SHEAR7 modes file

$\newcommand{\dcdm}{\tfrac{\ud\vec{c}}{\ud m}}$ $\newcommand{\dsdm}{\tfrac{\ud\vec{s}}{\ud m}}$

The OrcaFlex SHEAR7 interface is capable of generating SHEAR7 modes files and, depending on the coupling method, will do so automatically and effectively transparently. You may, however, wish to have the modes file itself, perhaps for further use with SHEAR7 independently of OrcaFlex, and you you can generate it as follows.

  1. use the built-in facility to export a SHEAR7 data file, if required
  2. calculate the static position of the model
  3. perform a modal analysis (via the results menu) for the line you want to analyse, including all modes that might be needed by SHEAR7 and calculating the mode shapes
  4. on the VIV page, select which modes to export to SHEAR7. The extent to which each mode is transverse (i.e. in the VIV direction), inline (in the normal drag direction), and axial, is reported; by default the (mostly) transverse modes are pre-selected for you
  5. click on the export SHEAR7 modes file button to generate a SHEAR7 modes file for those modes that are currently selected

Mode selection table

SHEAR7 can perform analysis of either transverse or inline VIV, but not both simultaneously: SHEAR7 assumes that all the modes in the modes file are in a single direction, and therefore the modes file contains one-dimensional input values. The OrcaFlex modal analysis is fully 3D, so in principle you should only export modes that are either all purely transverse or all purely inline, as appropriate to your intended SHEAR7 analysis.

In practice the natural modes do not always neatly divide into transverse, inline and axial directions, so you will sometimes have to export the modes that are nearest to being transverse or inline. OrcaFlex's mode selection table helps you decide which modes should be exported to SHEAR7.

The table includes the following columns for each calculated mode:

Values exported

The first line in the modes file contains the number of selected modes and the number of nodes in the line. Then follows a section giving the angular frequencies of the selected modes, in radians per second, and finally a section for each selected mode, giving the mode offset, mode slope and mode curvature.

Exported mode details

The OrcaFlex modal analysis gives vector values, but the one-dimensional SHEAR7 requires scalars. These are calculated as follows. Let

$\vec{v} \,=\,$the mode shape vector calculated by OrcaFlex at a given node

$\vec{v}\urm{i}, \vec{v}\urm{t}, \vec{v}\urm{a} =\,$the inline, transverse and axial component vectors, respectively, of $\vec{v}$

$\vec{v}\urm{L} =\, \vec{v}\urm{i}+\vec{v}\urm{t}$, the lateral component vector of $\vec{v}$

$m \,=\, \max |\vec{v}\urm{L}|$ over all nodes (the maximum lateral mode offset)

$\vec{s} \,=\,$ slope vector at the node, for the mean position (a vector tangent to the riser shape at each node)

$\dsdm =\,$ linear rate of change of $\vec{s}$ per unit maximum lateral mode offset, the change in slope vector at the node caused by applying the normalised mode offsets $\vec{v}/m$ to all the nodes

$\vec{c} \,=\,$ curvature vector at the node, for the mean position (a vector in the direction normal to the plane of curvature)

$\dcdm =\,$ linear rate of change of $\vec{c}$ per unit maximum lateral mode offset, the change in curvature vector at the node caused by applying the normalised mode offsets $\vec{v}/m$ to all the nodes

With these definitions, the scalar mode offset, slope and curvature values exported by OrcaFlex to the modes file for transverse modes are \begin{eqnarray*} & &\text{mode offset}\, = \, \sgn(\vec{v}\urm{t}) |\vec{v}\urm{L}| / m \\ & &\text{mode slope}\, = \, \sgn\left( \text{transverse component of } \dsdm\right) \left|\dsdm\right| \\ & &\text{mode curvature}\, = \, -\sgn\left( \text{inline component of } \dcdm\right) \left|\dcdm\right| \end{eqnarray*}

and for inline modes \begin{eqnarray*} & &\text{mode offset}\, = \, \sgn(\vec{v}\urm{i}) |\vec{v}\urm{L}| / m \\ & &\text{mode slope}\, = \, -\sgn\left( \text{inline component of } \dsdm\right) \left|\dsdm\right| \\ & &\text{mode curvature}\, = \, \sgn\left( \text{transverse component of } \dcdm\right) \left|\dcdm\right| \end{eqnarray*}

OrcaFlex judges a mode to be transverse or inline for the purposes of SHEAR7 output based only on whether the inline component of offset distribution is greater than the transverse component of offset distribution. This criterion is applied to all modes, including mixed or axial modes. Typically only transverse and mostly transverse, or inline and mostly inline, modes are exported to a modes file, so this classification for modes output will be correct in those situations.

With the mode classification in mind, the detailed reasoning behind the output formulae is as follows.

SHEAR7 assumes that the mode offset in the power-in zone is in the direction of VIV excitation. SHEAR7's power-out calculation will be valid, however, so long as the mode offset is lateral (i.e. no axial component), since fluid drag and damping occur in any lateral direction.

OrcaFlex should therefore ideally export the excitation direction component of mode offset for the power-in zone and the total lateral offset for the power-out zone. But these zones are internal to SHEAR7 and not known to OrcaFlex, so instead we output the lateral offset (suitably signed and normalised) throughout. This correctly removes the axial component, and if there is no remaining normal component perpendicular to the excitation direction then no error is introduced.

For a mode that does have some normal component perpendicular to the excitation direction, there will be an error introduced in the power-in calculation since SHEAR7 will assume that the lateral offset is in fact purely transverse or purely inline. This error is equivalent to rotating the VIV excitation to be in the lateral mode offset direction, so it should be conservative.

The mode curvature values are used in SHEAR7 to calculate the dynamic bending stresses that are induced when the mode is excited. Such stresses occur due to both transverse and inline oscillations, so it is appropriate to export the whole of the dynamic curvature, rather than just its transverse component.

Finally, the exported values are signed and normalised as specified by SHEAR7. That is, the mode offset value has maximum magnitude 1 and the mode slope and mode curvature are the changes in slope and curvature caused by applying the mode with that magnitude.

Discussion and examples

The OrcaFlex modal analysis is fully 3D, so for a general line configuration a mode can be a mixture of axial (i.e. tensile) and lateral (bending) motion. However, for many configurations, the modes broadly fall into one of three categories – tensile, in-plane bending and out-of-plane bending modes. Here, in-plane and out-of-plane refer to the vertical plane of the catenary in which the line is hanging.

This discussion considers a transverse SHEAR7 analysis, where it is simpler to choose an intended excitation direction.

Vertical riser

For an exactly straight vertical riser there is no such unique vertical plane. In this case the bending modes appear as a series of twins – pairs of modes with identical (or near-identical) amplitude and frequency in orthogonal directions.

Warning: In such cases it is important that only one of the pair is exported to SHEAR7 – the one nearest to the transverse direction.

In practice, however, current will make the riser bow out slightly in the current direction, so it is not precisely straight. This then defines a vertical plane for the static position, and the transverse direction is normal to this plane. The natural modes typically divide neatly into modes that are almost purely transverse (the out-of-plane lateral modes), inline (in-plane lateral modes) or axial (tensile modes). It is, therefore, clear which modes should be exported to SHEAR7 (the transverse or inline modes) and OrcaFlex can select these for you.

U-shape catenary, in plane current

In this case the transverse direction is the out-of-plane direction, so the transverse modes are the out-of-plane modes. These typically have virtually 100% of their power in the transverse direction, whereas the remaining modes have very little power in the transverse direction, and so it is again clear which modes to export to SHEAR7.

U-shape catenary, out of plane current

Here, the transverse direction is in-plane and normal to the line axis. It therefore varies along the line and so the transverse modes are some, but not all, of the in-plane modes.

The lowest in-plane mode is typically the in-plane fundamental swinging mode. In the parts of the line that are nearly vertical this mode is transverse, but near the bottom of the U the motion is near axial. This mode is therefore often displayed as mostly transverse. OrcaFlex removes the axial components of the modes when exporting to SHEAR7 so it is reasonable to export this mode.

Most of the remaining in-plane modes are bending modes in which the nodes oscillate laterally, with the wavelength decreasing as the frequency increases. These are predominantly in the transverse direction and so are suitable for export to SHEAR7.

However there are also some tensile in-plane modes present, in which the nodes oscillate in the axial direction, causing alternating tension and compression in the line. These tend to be in amongst the higher frequency modes, due to the typically high axial stiffness of a line.

U-shape catenary, oblique current

If the current is at 10°, say, to the plane of the catenary, then the transverse direction is at 80° to the plane. None of the modes will be purely in this direction, but the out-of-plane modes are nearest to this direction, so they are the best ones to choose.

SHEAR7 will assume that each exported mode is purely transverse, so an approximation is involved. This approximation gets worse as the angle of the current to the plane increases up to 45°. The approximation is worst for the low modes. For the higher modes the out-of-plane modes and the in-plane lateral modes tend to have quite similar frequencies and shapes, so the approximation is less of a problem.