﻿ Modal analysis: Data and results

# Modal analysis: Data and results

The modal analysis form, opened via the results menu, allows you to calculate and view the undamped natural modes of the whole system or of a single line.

Modal analysis is only available when the static position of the model has been calculated, since it reports modes of oscillation about that static mean position. For full details of the calculation, and a discussion of its limitations, see the modal analysis theory topic.

## Performing modal analysis

To carry out a modal analysis you need to define

• what to analyse: the whole system or a selected single line, and, for single line analysis, whether or not to include coupled objects
• which modes to calculate: All modes or a specified range (for large systems it is much quicker to calculate only a small number of modes)
• whether or not to calculate mode shapes. If you choose not to, the calculation is quicker but only the natural periods are calculated, not the mode shapes or mode loads.

### Degrees of freedom

The degrees of freedom analysed depend upon the first of the above choices.

Whole system analysis covers all free degrees of freedom in the model whose values are calculated by the static analysis.

Single line analysis not including coupled objects analyses the free degrees of freedom of that line.

Single line analysis including coupled objects analyses the free degrees of freedom of that line, together with all other free degrees of freedom in the model that are coupled to that line's degrees of freedom. Coupling is determined by examining the mass and stiffness matrices of the system.

Finally, for either type of single line analysis, the degrees of freedom in the analysis are augmented by any free degrees of freedom of child objects of the originally identified degrees of freedom.

 Note: The ability to include coupled objects in a single line analysis is especially useful when creating mode shapes files for use by external VIV programs. For some systems the mode shapes are unrealistic if the analysed line is considered in isolation; including coupled objects in the modal analysis may be necessary to obtain more realistic mode shapes.

### Mode shape and mode type

For a given mode, the mode shape consists of the collective offsets about the mean position (the normalised mode offset vector), when that mode is excited, of the free degrees of freedom in the modal analysis.

For a single-line modal analysis, if that line is subject to a non-zero current (relative to any starting velocity specified for the static analysis), then the offset distribution and a broad classification of the mode type is reported in the modes table.

This classification is based upon the mode offset distribution, the relative proportions of inline, transverse and axial contributions to the translational mode shape, and the size of any rotational offsets in the mode shape. The mode type provides a measure of the modal shape components, and is used to set the initial default selection of which modes should be exported to the SHEAR7 modes file if that facility is used.

• Offset distribution provides a measure of how inline, transverse, axial and (if torsion is included for that line) how rotational the mode is.
• Mode type classifies each mode according to the offset distribution. Transverse means that the transverse component is more than 90% of the total, mostly transverse means that it is between 50% and 90%, and similarly for inline, mostly inline, axial, mostly axial, rotational and mostly rotational. Mixed means that none of the components are more than 50% of the total.
 Note: The offset distribution and mode type are only available for single line analyses where there is relative flow normal to the line. So if there is no current defined, or if the line is entirely above the water, then this information will not be available.

## Modes view

If mode shapes have been calculated then the modes view page displays a wire frame 3D view of the system showing one selected mode shape superimposed on the static position of the system. The current direction is also shown on the view, and you can control the view angle, zoom etc., as on any 3D view. You may need to zoom out in order to see the system, and you may need to adjust the view angle to suit the mode that you are viewing. For example an out of plane mode for a catenary is best viewed by looking along the plane of the catenary.

Use the mode drop-down list to choose which mode is shown on the view. When that control has the focus (click it to give it the focus), you can use the up/down arrow keys to quickly change the selected mode shape.

The drawing exaggeration value allows you to vary the amplitude of the drawn mode shape. The draw node axes and animate mode shape options give you further control over the mode shape drawing.

If the mode shape is being animated then you may choose the animation period. Mode period gives the animation a cycle period equal to the selected mode period. However, for modes with either very long or very short periods, this can make visualisation of the mode shape quite difficult. The alternative, fixed, animates the mode with a 5s cycle period regardless of the mode's natural period.

For single line analyses, provided that there is relative flow normal to the line, the mode type and offset distribution for the selected mode are also reported.

## Modes table

The modes table displays a spreadsheet giving numerical details of the calculated modes. The modes are numbered in order of increasing frequency. If the mode shapes have not been calculated then the table only gives the periods and frequencies of the modes. Otherwise it also gives the mode shapes, reported with respect to your choice of global axes directions or local axes directions.

For single line analyses, provided that there is relative flow normal to the line, the mode type and offset distribution for the selected mode are also included in the table.

If the mode shapes are reported with respect to the global axes, then the associated modal mass and stiffness are also reported.

 Note: The dimensions used to report the modal mass and stiffness might seem counterintuitive because we have chosen to report the translational modal offsets as lengths. The modal mass and stiffness dimensions are then consistent with this choice. However, one is always free to scale the mode shape by any constant factor – even a dimensional one – because any linear scaling of the mode shape is still a valid mode shape. This, in turn, determines the dimensions of the modal mass and stiffness. For example, if you nominated that the translational modal offsets were dimensionless, and any rotational modal offsets were dimensioned as 1/length, then the modal mass would have dimensions of mass.

## Modes graph

The modes graph page displays the mode shapes as range graphs of normalised mode offset against arc length along the lines. Separate curves are plotted for $X$, $Y$ and $Z$, with respect to either global or local axes. To help you visualise the physical system being modelled, you can choose to have the arc length axis horizontal or vertical, and you can reverse either (or both) of the axes.

For a whole system modal analysis with multiple lines included, the curves for each of the lines follow one another across (or up or down, but let's just illustrate the case of arc length axis horizontal and not inverted) the graph. In this situation the arc length axis on the graph covers values from zero up to the sum of the lengths of all the lines in the system, and the curves for the first line occupy the left-hand side of the graph, followed by the mode shape curves for the other lines (in the same order as when viewed by types in the model browser), with each line's arc length range added on to the end of the cumulative total length of the previous lines. For example consider a system that has three lines, each 50 m long. Then the first line's mode shapes are plotted over arc length range 0 m to 50 m, followed by the second line's mode shapes plotted from 50 m to 100 m, and finally the third line's over arc length range 100 m to 150 m.

The mode loads are the amplitudes of the dynamic variations in shear force, tension, bend moment and torque, per unit mode amplitude, in the lines included in the modal analysis, which would arise if the objects included in the analysis oscillated in a given single mode. The mode loads are only available if you calculate mode shapes.

Both the mode shape and the mode loads represent dynamic oscillations about the mean static state condition, if the model or single line were to oscillate in that mode shape at that mode frequency. The mode loads therefore correspond to the mode shape given in the modes table, and their magnitudes are affected by the normalisation of the mode shape; they therefore correspond to the changes which would be obtained in line loads if the normalised mode shape was applied as an offset about the mean position, ignoring all nonlinear effects and (since it is an undamped modal analysis) fluid damping effects.

The mode loads are reported at the line ends (as components in the line end node axes directions) and at each mid-segment point (as components in the line axes directions at that mid-segment point).

For a whole system modal analysis, the mode loads for each line in the model are all presented together in a single table, one after another. The lines are ordered in the order in which they appear when viewed by types in the model browser.

You may select a single mode, from the drop-down list of those calculated, to populate the table for that mode or, alternatively, select all calculated modes from the list to produce a single table containing the mode loads for all available modes.

 Note: The modal analysis assumes that the system is linear. Most systems are not, however, and the OrcaFlex simulation includes (usually significant) nonlinear effects. Load variations obtained from an OrcaFlex simulation in which the line positions are constrained to follow the mode shape will therefore not, in general, match the corresponding mode loads exactly.

The loads graph page displays the mode loads as range graphs against arc length along the lines. Separate graphs are given for shear force, tension, bend moment and torque. The shear force and bend moment graphs include separate curves for the line $x$- and $y$-direction components of the load. The tension and torque graphs present only one curve, giving the tension or torque in the line axial direction.

For a whole system modal analysis including multiple lines, the curves for each of the lines follow one another across the graph, in the same manner as the modes graph.

## VIV

The VIV page provides a table of information that is useful for VIV analysis. This is only available for single line modal analyses, and only if the mode shapes are calculated and the line is at least partially under the water and subject to a non-zero relative current.

The table reports modes in order of increasing mode number. Each row of the table refers to a single mode and contains the following information:

• mode number
• mode period and frequency
• mode type and offset distribution
• Export to modes file: whether or not the mode will be included in the modes file produced by the export SHEAR7 modes file and export VIVA modes files buttons. The initial default selection is to export the transverse and mostly transverse modes.

You can use the filter modes boxes to choose which types of modes are included in the table. For example, you might wish to view only the transverse modes if you are studying transverse VIV.