Frequency Response and Transient Stress

[EngineerMickeyMouse]

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?

[John_Holtz]

Hi EMM

You should be able to duplicate the results of the Frequency Response analysis using the Transient analysis, but it looks like you have a constant load applied in the Transient analysis. The load in the Transient analysis needs to be sinusoidal. I am sure that I have done it a long time ago and got a good match.

About the comparison of Transient Direct Integration versus Modal Superposition, the modal superposition will be accurate only if the forcing frequency is somewhat close or between the natural frequencies. For example, a forcing frequency of 10 Hz will not "excite" a model very well whose lowest natural frequency is 100 Hz. (Or if the forcing frequency is 1000 Hz and the highest natural frequency calculated is 100 Hz.)

[EngineerMickeyMouse]

John, thanks for a quick response.

Could you please take a look at analysis parameters compared below?

I would appreciate help to set Transient Analysis in way it would mimick Frequency Response settings.

As per figure below: From scenario No.2 modal results are imported (from Natural Frequency analysis). Damping ratio assumed 0.01, however I am not sure if these are same values for both analysis since Transient is described with two coefficients (alpha and beta). At Transient Load Curve, as per your advice, I have selected Frequency of 67 Hz, since it was approx. value where resonance peak is observed at Frequency Response analysis.

With these settings, unfortunately I cannot see outputs of two different results being close to similar.

Could you please help?

[John_Holtz]

Hi,

I would suggest trying a different frequency, something not too close to resonance. In theory, the displacement is infinite at resonance if the damping is zero, so perhaps the difference between the damping in Frequency Response and the damping in Transient is causing the difference.

Then, I would make the damping 0 to eliminate it as a possible reason for the difference.

Unfortunately, the image only comes through about 700 pixels tall, so it is too small to read anything. It would be better if you can attach the image (instead of inserting it as a photo), or attach an archive would be better.

But I think I see that the transient analysis has 100 time steps. If that is over the several seconds shown in the previous post, then the time step size must be on the order of 0.1 seconds. To capture the dynamic effects, you probably need at least 10 time steps per cycle, and more like 20 time steps per cycle. So at 60 Hz forcing frequency (not too close to resonance), the time step size for the transient should be around (1/60 cycles/sec)*(1/20 steps/cycle) = 0.0008 seconds. And of course you need to run it long enough to get from a 0 initial velocity to a quasi-steady state solution. That is a lot of steps!

Good luck.

[EngineerMickeyMouse]

That may be a hint.

Figure is attached so it will be more legible right now. At Transient Stress analysis parameters there are inputs for time step and its size in two places, Event and Load Curve, should these be set the same or somehow otherwise? BTW, could you please describe a little bit more what is found in Help, but still in your words, as per your understanding, what is the results comparison between Frequency Response and Transient Stress? I think the main purpose of the latter is not so clear. I will appreciate your input.

[AstroJohnPE · Accepted solution]

Hi E.M.M.

For the time-steps in the transient analysis: In your case, the time step size for the Event, and the step size for the load curve, should be about the same because:

• you want about 20 time steps per cycle in the event to capture the dynamic motion
• you want about 20 time steps per cycle in the load curve so that your load looks like a sine curve. (You probably could get away with fewer steps on the load curve, but what you have currently is too coarse to capture all of the inflections.)

In general, the step size for the load curve only needs to be fine enough to define the load. If the load were constant, you would only need two data points. But you would still want 10-20 time steps per cycle in the Event in order to capture the vibration of the model (if that were important).

Frequency Response calculates the maximum displacement due to a sinusoidal (or harmonic) load. Transient Stress essentially solves F=ma, so it calculates the displacements during the entire analysis due to loads that change over time. The main difference between Transient Stress and MES is that Transient Stress is linear (meaning small deformation theory) where as MES is nonlinear (large deformation theory).

From this perspective, the two analysis types are completely different. Of course, you can apply a sinusoidal load in a Transient Stress analysis. After enough loading cycles, the part will gather enough speed so that the maximum displacements will eventually match the frequency response results.