Modal shapes in magnitudes

To use modal shapes you must do the following:

• Select one or more observer variables.

• Have at least one free state.

• Do a linear analysis at some time in the simulation. Strictly speaking this should be at an equilibrium point but experience indicates that we can do useful analysis at non-equilibrium points particularly if our objective is to speed up the simulation.

You initiate modal shapes analysis from the Modal Shapes Analysis dialog box which appears by selecting an eigenvalue and clicking on Modal shapes (as in figure Figure 71). Here is a very simple system involving only linear one-dimensional motion (using default values): TwoMassModeSpring.ame. You can get this model from the demo area in the Tutorials folder.

Figure 71: Simple mechanical system

Set the two mass velocities as observer variables. Set various linearization times and start a run. The eigenvalues are as follows:

Figure 72: Eigenvalues of a mechanical system

Remember that eigenvalues represent modes of the system and modal shape analysis determines how each observer responds to the selected mode. Selecting the first eigenvalue and clicking on Modal shapes gives the following dialog box:

Figure 73: Modal shapes for the first eigenvalue

This indicates as expected that the two velocities respond equally to this frequency.

We can see this more clearly if we plot the results, select the two observers (using the Ctrl or Shift keys) and click on the Plot button.

Figure 74: Modal shape plot of the 1st oscillating mode

• mass 1 = 100 kg

• mass 2 = 200 kg

To demonstrate another interesting aspect, we can modify the values of the two masses as follows and start a run:

• mass 1 = 50 kg

• mass 2 = 200 kg

If you select the first frequency, the resulting Modal Shapes Analysis is:

Figure 75: Modal shape plot of the first oscillating mode

If you select the last frequency, the resulting Modal Shapes Analysis is:

Figure 76: New Modal shapes for first eigenvalue

Note

Here we can see that the values in the Magnitude factor column are both 1. For an example where the magnitudes must be adjusted, refer to the demo Reducer.ame which can be found in the Infrastructure > Analysis Tools > LinearAnalysis > EigenvaluesModalshapes demo folder.

With the higher frequency (see figure Figure 77), we see that the smaller mass is affected more, and is out of phase with the larger mass. When we look at the lower frequency, we see that the larger mass is affected more, and this time the two are in phase. We can see this more clearly if we plot the results. Select the two observers using the Ctrl or Shift keys, and click on the Plot button:

Figure 77: Higher frequency Modal Shape plot

Figure 78: Lower frequency Modal Shape plot

What we have done corresponds to a magnitude modal shape analysis. It is very useful, but if the masses were very different, the analysis might be confusing. Let’s change m1 to 1 gram (1.0e-3 kg) and leave m2 at 200 kg. Now we start a new run and repeat the analysis, looking at the lower frequency. As we can see, there is very little difference from the previous plot with the velocities set as observer variables:

Figure 79: Lower frequency analysis