HELP - mode shape equations

[pipelinermike]

I am desparately trying to analyze a free spanning pipeline that may be subjected to vortex induced vibrations. DNV RP F105 requires calculation of the effective mass. This requires knowledge of the "assumed mode shape satisfying the boundary conditions". We are working out of a temporary office and I don't have any reference materials here. Can anyone help? The pipe span is about 143 ft long, the pipe is 8.625" OD x 0.500" WT.

 

[GregLocock]

Is it effectively a cable under tension? or a beam in bending? I hope it is the former.

if the ends are stationary then you just have the modes of a plucked string,

i=1,2,3...

f=i/(2*L)*(T0/m)^.5

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Denial]

Or, extending Greg's formula (for the i=1 case) to allow for the situation where it is partly a cable under tension and partly a simply supported beam:

f = 1/(2L) * [(T+[π][sup]2[/sup]EI/L[sup]2[/sup])/m][sup][½][/sup]

 

[Rob45]

And the vortex shedding frequency would be given by:
f=SVo/D
where Vo is the airflow velocity in fps, D is pipe diameter in feet, S is the Strovhal Number, approximately .2 for a reasonably smooth surface.