Page 175 - Pipelines and Risers

148 Chapter IO

Using the orthogonality properties results in:

The generalized equation of motion is therefore given by:
+
dz(Z (1))
d(Z (1))
+Cn
M, - - = i;. (10.9)
K,Z,(t)
dr dt
where:

When Equation (10.9) is solved the motion of the beam as a function of time and position
along the pipe is given by Equation (10.8).

There are two ways of determining the response time-history when using the time domain
model. One is to solve Equation (10.9) for a spectrum of representative regular waves; the
other is to generate an irregular wave velocity time history from the wave spectrum and use
this when solving Equation (10.9).

- Premration for numerical solution