Random vibration analysis of a cantilever beam

Hello,

I recently came across one youtube video of Random Vibration analysis using Abaqus. The link of this video is following : #ABAQUS Tutorials - Random Vibration Analysis

The problem statement is following

I tried to reproduce the same using PrePromax. The model is following

I had to model it using solid elements, as the shell elements (or beam elements in the video) were not giving me proper results that I desired.

Here are my confusions.
In the input data of frequency vs PSD, the PSD is given as g^2/hz. In prepromax I can only input the acceleration as mm/s^2. So I had to give 1/g^2 = 0.01039 m/s^2 as gravity component. I use mm-ton-mpa units so it was 10.39 mm/s^2, but to my surprise the results were not matching with the reference solution. only when I used false units of 0.01039 mm/s^2 my results were near to the reference solution. It can be seen as following

The first 2 modes in my results are 86.27 Hz and 516.108 Hz respectively. They are closed to the results from the reference solution of youtube video at 82.76 Hz and 518.89 Hz respectively.

I suspect that I have done a unit conversion error, bztI can not catch it. Can anyone please help me with it ?

Thank you in advance

Unlike Abaqus, CalculiX doesn’t have the random vibration analysis procedure. However, there were some attempts to perform equivalent analyses using available linear dynamics procedures (namely modal dynamics): Dynamic simulation of the PCB

Some time ago I used the same example as shown in this video but with beam elements. It’s from Abaqus documentation (Random response of a cantilever subjected to base motion). I compared it with modal dynamics in Abaqus but you can try the same in PrePoMax. I just used different signals - white noise in modal dynamics and its PSD in random response. Those signals were used to define acceleration base motion. Proper incrementation was needed in modal dynamics analysis. The stress results were comparable after multiplying RMS results from random response by 3 (assuming 3σ).

Thank you for the quick response.
If I use the modal Dynamics case then the results will be in time domain but the example has its results in frequency domain. I understand that steady state dynamics is for sinosoidal excitations but can we make some changes in to it to also perform random vibration ? or can we somehow convert the results of modal dynamics in frequency domain ?

That’s right, since you convert the input signal between frequency and time domain.

Regarding SSD, there is a procedure to obtain PSD response curve for individual outputs by postprocessing results from SSD. You would have to multiple input (excitation) PSD by the square of the frequency response function (FRF) to get the response PSD. Then integrate it to get the variance and calculate square root from it to get the response RMS.

are beam elelements supported now in Calculix? and how do I activate them

Not yet. But they are supported in FreeCAD FEM.

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