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:
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
** Generated by Mecway 26
*NODE
1,0,0,0
2,0,0,1
3,0,0,0.25
4,0,0,0.5
5,0,0,0.75
6,0,-0.001,0
7,0.001,-0.001,0
8,0.001,0,0
9,0,0,0
10,0,-0.001,0.001
11,0.001,-0.001,0.001
12,0.001,0,0.001
13,0,0,0.001
*ELEMENT,TYPE=SPRINGA
1,5,2
2,1,3
3,3,4
4,4,5
*ELEMENT,TYPE=C3D8
5,6,7,8,9,10,11,12,13
*ELEMENT,TYPE=MASS
6,3
7,4
8,5
9,2
*NSET,NSET=BASE
1
*ELSET,ELSET=K
1
*ELSET,ELSET=4K
2
*ELSET,ELSET=3K
3
*ELSET,ELSET=2K
4
*ELSET,ELSET=COMPONENT
5
*ELSET,ELSET=MASS_1
6
*ELSET,ELSET=MASS_2
7
*ELSET,ELSET=MASS_3
8
*ELSET,ELSET=MASS_4
9
*MATERIAL,NAME=CUBE
*ELASTIC,TYPE=ISOTROPIC
2.1E+14,0
*DENSITY
1E-10
*SPRING,ELSET=K
1.000000000000E+006
*SPRING,ELSET=4K
4.000000000000E+006
*SPRING,ELSET=3K
3.000000000000E+006
*SPRING,ELSET=2K
2.000000000000E+006
*SOLID SECTION,ELSET=COMPONENT,MATERIAL=CUBE
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
2,1,,0
2,2,,0
3,1,,0
3,2,,0
4,1,,0
4,2,,0
5,1,,0
5,2,,0
6,1,,0
6,2,,0
6,3,,0
7,1,,0
7,2,,0
7,3,,0
8,1,,0
8,2,,0
8,3,,0
9,1,,0
9,2,,0
9,3,,0
*MASS,ELSET=MASS_1
5
*MASS,ELSET=MASS_2
5
*MASS,ELSET=MASS_3
5
*MASS,ELSET=MASS_4
5
*STEP,PERTURBATION
*FREQUENCY
4
*NODE FILE,GLOBAL=YES
U
*EL FILE
S,NOE,ENER
*END STEP
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 
>> 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.
** Generated by Mecway 26
*NODE
1,0,-3,0
2,0,-3,3
3,0,-3,6
4,0,-3,9
5,0,-2.8125,3
6,0,0,3
7,0,0,6
8,0,0,9
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10,0,0,0
11,0,-3,4.3125
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13,0,-3,5.0625
14,0,-3,5.4375
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17,0,-3,6.9375
18,0,-3,7.3125
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23,0,-2.0625,3
24,0,-1.6875,3
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26,0,-0.9375,3
27,0,-0.5625,3
28,0,-2.8125,6
29,0,0,0.1875
30,0,0,0.5625
31,0,0,0.9375
32,0,0,1.3125
33,0,0,1.6875
34,0,0,2.0625
35,0,-3,0.375
36,0,-3,0.75
37,0,-3,1.125
38,0,-3,1.5
39,0,-3,1.875
40,0,-3,2.25
41,0,-3,2.625
42,0,-3,3.375
43,0,-3,3.75
44,0,-3,4.125
45,0,-3,4.5
46,0,-3,4.875
47,0,-3,5.25
48,0,-3,5.625
49,0,-3,6.375
50,0,-3,6.75
51,0,-3,7.125
52,0,-3,7.5
53,0,-3,7.875
54,0,-3,8.25
55,0,-3,8.625
56,0,-2.4375,6
57,0,-2.0625,6
58,0,-1.6875,6
59,0,-1.3125,6
60,0,-0.9375,6
61,0,-0.5625,6
62,0,-2.8125,9
63,0,-2.625,3
64,0,-2.25,3
65,0,-1.875,3
66,0,-1.5,3
67,0,-1.125,3
68,0,-0.75,3
69,0,-0.375,3
70,0,-2.625,6
71,0,-2.25,6
72,0,-1.875,6
73,0,-1.5,6
74,0,-1.125,6
75,0,-0.75,6
76,0,-0.375,6
77,0,-2.625,9
78,0,-2.25,9
79,0,-1.875,9
80,0,-1.5,9
81,0,-1.125,9
82,0,-0.75,9
83,0,-0.375,9
84,0,-2.4375,9
85,0,-2.0625,9
86,0,-1.6875,9
87,0,-1.3125,9
88,0,-0.9375,9
89,0,-0.5625,9
90,0,0,2.8125
91,0,0,0.375
92,0,0,0.75
93,0,0,1.125
94,0,0,1.5
95,0,0,1.875
96,0,0,2.25
97,0,0,2.625
98,0,0,3.375
99,0,0,3.75
100,0,0,4.125
101,0,0,4.5
102,0,0,4.875
103,0,0,5.25
104,0,0,5.625
105,0,0,6.375
106,0,0,6.75
107,0,0,7.125
108,0,0,7.5
109,0,0,7.875
110,0,0,8.25
111,0,0,8.625
112,0,0,5.8125
113,0,0,8.8125
114,0,-3,2.0625
115,0,-3,0.1875
116,0,-3,0.5625
117,0,-3,0.9375
118,0,-3,1.3125
119,0,0,2.4375
120,0,0,3.1875
121,0,0,3.5625
122,0,0,3.9375
123,0,0,4.3125
124,0,0,4.6875
125,0,0,5.0625
126,0,0,5.4375
127,0,0,6.1875
128,0,0,6.5625
129,0,0,6.9375
130,0,0,7.3125
131,0,0,7.6875
132,0,0,8.0625
133,0,0,8.4375
134,0,-0.1875,6
135,0,-3,3.5625
136,0,-3,3.9375
137,0,-3,2.8125
138,0,-3,5.8125
139,0,-3,8.8125
140,0,-3,1.6875
141,0,-3,2.4375
142,0,-3,3.1875
143,0,-0.1875,3
*ELEMENT,TYPE=B31
1,68,27
2,27,69
3,3,28
4,28,70
5,71,57
6,57,72
7,72,58
8,70,56
9,56,71
10,35,116
11,10,29
12,29,91
13,43,136
14,136,44
15,44,11
16,11,45
17,45,12
18,12,46
19,46,13
20,13,47
21,91,30
22,30,92
23,92,31
24,31,93
25,93,32
26,32,94
27,94,33
28,33,95
29,95,34
30,34,96
31,96,119
32,119,97
33,6,120
34,120,98
35,98,121
36,121,99
37,99,122
38,122,100
39,100,123
40,123,101
41,101,124
42,124,102
43,102,125
44,125,103
45,103,126
46,126,104
47,7,127
48,127,105
49,58,73
50,73,59
51,59,74
52,74,60
53,60,75
54,75,61
55,61,76
56,4,62
57,62,77
58,77,84
59,84,78
60,78,85
61,85,79
62,79,86
63,86,80
64,80,87
65,87,81
66,81,88
67,88,82
68,82,89
69,89,83
70,116,36
71,36,117
72,117,37
73,37,118
74,118,38
75,38,140
76,140,39
77,105,128
78,128,106
79,106,129
80,129,107
81,107,130
82,130,108
83,108,131
84,131,109
85,109,132
86,132,110
87,110,133
88,133,111
89,67,26
90,42,135
91,135,43
92,41,137
93,137,2
94,48,138
95,138,3
96,55,139
97,139,4
98,39,114
99,114,40
100,97,90
101,90,6
102,104,112
103,2,142
104,142,42
105,47,14
106,14,48
107,3,15
108,15,49
109,49,16
110,16,50
111,50,17
112,17,51
113,51,18
114,18,52
115,52,19
116,19,53
117,53,20
118,20,54
119,54,21
120,21,55
121,26,68
122,112,7
123,111,113
124,113,8
125,40,141
126,141,41
127,1,115
128,115,35
129,69,143
130,143,6
131,76,134
132,134,7
133,83,22
134,22,8
135,2,5
136,5,63
137,63,9
138,9,64
139,64,23
140,23,65
141,65,24
142,24,66
143,66,25
144,25,67
*NSET,NSET=FLOOR1
5
9
23
24
25
26
27
63
64
65
66
67
68
69
143
*NSET,NSET=FLOOR2
28
56
57
58
59
60
61
70
71
72
73
74
75
76
134
*NSET,NSET=ROOF
22
62
77
78
79
80
81
82
83
84
85
86
87
88
89
*NSET,NSET=ROOF_FLOORS_NODES
5
9
22
23
24
25
26
27
28
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
134
143
*ELSET,ELSET=EALL
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
*ELSET,ELSET=W3
56
57
58
59
60
61
62
63
64
65
66
67
68
69
133
134
*ELSET,ELSET=COLUMNS
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
122
123
124
125
126
127
128
*ELSET,ELSET=W2
3
4
5
6
7
8
9
49
50
51
52
53
54
55
131
132
*ELSET,ELSET=W1
1
2
89
121
129
130
135
136
137
138
139
140
141
142
143
144
*SURFACE,NAME=PILAR1
100,S1
100,S2
100,S3
100,S5
101,S1
101,S2
101,S3
101,S5
102,S1
102,S2
102,S3
102,S5
122,S1
122,S2
122,S3
122,S5
123,S1
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123,S3
123,S5
124,S1
124,S2
124,S3
124,S5
11,S1
11,S2
11,S3
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12,S1
12,S2
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12,S5
21,S1
21,S2
21,S3
21,S5
22,S1
22,S2
22,S3
22,S5
23,S1
23,S2
23,S3
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24,S1
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25,S1
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26,S1
26,S2
26,S3
26,S5
27,S1
27,S2
27,S3
27,S5
28,S1
28,S2
28,S3
28,S5
29,S1
29,S2
29,S3
29,S5
30,S1
30,S2
30,S3
30,S5
31,S1
31,S2
31,S3
31,S5
32,S1
32,S2
32,S3
32,S5
33,S1
33,S2
33,S3
33,S5
34,S1
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34,S3
34,S5
35,S1
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37,S3
37,S5
38,S1
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39,S1
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42,S1
42,S2
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42,S5
43,S1
43,S2
43,S3
43,S5
44,S1
44,S2
44,S3
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45,S1
45,S2
45,S3
45,S5
46,S1
46,S2
46,S3
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47,S1
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47,S3
47,S5
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48,S3
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77,S1
77,S2
77,S3
77,S5
78,S1
78,S2
78,S3
78,S5
79,S1
79,S2
79,S3
79,S5
80,S1
80,S2
80,S3
80,S5
81,S1
81,S2
81,S3
81,S5
82,S1
82,S2
82,S3
82,S5
83,S1
83,S2
83,S3
83,S5
84,S1
84,S2
84,S3
84,S5
85,S1
85,S2
85,S3
85,S5
86,S1
86,S2
86,S3
86,S5
87,S1
87,S2
87,S3
87,S5
88,S1
88,S2
88,S3
88,S5
*SURFACE,NAME=PILAR2
92,S1
92,S2
92,S3
92,S5
93,S1
93,S2
93,S3
93,S5
94,S1
94,S2
94,S3
94,S5
95,S1
95,S2
95,S3
95,S5
96,S1
96,S2
96,S3
96,S5
97,S1
97,S2
97,S3
97,S5
127,S1
127,S2
127,S3
127,S5
128,S1
128,S2
128,S3
128,S5
10,S1
10,S2
10,S3
10,S5
70,S1
70,S2
70,S3
70,S5
71,S1
71,S2
71,S3
71,S5
72,S1
72,S2
72,S3
72,S5
73,S1
73,S2
73,S3
73,S5
74,S1
74,S2
74,S3
74,S5
75,S1
75,S2
75,S3
75,S5
76,S1
76,S2
76,S3
76,S5
98,S1
98,S2
98,S3
98,S5
99,S1
99,S2
99,S3
99,S5
125,S1
125,S2
125,S3
125,S5
126,S1
126,S2
126,S3
126,S5
103,S1
103,S2
103,S3
103,S5
104,S1
104,S2
104,S3
104,S5
90,S1
90,S2
90,S3
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
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120,S1
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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
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6,4,,0
7,1,,0
7,5,,0
7,4,,0
8,1,,0
8,5,,0
8,4,,0
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10,3,,0
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10,5,,0
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127,1,,0
128,1,,0
129,1,,0
130,1,,0
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134,1,,0
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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!
who said that Ansys is 
I heard it through the grapevine 
