Linear analysis

The Linear analysis facility allows you to:

• Compute eigenvalues.

• Check the natural frequencies and damping of your model.If you have some very high natural frequencies, it could explain why your simulation is slow, in particular when the associated damping ratio is low (your system can oscillate for a long time at a very high frequency).

• Compute modal shapes in order to identify which variables are associated with the natural frequencies.

• Plot Bode diagrams.

Here is a typical example of use:

Procedure

1. Switch to Simulation mode and select the Linear analysis mode.

2. Use Ctrl+A, right-click the model and select All states observer.

3. Next, set a linearization time at or near the beginning of the simulation(Simulate > Linear analysis > LA Times).

4. In the Run Parameters dialog box, enable the Lock non-prop. states option, and start a stabilizing run.

5. Now look at the eigenvalues and sort them according to frequency.

For a fuel system, you should not normally exceed 1.0e7 Hz. If you do have frequencies higher than this, it is a good idea to try to eliminate them or damp them out.

6. Select the most extreme eigenvalue and click on the Modal shapes button.

You get a list of all the state variables which are associated with the frequency in question. The one with the greatest magnitude is the most important. Double-click it to find the corresponding component.

Other possibilities are:

• Live with the existing situation. Be reasonable. If you have very big systems and you want to keep very high frequency eigenvalues, you will probably have a slow simulation.

• Cheat on the data. Decrease the stiffness of a strong spring. Increase the volume of a small hydraulic chamber. Increase the mass/moment of inertia of a very small inertia. This is not as bad as it might appear. Often you can adjust parameters to change extreme eigenvalues without significantly altering the overall system behavior. For running a system in a real time environment this is often necessary.