Page 177 - Pipelines and Risers

150 Chapter IO

The accuracy of the solution increases when m increases. Unfortunately the number of
simultaneous equations that are to be solved increases by two times m. The value of m is
therefore determined from test runs.

- Stress calculation

When the beam motion as a function of time and position along the x-axis is obtained, the
stress range is given by:

AS = E- d*Z(X,f)
dX2

If the beam has elementary supports (pin-pin, fix-fix, pin-fix), the maximum bending moment
will occur at the beam middle or ends. If the beam is supported by springs the maximum
moment does not necessarily occur at these positions.

10.3.4 Frequency Domain Solution
- The generalized ecluation of motion

The frequency domain model presented herein is based on a linearised version of the Morison
equation. In order to linearise the non-linear drag term it is assumed that u))*, the following
at
linearisation is then proposed (Verley (1992)):

A value for the absolute velocity being used in a statistical sense is averaged over the entire
sea-state,
[VI =tffu
,
RMS(U(f))
=
ffu
then
[ a,:] U-- =KLU-2KL-
d.?
U--
at

The equation of motion can then be re-expressed as:
K,K,c/+K, -
a
'
(M +M,)~+(C+2R,R,}~+Nd--Td'Z= au
at' at dxb ax= at
where:
1
KO = ypDC,