Postprocessing of Eigenmodes
Eigenmode Scaling
The eigenmodes that form the solution to eigenvalue problems, like eigenfrequency and linear buckling, have some special properties that require attention. The most important property is that an eigenmode is only defined up to an arbitrary multiplicative factor. Thus, the actual values of the modal displacements have no physical significance. In order to emphasize this, the default eigenmode plots have no color legend.
The underlying theory does, however, assume that the mode shape is an infinitesimal perturbation to the geometric shape.
If the eigenmodes have an unfortunate scaling, confusing effects can appear during postprocessing:
•
Any variable or expression used during postprocessing of an eigenvalue solution will be evaluated using the setting of the Include geometric nonlinearity check box of the eigenfrequency study step. If the values of the modal displacements are large and the study step is geometrically nonlinear, then the nonlinear parts of the strain tensor may become large. This is not consistent with the assumption of a small perturbation.
•
If the study step is geometrically linear, there can be other types if inconsistencies if the modal displacements are large. Many variables are then defined under the assumption that angles are small. As an example, the normal vectors to a shell can appear to no longer have unit length.
•
Rotational degrees of freedom scale the same way as the displacements. Computed rotations can potentially get values of more than a full revolution.
In most cases, you only have to be aware of these phenomena. But if you really need to access quantitative values (for example, as modal stresses), you need to use some caution.
In a response spectrum analysis, all result quantities are computed by scaling the modal results. In this case, it is necessary that all eigenmodes are scaled so that the assumptions of geometric linearity are fulfilled.
The scaling of eigenmodes can be controlled in the Output section in the settings for the Eigenvalue Solver node. By setting Scaling of Eigenvectors to Maximum and using a small value for the Maximum absolute value, you can force the eigenmodes to be small. All structural mechanics interfaces override the default value and set it to 10-6 times the size of the bounding box of the geometry in order to keep the eigenmode displacements small.
Deformation Plot Artifacts
The automatic scaling of a deformation plot can give strange impressions, in particular when the main deformation shape is a rotation. The geometry then seems to become wider, since the displacements are directed in the infinitesimal tangential direction rather than along a circular path.
Figure 2-41: A torsional eigenmode in a box beam.
Eigenmodes in a Deformed Structure
When you perform a prestressed eigenvalue analysis, it is possible that the prestress load case causes a significant deformation to the structure. The default eigenmode plot will still show the mode relative to the original undeformed structure. Sometimes this does not give a good enough representation of actual mode shape.
To improve the visualization, do the following:
1
Go to the settings for the 2D or 3D plot group containing the mode shape plot. Under Plot dataset edges, set Frame to Spatial. This will make the outline to be given by the deformed shape from the prestress load case.
2
In the dataset for the eigenvalue solution, set Frame to Spatial. The mode shapes are now plotted relative to the deformed shape.