS FLOW 

 VELOCITY BY (FOR ITH MODE) 



Vcrit= (fnD) V,,crlt 

 Vr, crit = 3.5. Re > 106 

 v'crit= 5,Re<105 



IS THE NORMAL COMPONENT 

 OF V, THE INCIDENT VELOCITY, 

 GREATER THAN Vcri,? 



V > VcMt? 



NO 



YES 



END 



NO OSCILLATION 



CALCULATE THE REDUCED DAMPING k, 

 FOR THE ith MODE 



2m„ 6 = 



eD2 



:LOG DECREMENT OF STRUCTURAL 

 DAMPING 



IS THE REDUCED DAMPING FOR THE 

 ith MODE GREATER THAN 



k<:i > 10? 



NO 



YES 



END 



NO OSCILLATION 



CALCULATE MAXIMUM AMPLITUDE 

 DISTRIBUTION Ymax (s) IN ith MODE 



A. SG = 27r St2ksi 



B. Y_EFF, MAX =1.29/(1 +0.43 SqI^-^B 



C. Ymax(s)/D = Yeff, MAX |"'f |l/'i(s)| 



CALCULATE VIRTUAL DRAG COEFFICIENT 

 Cdv 



A. Wr(s) = [1 +2Ymax(s)/D] ( fn/fs ) 



B. Cd(s)/Cdo = 10, Wr(s) <1 



Cd(s) / Cdo = 1 .0 + 1 .1 6[w,(s) - 1 ]0-65 

 w,(s)>1 (LOCAL) 



C. CDv/CDo = n /L) S^ [Cd(s)/Cdo1 ds 



(AVERAGE) 



Figure 4.2 Flow diagram of tine steps required for the calculation of the steady drag amplification due to vortex- 

 excited oscillations; from Griffin (3). This procedure originally was developed for an analysis of the SEACON 11 

 experimental mooring (59). 



98 



