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Frequency Response Analysis - Short question 3

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isponmo

isponmo

Aerospace
Jul 20, 2012
39
Dear All,

Maybe this is a silly question, but I am getting a bit confused.

Today I was thinking about what happens if a structure is loaded with a frequency dependent load which is a combination of sines at different frequencies, all acting simulaneusly. If they are all acting simultaneously, should I assess the stresses by superimposing the responses? The thing is that if I perfrom a frequency response analysis with FEM and extract the stresses, I get them separately for each frequency. How should I combine them?

Thank you very much.

Kind regards,

Israel
 
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Dear Israel,
You may have many excitations of force, pressure, etc.., each varying with different shape & amplitude vs. frequency, but when you perform a modal frequency dynamic response using for instance NX NASTRAN (SOL111) solver what you get is a response of the model (say nodal displacements & element stress) for every frequency step using modal superposition at every frequency step requested. In Dynamic analysis the concept of LOAD CASE of linear static analysis do not exist.

Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48011 BILBAO (SPAIN)
WEB: Blog de FEMAP & NX Nastran:
 
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Dear Blas,

Thank you very much for your reply.

I think I understand your point. But then... is there no way to assess the real, total stresses that the structure is to withstand? Is it only possible to get stresses for each frequency separately? This is a problem if the aim of the analysis is to find out if the structure can resist certain dynamic loads in terms of strength.

I was wondering if there is a technique, even if it is just a rule of thumb or approximate calculation, that allows you to have an idea (an upper bound) of what would happen with the structure. For instance, for random vibrations it is common to combine the responses using the root mean square...

By the way, congratulations for your blog, I find it very useful :)

Best regards,

Israel
 
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Dear israel,
Is very simply, you can postprocess the response results of dynamic stress vs. frequency using XY-PLOTS selecting the maximum response of the model at every frequency, this a a single value, this way you have the full picture of how the whole model resist to frequency excitation. The maximum peak stress value is the maximum stress that suffer the structure, simply!.

Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48011 BILBAO (SPAIN)
WEB: Blog de FEMAP & NX Nastran:
 
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Dear Blas,

Ok, it is very straightforward!

Then, can I assume that, from a frequency response analysis point of view, the following two cases are equivalent and will lead to the same results?

a) The load is a sine sweep which changes its frequency very slowly.
b) The load is a superposition of sines with different frequencies happening simultaneously.

Again, thanks a lot,

Israel
 
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Dear Israel,
I use to perfom frequency sweeps, and the excitation could be in may forms: constant, variable, etc.

According nx nastran manuals:

Code: 
[b]Frequency response analysis[/b] is used to compute structural response to steady-state oscillatory excitation. 
Examples of oscillatory excitation include rotating machinery, unbalanced tires, and helicopter blades. 
In frequency response analysis the excitation is explicitly defined in the frequency domain. 
Excitations can be in the form of applied forces and enforced motions (displacements, velocities, or accelerations).

To fully specify a dynamic load, you must:
• Define the location and direction that the load is applied to the structure. Because this characteristic locates the loading in space, 
it is called the spatial distribution of the dynamic loading.
• Define the frequency variation in the load. This characteristic of a dynamic load differentiates it from a static load. 
The frequency variation is called the temporal distribution of the load.

NX Nastran makes it possible for you to apply many complicated and temporally similar loadings with a minimum of input by using Table IDs and Set IDs. 
You can also easily combine simple loadings to create complicated load distributions that vary in position as well as frequency.

Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48011 BILBAO (SPAIN)
WEB: Blog de FEMAP & NX Nastran:
 
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Dear Blas,

Again, thank you for the aid :)

Yes, I read something very similar in the MSC Nastran manuals, but I was not happy with it.

I am not able to understand why applying a frequency sweep (one frequency at a time) should be the same as applying a load in which all the frequencies are acting simultaneously. For instance, in the sweep case, when you reach a resonant frequency, the system should react accordingly: the mode associated to that resonant frequency should be predominant. In the second case, though, if all frequencies are acting simultaneosly, then several modes associated to several resonant frequencies should be excited simultaneously, being the results a combination of all of them.

I think my point is a bit difficult to explain...

Thanks a lot

Best regards,

Israel
 
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Dear Israel,

Probably you are referring to the term "Double Amplitude (D.A.) in Sine Vibration"?. What this means?.

When you input your frequency and acceleration data into a sine vibration frequency response NASTRAN deck, you may run into that cryptic notation: "0.32 inch D.A. from 10-20Hz". This is what is known as a vibrational amplitude. But since NASTRAN does not know what D.A. is, and many of us probably don't either, you need to convert that value into something everyone understands, such as a vibrational acceleration, which could be measured in g's or in/sec2 or m/s2.

Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48011 BILBAO (SPAIN)
WEB: Blog de FEMAP & NX Nastran:
 
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Dear Blas,

Actually I was not refering to double amplitude. I have the feeling that I may be missing something basic from the vibrations course, and that's why I am not able to fully understand this. The best option will be that I brush up my coursenotes and see if I get it. Otherwise, I will be asking all the time! ;)

In any case, the conclusion of this thread for practical purposes would be your second post:

"You can postprocess the response results of dynamic stress vs. frequency using XY-PLOTS selecting the maximum response of the model at every frequency, this a a single value, this way you have the full picture of how the whole model resist to frequency excitation. The maximum peak stress value is the maximum stress that suffer the structure, simply!."

Thank you very much for answering this thread. I am very grateful :)

Have a nice day,

Israel
 
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Dear Israel,
Here you are the typical XYplot output result of a sine vibration - modal frequency response of a dynamic enforced motion analysis of a simply cantilever beam, including both the input excitation of base motion acceleration AY=0.25G and the output response of acceleration in the frequency range. Please note how the peaks response of acceleration coincide with the natural frequency modes of the structure. Also please note the dynamic amplification of response ...

ay_output_freq_response_xyplot.png


Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48011 BILBAO (SPAIN)
WEB: Blog de FEMAP & NX Nastran:
 
Upvote 0 Downvote
Dear Blas,

I see. So I should take around 4G as maximum response and therefore the peak stresses associated to that frequency, which will be probably the highest.

Again, thanks a lot!

Kind regards,

Israel
 
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NO

or no.

Your input spectrum may not be a nice flat line, for instance the input from a car's wheels at 100 kph will be very strongly biased to around 10 or 11 Hz. There will also be a bit of second and third harmonic of that fundamental. So you cannot generalise.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376
 
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Dear GregLocock,

Thank you for your answer.

How should I proceed in such case then?

Kind regards,

Israel
 
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Linearity says that you can add the stresses from different frequencies.

I'm guessing your force spectra are in the form of magnitude vs frequency, with no phase? In that case the worst case stress due to that force spectrum F is the sum of the individual frequency components from F.*FRF where FRF is the transfer function from that driving point to stress at the response point of interest.

This is rather elementary stuff, hopefully I have misread your question. Can you restate your question as a result of Blas' comments?

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376
 
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Dear GregLocock,

First of all, thanks a lot for your reply. I really appreciate that members of this forum share their knowledge and try to help the members with less experience. Thanks to Blas as well for all the answers!

What you mentioned is more or less what I was asking. From my first post:

" If they are all acting simultaneously, should I assess the stresses by superimposing the responses? The thing is that if I perfrom a frequency response analysis with FEM and extract the stresses, I get them separately for each frequency. How should I combine them?"

(Actually I asked this question because the software I use does not supermimpose the stresses from all frequencies, so I was hesitating a bit because normally it does everything automatically. For instance, for random vibration, it calculates the total rms by default.)

Then Blas kindly answered to my question and suggested that I only would have to consider the stresses from the peak response:

Is very simply, you can postprocess the response results of dynamic stress vs. frequency using XY-PLOTS selecting the maximum response of the model at every frequency, this a a single value, this way you have the full picture of how the whole model resist to frequency excitation. The maximum peak stress value is the maximum stress that suffer the structure, simply!.

But I did not fully understand that because for me it is not the same having a sine sweep than a composed load in which all the frequencies act simultaneously:

I am not able to understand why applying a frequency sweep (one frequency at a time) should be the same as applying a load in which all the frequencies are acting simultaneously. For instance, in the sweep case, when you reach a resonant frequency, the system should react accordingly: the mode associated to that resonant frequency should be predominant. In the second case, though, if all frequencies are acting simultaneosly, then several modes associated to several resonant frequencies should be excited simultaneously, being the results a combination of all of them.

That is a summary of everything :)

Best regards,

Israel


 
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yes, I see what you are getting at. You don't only look look at the peak in the stress spectrum, for example a car has a fairly flat repsonse, with many peaks, so just using the highest peak value would ignore the vast contribution from the rest.

As to the rest, you need to read up on signal processing and in particular psd's.


"For instance, in the sweep case, when you reach a resonant frequency, the system should react accordingly: the mode associated to that resonant frequency should be predominant. In the second case, though, if all frequencies are acting simultaneosly, then several modes associated to several resonant frequencies should be excited simultaneously, being the results a combination of all of them."

That is correct.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376
 
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Dear GregLocock and Blas,

Perfect. It is totally clear now :D Thank you very much to both of you for spending some of your time replying this post.

Have a nice day.

Best regards,

Israel
 
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