Understanding Random Response Analysis & PSD Input

[jthomas2SNH8G]

I am trying to understand what is happening in a Random Response analysis when I provide it with a PSD Input, have Gravity Load and an external load acting on the body.

I've attached images of the input provided for the analysis I'm running.

Is there a documentation I could go through to understand how the software is using the input parameters provided, so I can verify if it is how I want to model my simulation?

@John_Holtz 

   

[jthomas2SNH8G]

@John_Holtz 

Would like to elaborate/break it down a bit -

Firstly, per the little research I did on Modal Frequency Response, I know the load provided would be applied in a sinusoidal waveform, be it gravity load or an external load. So I'm confused on how the load factor table is being used. Could you please help me understand this?

Secondly, I know in the Random Response what is happening vaguely is the software is doing a Modal Frequency Response and then scaling it per the PSD Input provided and giving the RMS output.  Could you please help me understand what is happening in a Model Frequency Analysis i.e. the relation between the load and frequency and how a PSD is used to scale frequency response?

[John_Holtz]

Hi @jthomas2SNH8G 

Essentially, you cannot have an "external load" in a random vibration analysis. The random response analysis should only include the load that is related to the PSD (usually an acceleration going through the supports, but it could be any load applied anywhere to the model). All loads applied to the analysis create displacement/stress according to the PSD. 

1. The PSD scales frequency response analysis results and performs an final root mean square (RMS) summation to calculate the random response (random vibration) results.
2. The frequency response analysis performs a sine sweep using all the applied loads applied sinusoidally to the model at the frequencies specified in the Dynamic Setup to calculate the frequency response results.

The labels in the PSD chart are basically labels. The analysis only looks at the numbers and doesn't know if they are g^2/Hz, (m/s^2)^2/Hz, or rabbits^2/Hz. The labels only change the numbers shown in the UI if you change the units.

Some reference articles:

• Autodesk Inventor Nastran 2022 Help | How to run a random response analysis with no outside loads in...
• Autodesk Inventor Nastran 2022 Help | How to interpret random vibration analysis results from Nastra...
• Results of random response are inaccurate when using log-log interpolation of PSD in Nastran | Searc...

Let us know if you have any questions.

John

[jthomas2SNH8G]

@John_Holtz 

Thank you for the response sir. 

1. So the Frequency Response Analysis takes a given "X" load and applies it sinusoidal at each frequency in the range mentioned in the Dynamic Setup and provides the outcome result. Is that a correct understanding?

2. In your first point, you mention PSD scales the frequency response results. Can you please elaborate that a bit? I'm having trouble understanding this part and haven't found any good resource online. 

[John_Holtz · Accepted solution]

(Your replies are coming in faster than my typing! This reply is to your second post. I will reply to your third post next, if I have time.)

I wish I had seen your first reply before I posted my first reply. You answered all the questions!

Here's some clarifications on your post:

• Firstly, per the little research I did on Modal Frequency Response, I know the load provided would be applied in a sinusoidal waveform, be it gravity load or an external load. So I'm confused on how the load factor table is being used. Could you please help me understand this?
  • Your statement is correct.
  • The short answer is this: the load table indicates how the applied load changes with the sine sweep frequency.
  • Some loads are independent of the forcing frequency. For example, gravity is generally constant. 😁 (Now that I think about it, gravity is usually not sinusoidal either, so maybe not the best example.) Therefore the load table should just be a flat line with a load scale factor of 1. (The table is extrapolated, so the frequencies in the load table are not critical.)
  • Some loads are not independent of the forcing frequency. Centripetal force is an example. The force is a function of the rotation speed squared. (The rotation speed, converted to Hz, is the same as the forcing frequency.) If you are including a centripetal force, you apply a force F that corresponding some chosen frequency f, then the magnitude of the force F' at any frequency f' in the sine sweep is F' = F*(f'/f)^2. The load table for the load gives the frequencies f' from 1 to N Hz and the load multiplier (f'/f)^2.

• Could you please help me understand what is happening in a Model Frequency Analysis i.e. the relation between the load and frequency and how a PSD is used to scale frequency response?
  • Think of it like this:
    • The frequency response analysis creates steps from 1 to N which corresponds to each of the specified frequencies f' in the Dynamics Setup.
    • At step 28 the forcing frequency f'=100 Hz for example. The load table is interpolated for 100 Hz to get the multiplier. The load is multiplied by the multiplier. The displacements, stress, etc of the frequency response are calculated at the multiplied load value acting at 100 Hz.
    • The frequency response analysis ends after all N forcing frequencies are calculated.
    • Now the random response analysis begins. The result for each frequency response step 1 to N is read.
    • At step 28, the forcing frequency was f'=100 Hz. The PSD is interpolated (either linearly or Log-Log, depending on what was chosen) for the frequency f' to get a value.
    • The frequency response results from step 28 are scaled by the value from the PSD. (I believe the scaling is a straight multiplication, but it could be more elaborate and involve the mass participation factor and other terms that make it not so easy.)
    • This produces 1 to N "PSD" steps or results that can be viewed. 
    • The 1 to N "PSD" results are used to compute the RMS result. 

John

[John_Holtz]

I will try to type faster. 😀 For reference, this is my third post in response to your third post, if that makes sense.

1. The Frequency Response Analysis takes a given "X" load and applies it sinusoidal at each frequency in the range mentioned in the Dynamic Setup and provides the outcome result. Is that a correct understanding?
   1. Yes if you include the Load Scale Factor from the Load Data table.
2. In your first point, you mention PSD scales the frequency response results. Can you please elaborate that a bit? I'm having trouble understanding this part and haven't found any good resource online. 
   1. My second post touches on that, but I do not know the mathematical answer. The websites created by "Tom Irvine" generally give good, simple explanations for all things vibration. I do not know if this website is the most current or not, but it would be a good starting point. http://www.vibrationdata.com/random.htm

John

[jthomas2SNH8G]

@John_Holtz 

Haha I apologize for the quick replies.

Just wanted to make sure I provided all the information I had on the problem to help you help me (if that makes sense) understand what I'm missing out on.

Anyway, I appreciate your help a lot! Thank you for sharing the website.

One last doubt - 

If in a frequency response analysis, I have a "X" load acting externally and I do not provide the load factor table information, does it assume a multiplier of 1 all through the analysis?

[John_Holtz]

Yes. A default table with a constant load scale factor is created if the load table is not defined for a load.

John