8.2 Performing Modal Analysis

The algorithm used by DIRAC is based on the Principal Response Function (PRF). The PRF helps to reduce the effect of noise and to fit modes on a large number of FRFs quickly. The LSCF algorithm (Guillaume et al., 2003, link) is used to find the poles of the system. Doing this over multiple iterations results in the stabilization diagram, from which the stable poles are selected. These are then used to find the mode shapes for each mode of the system.

The modes of your structure are calculated using the Principal Response Function (PRF) algorithm.

Calculating modes

To calculate the modes in DIRAC, you have to:

1. Select the correct preset.
2. Choose the correct modal fit settings.
3. Compute.

Editing modes

After calculating the modes, you can change their frequency, damping and name, according to your liking.

To edit a mode, complete the next steps:

1. Double-click on the field you want to edit.
2. Type the desired value/name and press Enter.

Deselecting modes for the synthesized FRF

You can decide whether a mode should be used or not for the calculation of the synthesized FRF. By default, all calculated modes are used.

To deactivate a mode, you have to:

1. Un-tick the Active checkbox next to the selected mode.

Choose modal settings

To calculate the modes, you have to select the preset to use and define the desired settings in the Modal Fit Settings card. The settings are the following:

• Minimum and maximum frequencies: minimum and maximum frequencies at which the algorithm will look for poles.
• PRF tolerance: relative magnitude of singular values below which the associated PRFs are excluded.
• Min and max # of poles: minimum and maximum number of poles the algorithm will try to fit.
• Stability threshold: threshold used to determine the stability of poles through the iterations.
• Frequency and damping tolerances: relative differences in frequency and damping permitted between poles from different iterations to be considered stable.
• Residue fit method: the residues can be computed using linear least squares or by minimizing a logarithmic cost. The linear method is faster, but the logarithmic can result in a better fit when the FRF magnitude is small, for instance at an anti-resonance.
• Mode type: residues and residuals can be computed on the basis of real-valued (normal) modes or complex-valued modes.
• Drive point strategy: possibility to apply a drive point strategy to obtain normalized mode shapes and residues that contain all input and output DoFs.
• Lower and higher residuals: number of singular vectors used to describe the lower and higher residual modes.

Stabilization

The stability diagram shows how the algorithm determines the true number of poles in the system. Poles are compared according to two metrics: their eigenfrequency and damping value. The stability of a pole is determined by comparing each pole to the poles from different iterations. Poles can be marked as:

• Stable: poles that are stable both in frequency and damping.
• Stable in Frequency: poles that are stable in frequency but not in damping.
• Unstable: poles that are not stable in frequency or in damping.
• Selected: poles selected by the algorithm.
• Inactive: poles deactivated by the user.

Visualizing the stability diagram

In the stability diagram, you can visualize the poles and the iterations.

To visualize the stability diagram in the Stabilization card, you have to:

1. Toggle the Stabilization mode.

Manually selecting and deselecting poles

You can manually select and deselect poles in the stability diagram.

To select a pole, you have to:

1. Click on the pole in the stability diagram.