How to define a PSD ?

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How to define a PSD ?

ClementB
Hello, I'm trying to run a random response analyse. I want to define a PSD spectrum in Abaqus and i don't know what should i put in the PSD table (gravity base motion). I only have the RMS of my PSD spectrum and for each frequency the amplitude in term of acceleration (ie : from 20 to 100Hz i have 0.0044g2/Hz; from 100 to 300Hz ... ). However Abaqus wants me to fill a real and a imaginary part to define the spectrum. Unfortunately, I didn't find anything about that on the Abaqus User's Guide so i really don't know how to procede. Should i only fill the real part ? Your help will be greatly appreciated and by the way, I appologize for my english. Clement
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Re: How to define a PSD ?

George Papazafeiropoulos
- In case of linear system, see the section 6.3.11 Random response analysis of the Abaqus Analysis User's Guide of the Abaqus/Documentation
 

- If the system is nonlinear you can generate an excitation process from the acceleration spectrum using the Inverse Fast Fourier Transform. After this, you can carry out a dynamic time history analysis with base excitation equal to the excitation process that you have found above.
 

 Best regards,
 

 _______________________________________________
George Papazafeiropoulos
Captain, Infrastructure Engineer, Hellenic Air Force
Civil Engineer, M.Sc., Ph.D. candidate, NTUA
Email: [hidden email]

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Re: How to define a PSD ?

ClementB
Hello and thank you for your answer. My system is linear so i tried to run the analysis with the standard mode (the one presented in the section 63.11). But my problem occurs when i have to define the PSD spectrum. I do not know how to fill the data table. I have the power spectral density that means that i know the PSD related to a specific frequency (for example between 20Hz and 100Hz i have a PSD equal to 0.0044g2). But i don't know how to find the real part and the imaginary part Abaqus is asking me for each frequency. Do you think it's correct to only fill the real part ? Thank you, Clement
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Re: How to define a PSD ?

George Papazafeiropoulos
Dear Clement,
 

 What does "0.0044g2" mean? Is it the amplitude of the PSD spectrum or its real part? Which is its unit? You have to find out this and then you can define the PSD spectrum in Abaqus by entering the appropriate values
 

 Best regards,
 ________________________________________________________
George Papazafeiropoulos
Captain, Infrastructure Engineer, Hellenic Ministry of National Defence
Civil Engineer, M.Sc., Ph.D. candidate, NTUA
Email: [hidden email]


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Re: How to define a PSD ?

ClementB
Yes it's the amplitude of the PSD on the interval 20 to 100Hz. The unit is the square of gravity so 0,0044g2 stands for 0,0044*(9,81)^2 m/s2 My main problem is that i don't know how to transform this data into a complex function in order to fill the real and the imaginary parts of the PSD table on Abaqus. Regards, Clement B
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Re: How to define a PSD ?

George Papazafeiropoulos
There is not a unique way to transform the PSD amplitude into its real and imaginary parts since you do not know the PSD phase spectrum. You can assume a random PSD phase spectrum in order to find the real and imaginary parts of the PSD spectrum that are required by Abaqus.
 

 Best,
 

 ________________________________________________________
George Papazafeiropoulos
Captain, Infrastructure Engineer, Hellenic Ministry of National Defence
Civil Engineer, M.Sc., Ph.D. candidate, NTUA
Email: [hidden email]


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Re: How to define a PSD ?

ClementB
Thank you for your help !!

Just to be sure in this case, if i consider the phase spectrum to be equal
to 0 then my real part will be the amplitude of my PSD, is that correct ?

When i run several simulations with and without an imaginary part i get the
same results so i guess it doesn't matter to work with a 0 phase spectrum.
But i don't like the fact that i don't know why i can work with a 0 phase
spectrum. I tried to seek information on that on the web but i didn't find
what i was looking for. Could you explain to me what the imaginary part
represents in terms of physics (except the phase of my PSD) ?

Regards,
Clement



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