Shock Response Spectrum - Is there a workaround?

participation factors are independent of the normalization used, the formula to use has to include it to be consistent. In CCX and most FEM software:

in Wijker’s book:

imagen

both give same participation factors, but formulas to calculate them are different (that’s the normalization value).

Hope this helps to clarify.
Fig. 10.6. Four mass-spring-system.
Mechanical Vibrations in Spacecraft Design
Mr J.Wisker

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Hi JuanP74, Disla, Calc_em, xyont,
I really appreciate your work on this subject; I am following closely and studying the reference and examples cited by you. You are stretching my FE theory knowledge and I appreciate that greatly. I keenly anticipate the unfolding matter of the scale factors.
Tim

I think there is something wrong in Wijker’s example, if I do the calculations with the modal matrix provided I do not get the modal participation factors given in the book, in fact I retrieve CCX results when corrected by the mass normalization

>> phi
phi =

   0.776600  -0.597800   0.197200  -0.023210
   0.526100   0.445800  -0.697400   0.195000
   0.316000   0.578500   0.437200  -0.611800
   0.142000   0.330300   0.532500   0.766300

>> M
M =

   5   0   0   0
   0   5   0   0
   0   0   5   0
   0   0   0   5

>> T=[0;0;0;1]
T =

   0
   0
   0
   1

>> gamma(1)=phi(:,1)'*M*T/(phi(:,1)'*M*phi(:,1))
gamma = 0.1420
>> gamma(2)=phi(:,2)'*M*T/(phi(:,2)'*M*phi(:,2))
gamma =

   0.1420   0.3303

>> gamma(3)=phi(:,3)'*M*T/(phi(:,3)'*M*phi(:,3))
gamma =

   0.1420   0.3303   0.5325

>> gamma(4)=phi(:,4)'*M*T/(phi(:,4)'*M*phi(:,4))
gamma =

   0.1420   0.3303   0.5325   0.7662

>> gamma=gamma'
gamma =

   0.1420
   0.3303
   0.5325
   0.7662

>> gamma*sqrt(5)
ans =

   0.3176
   0.7387
   1.1908
   1.7134

So I was wrong in fact saying modal participation factors are the same, in fact they depend on the modal matrix selected, however actual displacements or accelerations are obtained when modal coordinates are multiplied by the modal matrix, and those have to be the same, this is the result of the 3 story building. Actual dof accelerations are used to compute the shears.

Hi Juan,
Thanks for looking at this.

This are my numbers using book’s mode shape displacements.All vector of mode participation factors match. Book uses a different normalization criteria (5). If mode shape matrix is scaled before computation, ccx results are obtained. I would say this book reference is in good agreement with ccx result.

3-Story building is a different thing. It is certainly a more complex problem and I don’t have any other software solution to compare/validate. Anyway, I dare there is something wrong on it (model set up or ccx algorithm). According to the results, one of the modes has >12% of the mass movilized out of the plane.That’s not possible. All the mode shapes has X component =0

my mistake again, I was taking the rigid body vector as T=[0 0 0 1]’ but it is T=[1 1 1 1]', that’s all dof taking the same value :sweat_smile:

>> T=[1;1;1;1]
T =

   1
   1
   1
   1

>> phi(:,1)'*M*T
ans = 8.8035
>> gamma(4)=phi(:,4)'*M*T/(phi(:,4)'*M*phi(:,4))
gamma =

   0.1420
   0.3303
   0.5325
   0.3263

>> gamma(3)=phi(:,3)'*M*T/(phi(:,3)'*M*phi(:,3))
gamma =

   0.1420
   0.3303
   0.4695
   0.3263

>> gamma(2)=phi(:,2)'*M*T/(phi(:,2)'*M*phi(:,2))
gamma =

   0.1420
   0.7569
   0.4695
   0.3263

>> gamma(1)=phi(:,1)'*M*T/(phi(:,1)'*M*phi(:,1))
gamma =

   1.7609
   0.7569
   0.4695
   0.3263

Some few notes on the 3-Story building from above which Disla generated with B31 elements.
The B31 element is expanded to C3D8I elements and in the first record of the output file for the B31 simulation the coordinates and elements C3D8I are listed.

By extracting the beams from there, connecting the beams with Rigid Body elements and locking the beams in the x-direction I got some more reliable results.


As control for this simulation, I generated a 3-Story building with C3D20 element. Off course to make an exact comparison I should had made the connection of the beams with Rigid Body elements also but anyway the results seem to have corresponding values.


So, the strange values for simulation with the B31 elements must be boundary problems either internal in CCX or in the data set.

Thank you very much fgr and JuanP74.
When using solid elements numbers makes much more sense to me.

Two thinghs based on your results.
I have found constraining rotations on my beams is the source of those nonsense large values in the X and RZ factors .I have remove them limiting them to just a few nodes.

Total effective mass when using beam elements is wrong ( Should be 0.5688E6 / Shows 0.51192E+07)

   T O T A L   E F F E C T I V E   M A S S

MODE NO.   X-COMPONENT     Y-COMPONENT     Z-COMPONENT     X-ROTATION      Y-ROTATION      Z-ROTATION

          0.2681202E+07   0.5119266E+07   0.5119286E+07   0.2339553E+09   0.1145151E+09   0.7985956E+07

3 Story building File updated.

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90,S5
91,S1
91,S2
91,S3
91,S5
13,S1
13,S2
13,S3
13,S5
14,S1
14,S2
14,S3
14,S5
15,S1
15,S2
15,S3
15,S5
16,S1
16,S2
16,S3
16,S5
17,S1
17,S2
17,S3
17,S5
18,S1
18,S2
18,S3
18,S5
19,S1
19,S2
19,S3
19,S5
20,S1
20,S2
20,S3
20,S5
105,S1
105,S2
105,S3
105,S5
106,S1
106,S2
106,S3
106,S5
107,S1
107,S2
107,S3
107,S5
108,S1
108,S2
108,S3
108,S5
109,S1
109,S2
109,S3
109,S5
110,S1
110,S2
110,S3
110,S5
111,S1
111,S2
111,S3
111,S5
112,S1
112,S2
112,S3
112,S5
113,S1
113,S2
113,S3
113,S5
114,S1
114,S2
114,S3
114,S5
115,S1
115,S2
115,S3
115,S5
116,S1
116,S2
116,S3
116,S5
117,S1
117,S2
117,S3
117,S5
118,S1
118,S2
118,S3
118,S5
119,S1
119,S2
119,S3
119,S5
120,S1
120,S2
120,S3
120,S5
*SURFACE,NAME=FLOORS1
130,S4
132,S4
134,S4
*SURFACE,NAME=FLOORS2
135,S6
3,S6
56,S6
*SURFACE,NAME=REACTION1
127,S6
11,S6
*MATERIAL,NAME=W3
*ELASTIC,TYPE=ISOTROPIC
2.1E+13,0
*DENSITY
6116207.951
*MATERIAL,NAME=COLUMNS
*ELASTIC,TYPE=ISOTROPIC
33500000000,0
*DENSITY
1E-10
*MATERIAL,NAME=W2
*ELASTIC,TYPE=ISOTROPIC
2.1E+13,0
*DENSITY
7339449.541
*MATERIAL,NAME=W1
*ELASTIC,TYPE=ISOTROPIC
2.1E+13,0
*DENSITY
5504587.156
*BEAM SECTION,ELSET=W3,MATERIAL=W3,SECTION=RECT
0.1,0.1
1,0,0
*BEAM SECTION,ELSET=COLUMNS,MATERIAL=COLUMNS,SECTION=RECT
0.1,0.1
1,0,0
*BEAM SECTION,ELSET=W2,MATERIAL=W2,SECTION=RECT
0.1,0.1
1,0,0
*BEAM SECTION,ELSET=W1,MATERIAL=W1,SECTION=RECT
0.1,0.1
1,0,0
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
1,4,,0
1,5,,0
1,6,,0
2,1,,0
2,5,,0
2,4,,0
3,1,,0
3,5,,0
3,4,,0
4,1,,0
4,5,,0
4,4,,0
5,1,,0
6,1,,0
6,5,,0
6,4,,0
7,1,,0
7,5,,0
7,4,,0
8,1,,0
8,5,,0
8,4,,0
9,1,,0
10,1,,0
10,2,,0
10,3,,0
10,4,,0
10,5,,0
10,6,,0
11,1,,0
12,1,,0
13,1,,0
14,1,,0
15,1,,0
16,1,,0
17,1,,0
18,1,,0
19,1,,0
20,1,,0
21,1,,0
22,1,,0
23,1,,0
24,1,,0
25,1,,0
26,1,,0
27,1,,0
28,1,,0
29,1,,0
30,1,,0
31,1,,0
32,1,,0
33,1,,0
34,1,,0
35,1,,0
36,1,,0
37,1,,0
38,1,,0
39,1,,0
40,1,,0
41,1,,0
42,1,,0
43,1,,0
44,1,,0
45,1,,0
46,1,,0
47,1,,0
48,1,,0
49,1,,0
50,1,,0
51,1,,0
52,1,,0
53,1,,0
54,1,,0
55,1,,0
56,1,,0
57,1,,0
58,1,,0
59,1,,0
60,1,,0
61,1,,0
62,1,,0
63,1,,0
64,1,,0
65,1,,0
66,1,,0
67,1,,0
68,1,,0
69,1,,0
70,1,,0
71,1,,0
72,1,,0
73,1,,0
74,1,,0
75,1,,0
76,1,,0
77,1,,0
78,1,,0
79,1,,0
80,1,,0
81,1,,0
82,1,,0
83,1,,0
84,1,,0
85,1,,0
86,1,,0
87,1,,0
88,1,,0
89,1,,0
90,1,,0
91,1,,0
92,1,,0
93,1,,0
94,1,,0
95,1,,0
96,1,,0
97,1,,0
98,1,,0
99,1,,0
100,1,,0
101,1,,0
102,1,,0
103,1,,0
104,1,,0
105,1,,0
106,1,,0
107,1,,0
108,1,,0
109,1,,0
110,1,,0
111,1,,0
112,1,,0
113,1,,0
114,1,,0
115,1,,0
116,1,,0
117,1,,0
118,1,,0
119,1,,0
120,1,,0
121,1,,0
122,1,,0
123,1,,0
124,1,,0
125,1,,0
126,1,,0
127,1,,0
128,1,,0
129,1,,0
130,1,,0
131,1,,0
132,1,,0
133,1,,0
134,1,,0
135,1,,0
136,1,,0
137,1,,0
138,1,,0
139,1,,0
140,1,,0
141,1,,0
142,1,,0
143,1,,0
*EQUATION
2
6,3,1,2,3,-1
*EQUATION
2
7,3,1,3,3,-1
*EQUATION
2
8,3,1,4,3,-1
*EQUATION
2
6,2,1,2,2,-1
*EQUATION
2
7,2,1,3,2,-1
*EQUATION
2
8,2,1,4,2,-1
*STEP,PERTURBATION
*FREQUENCY
6
*NODE FILE,GLOBAL=YES
U
*EL FILE
S,NOE,ENER
*END STEP

EDITED: I posted liml files in the Mecway forum. Set up and geometry can be read more easy.

i’m not sure if solid model or expanded beam can work well in response spectrum analysis after modal combination, both outer fiber stress in beam and column will always be positive. Hopefully i can be wrong, since it’s not a problem when using output of section force based.

¿?

Hi, Disla,

but your model has a first eigenfrequency of 0.08 Hz and the one in the video is 1/T1=1/0.282 s = 3.54 Hz = f1 (more realistic for a building).
The video uses what in Nastran is called point normalization, setting a value of 1 to a specific dof, however if I do that with your model (the original one posted, not the latest) I get the following values for mode 1:
phi11’ = 1.00, phi21’ = 1.85, phi31’ = 2.25, very different to the values used in the video.
Regarding the participation factor calculation, modes are mass normalized so the issue has to be anywhere else, maybe this question is related to it seems B31 beams have issues (TBC): Total effective mass differs if using density or lumped masses

there’s fairly new implementation using signed from dominant modes, it did not cover on my old textbook references i.e Dynamics of Structures 1st Ed. by Anil K. Chopra. These approach known as helper for most RSA problems, interesting me to do some comparison.

You are right JuanP74. The video is only useful as reference to apply the method. Unfortunately, the dimensions and material properties were not provided to use it as a numeric reference. I warn about that at the end of my first post. My model is different from the one in the video but useful anyway. Sorry about the confusion.

Seems I have fall into an old issue (2021). I should have navigated and search more carefully in the forum. Second order beam has put things in place.

I still need to understand why Mx and rotational Masses are different but that’s another story.

If participation factors are not right with linear beam elements, dynamic analysis based on modal superposition with beams will be wrong too ¿right?.

learning is in part re-learning so I find this discussion fruitful. We have to keep a warning over B31 elements!

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who said that Ansys is :rofl:

I heard it through the grapevine :crazy_face: