10
Continuons Systems
James F. Wilson
The dynamic models of offshore structures discussed so far hâve involved only
a finite number of independent coordinates and ordinary differential équations
of motion. In the single degree of freedom Systems, one coordinate was chosen
to describe the dominant structural vibration mode in the plane. In the multidegree of freedom Systems, examples included the rigid gravity platform with
coordinates to describe sliding and rocking motion and jacket template platforms
with coordinates to describe the motion of discrète masses lumped at node
points.
For line components such as rather long beams, pipelines, and cables, alternative continuons System models may provide more précisé and sometimes more
economical descriptions of component motion. Since a partial differential équation is used to characterize the motion of a continuous line component, solutions
are generally more involved mathematically than for a corresponding lumped
System. However, if the continuous models are chosen judiciously, closed form
expressions can be derived for the characteristic frequencies and mode shapes of
line components, which then lead to upper and lower bounds on their dynamic
responses.
Two classes of continuous line components are analyzed in this chapter. The
first component is designated as a beam for which bending stiffness and longitudinal tension are incorporated in the model. Examples include: pipelines
for diedging manganèse nodules from the sea floor as depicted in Figure 1.10a;
pipelines for océan thermal energy conversion as shown in Figure 1.10b; gathering Unes and risers; and the long structural bracing members of the varions
offshore platforms. The second structural component considered here is the cable which resists tension but whose bending stiffness is negligible. Examples
include the Steel and synthetic fiber ropes and Steel chains used to stay buoys,
floating platforms, compilant towers, and ships.
Excitation of line components cornes about in several ways. For instance,
a flexible cylinder in a steady current may undergo adverse transverse motion
and can be destroyed by the periodic shedding of vortices. This can occur if
one of the lower natural frequencies of the cylinder is coincident with that of
the vortices. There is also direct transverse excitation due to waves, and there
248
Continuons Systems
James F. Wilson
The dynamic models of offshore structures discussed so far hâve involved only
a finite number of independent coordinates and ordinary differential équations
of motion. In the single degree of freedom Systems, one coordinate was chosen
to describe the dominant structural vibration mode in the plane. In the multidegree of freedom Systems, examples included the rigid gravity platform with
coordinates to describe sliding and rocking motion and jacket template platforms
with coordinates to describe the motion of discrète masses lumped at node
points.
For line components such as rather long beams, pipelines, and cables, alternative continuons System models may provide more précisé and sometimes more
economical descriptions of component motion. Since a partial differential équation is used to characterize the motion of a continuous line component, solutions
are generally more involved mathematically than for a corresponding lumped
System. However, if the continuous models are chosen judiciously, closed form
expressions can be derived for the characteristic frequencies and mode shapes of
line components, which then lead to upper and lower bounds on their dynamic
responses.
Two classes of continuous line components are analyzed in this chapter. The
first component is designated as a beam for which bending stiffness and longitudinal tension are incorporated in the model. Examples include: pipelines
for diedging manganèse nodules from the sea floor as depicted in Figure 1.10a;
pipelines for océan thermal energy conversion as shown in Figure 1.10b; gathering Unes and risers; and the long structural bracing members of the varions
offshore platforms. The second structural component considered here is the cable which resists tension but whose bending stiffness is negligible. Examples
include the Steel and synthetic fiber ropes and Steel chains used to stay buoys,
floating platforms, compilant towers, and ships.
Excitation of line components cornes about in several ways. For instance,
a flexible cylinder in a steady current may undergo adverse transverse motion
and can be destroyed by the periodic shedding of vortices. This can occur if
one of the lower natural frequencies of the cylinder is coincident with that of
the vortices. There is also direct transverse excitation due to waves, and there
248