Learning Forum

[byungchun]

hello 

I am doing some modal analysis for simple beam 

11 beams in a row and it has same material and stiffness.

total 22 modes for 1st mode(x,z dir) 

but only 12 modes for 2nd mode 

I do not understand why it has only 12 mode it should be 22 modes for 2nd mode

top and bottom are fixed all 

could you explain this?

here is my model and results

 *** FREQUENCIES FROM BLOCK LANCZOS ITERATION ***

 

  MODE    FREQUENCY (HERTZ)      

 

 

    1     2.202637444537    

    2     2.202637444537    

    3     2.202637444537    

    4     2.202637444537    

    5     2.202637444537    

    6     2.202637444537    

    7     2.202637444537    

    8     2.202637444537    

    9     2.202637444538    

   10     2.202637444538    

   11     2.202637444538    

   12     2.202637444538    

   13     2.202637444538    

   14     2.202637444538    

   15     2.202637444538    

   16     2.202637444538    

   17     2.202637444538    

   18     2.202637444538    

   19     2.202637444538    

   20     2.202637444538    

   21     2.202637444538    

   22     2.202637444538    

   23     4.962273009864    

   24     4.962273009864    

   25     4.962273009864    

   26     4.962273009864    

   27     4.962273009864    

   28     4.962273009864    

   29     4.962273009864    

   30     4.962273009864    

   31     4.962273009864    

   32     4.962273009864    

   33     4.962273009864    

   34     4.962273009865    

   35     11.90362864830    

   36     11.90362864830    

   37     11.90362864830    

   38     11.90362864830    

   39     11.90362864830    

   40     11.90362864830    

   41     11.90362864830    

   42     11.90362864830    

   43     11.90362864830    

   44     11.90362864830    

   45     11.90362864830    

   46     11.90362864830    

   47     11.90362864830    

   48     11.90362864830    

   49     11.90362864830    

   50     11.90362864830    

   51     11.90362864830    

   52     11.90362864830 

 

[jj77]

One possibility is that The first two are similar modes, with same freq. but vibration in different planes. (say pipe will have the first 2 bending modes with same freq. in two different planes due to symmetry). In fact though the first 11 are one mode shape, and the others nr. 12-22 are for another mode shape in a different plane with the same freq.

3rd mode (nr. 23 - 34) which is at 4.96 Hz for all beams does not have such a thing hence you get 11 x 4.96 Hz.

 

[byungchun]

Thank you for response ^^

I don't understand fully, I may dont have enough knowledge

but they are not connected just single beam

so they have to have their individual mode 

 

[jj77]

Ok - let's do a simple example.

 

A beam with a circular cross section (so the cross section has a symmetry), will have the two first bending modes with the same frequency but with a predominant motion of the mode shapes along two different perp. axis (say e.g., z and y). Thus we expect 2 equal frequencies (similar mode shapes also) for 1 beam, but with different main motion (different dir.). If we have two beams we expect 4. Below is an example with two circular beams that are fixed, and as we said they have 4 modes with same frequency (~86 Hz) - this mode shapes are all first bending modes for the two beams - so 2 for 1 beam (but in different planes) and two for the other beam.

 

The highlighted modes at ~ 780 Hz is a torsional mode and of course one mode for each beam (thus two freq. and two modes total, one for each beam). The second highlighted one is a longitudinal mode and again since they are not bending in different planes we get 2 in total just as for the torsional one. 

 

I can not explain this better - so you need to look at the mode shapes of your model and see what they are.

[byungchun]

thanks for giving me informative info.