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# Frequency Response and Transient Stress

## Frequency Response and Transient Stress

(OP)
Hi All,
Today my questions consider linear dynamics. Please see them below.

1.Could you please tell me should one expect results from Frequency Response to be somehow corresponding with results from Transient Stress analysis?
2. If yes, please let me know the relationship.
3. What output/result difference is important between Transient Stress Modal Superposition and Transient Stress Direct Integration?

Some insights of my analysis (and description of the figures attached):

As per benchmark I have calculated Natural Frequencies and used them for Frequency Response to readout max displacements for my structure for resonance frequencies. Afterwards I have performed Transient Stress Modal Superposition and plotted max Displacement vs Time which is showing that analysis in first seconds sees max displacements smaller than max values recorded at Frequency Response, second observation is that Modal Superposition is converging for 1.077 mm, while from Static Linear max displacement was 0.25 mm. Next analysis performed was Transient Stress Direct Integration, where 1st observation was max displacements are smaller than max values recorded at Frequency Response, second observation is that Direct Integration is converging for 0.25 mm which corresponds well to the Static Linear. Should I expect to see max displacement values as per Frequency Response, in the Transient Stress analysis?

### RE: Frequency Response and Transient Stress

I'd double check your setup again. The values after the vibration is damped beings vastly different tells me that something isn't setup equivalently. If you had different values in the vibrations themselves it could be different values/methods of damping but those two values being different are cause for concern in setup.

The frequency response graph simply shows the relative contributions of each natural frequency. So in your 68Hz contributes the most significantly to the response when it's excited by the load.

### RE: Frequency Response and Transient Stress

Hi
I don't think I understand your analysis.

For the Frequency Response (harmonic?) I assume that you apply a load and then run the analysis while "sweeping" trough frequencies between 0.0 Hz and approx 140 Hz. 0.0 Hz and static can be seen as equivalent And then you seem to have a resonance effect at approx 68 Hz and another (smaller) at 102 Hz.

Then there is two transient options but how do you apply the load?
My impression is that the load is "dropped" on the structure, basically you apply it to an un-deformed structure. Then the structure starts to vibrate to find a new deformed equilibrium with the added load. Then I would expect the converged solution to be equal to the static solution. But max displacement (transient) does not have to be equal to max displacement (frequency) because max for frequency is based om harmonic loads and resonance. That why I ask how you apply the loading in the transient analysis.

Regarding Modal superposition vs Direct integration. In my experience direct integration gives higher values if the results differ at all. Modal superposition means that you superpose (or add) the results from a certain number of modes. Direct integration means that you solve the dynamic system directly and include "all" modes. So it seems reasonable that direct integration gives higher results. That is also my experience.

I don't know if there is something software specific in your analysis (Transient stress?). My experience is that when I run a transient analysis for a fixed frequency and compare it to frequency response (harmonic load) I get the same results.

Thomas

### RE: Frequency Response and Transient Stress

#### Quote (OP)

1.Could you please tell me should one expect results from Frequency Response to be somehow corresponding with results from Transient Stress analysis?
2. If yes, please let me know the relationship.
3. What output/result difference is important between Transient Stress Modal Superposition and Transient Stress Direct Integration?
1: Yes.
2: Frequency response provides a signature of the system when excited by sine waves of different frequencies. Transient Analysis has the ability of arbitrary excitation.
3. The same... mostly.

In Pete's lecture notes slide 12, the oscillation around the step plateau vibrates at the damped natural frequency. Your Figures 2 & 3 have approximately 10 cycles in the first 2 seconds (i.e. ~5Hz). ~5Hz is far below the first resonance of 68ish Hz. Unfortunately, Figure 2 or 3 does not match analytical expectations.

Suggested settings for both full transient and modal superposition:
1. Reduce your time step to 1/4 or less of the highest mode period of interest (e.g. 0.002s to capture first mode, smaller time step if other modes are participating strongly).
2. Include Raleigh Damping in your analysis.

Best regards,
Sze Kwan (Jason) Cheah

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