## General Mechanical

• byungchun
Subscriber

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
Subscriber

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
Subscriber

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
Subscriber

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
Subscriber

thanks for giving me informative info.