Page 159 - Pipelines and Risers

132 Chapter 9

flow) directions. The in-line eigen mode values (natural frequencies) tend to be lower than the
cross-flow values due to the stiffness of the span end conditions. To limit the amount of data
processed for this exercise, the fatigue is assessed for the first ten modes.

The eigen modes for in-line and cross-flow are presented below for the 40" pipeline:

Figure 9.5 In-line Modes for the 40" Pipe.

I " " " " ' : " " I
1500 2wo 2500 3wo 3500
Chainage (m)

Figure 9.6 Cross-flow Modes for the 4W' Pipe.
The modal analyses also generate unit stress amplitude results i.e. the stress at each node for
one metre of modal deflection. This is used to find the stresses along the pipe for VIV and
wave induced vibrations. The location of the maximum bending stress over the section is thc
point where the fatigue damage is evaluated. The maximum stress is normally located on the
shoulder or at the mid-span of the dominating free span in each mode.