Refine Nodal Mesh
Refinement of Nodal Mesh based on Mass Modeling Frequency
The purpose of this feature is to ensure that there are a sufficient number of mass points for an accurate dynamic model for the dynamic loading under consideration.
Intermediate mass points along a span are generated based on the free vibration of an equivalent simply supported beam. Optimum element length is calculated from:

Lopt = Optimum length required to capture the span dynamic behavior
f = mass modeling frequency
g = acceleration due to gravity
E = modulus of elasticity of pipe material
Although the above equation is valid for any temperature, to generate intermediate nodes, E is taken at the reference temperature entered in CAEPIPE.
I = moment of inertia of pipe cross section
w = weight per unit length of pipe (including insulation, lining and content)
Intermediate mass points can be automatically generated in CAEPIPE by selecting the radio button “Dynamic Analysis” through Layout window > Edit > Refine Nodal Mesh. Enter the Mass modeling Frequency in the dialog box shown and press the button “OK”. See figures shown below for details.


While refining the Nodal Mesh, the new node numbers will be generated by adding the node increment specified through Layout window > Options > Node increment to get the new node numbers (without affecting the original node numbers used in the Layout window). Hence, set the node increment value as required before refining the Nodal Mesh.
Upon refining the Nodal Mesh based on Mass modeling frequency, CAEPIPE will prompt for renumbering of nodes as shown below.


Press the button “Yes” to renumber the nodes and enter the details required by CAEPIPE in the dialog box. See snap shot shown above.
Example
A sample CAEPIPE model (with graphics and layout details as shown below) was chosen for verification of implementation. Modal analysis was then performed by defining the cut-off frequency and number of modes as “110 Hz” and 175 respectively in the CAEPIPE model through Layout window > Options > Analysis > Dynamics with the node points as defined by the stress analyst.

Wireframe layout without addition of mass points

Rendered layout without addition of mass points
Caepipe dynamic_model_original Page 1
Version 8.00 May 30,2018
-----------------------------------------------------------------------------------
Options
-----------------------------------------------------------------------------------
Piping code = B31.3 (2016)
Do not use liberal allowable stresses
Include axial force in stress calculations
Reference temperature = 40 (F)
Number of thermal cycles = 7000
Number of thermal loads = 1
Thermal = Operating - Sustained
Use modulus at reference temperature
Include hanger stiffness
Include Bourdon effect
Use pressure correction for bends
Pressure stress = PD / 4t
Peak pressure factor = 1.00
Cut off frequency = 110 Hz
Number of modes = 175
Include missing mass correction
Use friction in dynamic analysis
Vertical direction = Y
-----------------------------------------------------------------------------------
# Node Type DX(ft'in") DY(ft'in") DZ(ft'in") Mat Sec Load Data
-----------------------------------------------------------------------------------
1 Title =
2 10 From Anchor
3 20 Bend 11'0" API 54I 54I
4 30 -20'0" API 54I 54I
5 40 Bend -10'9" API 54I 54I
6 50 9'0" API 54I 54I Y restraint
7 60 2'0" API 54O 54O
8 65 10'0" API 54O 54O
9 70 12'0" API 54O 54O Y restraint
10 75 12'0" API 54O 54O
11 80 12'0" API 54O 54O Y restraint
12 85 12'0" API 54O 54O
13 90 12'0" API 54O 54O Y restraint
14 100 11'0" API 54O 54O
15 110 3'0" API 54O 54O Anchor
16 120 3'0" API 54O 54O
17 130 Reducer 3'0" API 54O 54O
18 140 Bend 3'8" API 36I 36I
19 150 Bend 2'11" -4'6" 4'6" API 36I 36I
20 160 6'0" API 36I 36I Y restraint
21 165 7'0" API 36I 36I
22 170 7'0" API 36I 36I Y restraint
23 180 Bend 6'0" API 36I 36I
24 190 7'3" API 36I 36I Y restraint
25 200 12'0" API 36I 36I Y restraint
26 210 12'0" API 36I 36I
27 220 12'0" API 36I 36I Y restraint
28 230 Bend 4'5" API 36I 36I
29 240 4'5" API 36I 36I Y restraint
30 250 12'0" API 36I 36I
31 260 12'0" API 36I 36I Y restraint
32 270 12'0" API 36I 36I
33 280 12'0" API 36I 36I XY restraint
Caepipe dynamic_model_original Page 2
Version 8.00 May 30,2018
-----------------------------------------------------------------------------------
# Node Type DX(ft'in") DY(ft'in") DZ(ft'in") Mat Sec Load Data
-----------------------------------------------------------------------------------
34 290 12'0" API 36I 36I
35 300 12'0" API 36I 36I Y restraint
36 310 12'0" API 36I 36I
37 320 12'0" API 36I 36I Y restraint
38 330 16'0" API 36I 36I XY restraint
39 340 12'0" API 36I 36I
40 350 12'0" API 36I 36I Y restraint
41 360 12'0" API 36I 36I
42 370 12'0" API 36I 36I Y restraint
43 380 12'0" API 36I 36I
44 390 12'0" API 36I 36I XY restraint
45 400 12'0" API 36I 36I
46 410 12'0" API 36I 36I Y restraint
47 420 12'0" API 36I 36I
48 430 12'0" API 36I 36I Y restraint
49 440 12'0" API 36I 36I
50 450 12'0" API 36I 36I XY restraint
51 460 12'0" API 36I 36I
52 470 12'0" API 36I 36I Y restraint
53 480 12'0" API 36I 36I
54 490 12'0" API 36I 36I Y restraint
55 500 12'0" API 36I 36I
56 510 12'0" API 36I 36I Anchor
57 520 12'0" API 36I 36I
58 530 12'0" API 36I 36I Y restraint
59 540 12'0" API 36I 36I
60 550 12'0" API 36I 36I Y restraint
61 560 Bend 4'5" API 36I 36I
62 570 -4'5" API 36I 36I Y restraint
63 580 -12'0" API 36I 36I
64 590 -11'7" API 36I 36I Y restraint
65 600 -12'0" API 36I 36I
66 610 -12'0" API 36I 36I XY restraint
67 620 -12'0" API 36I 36I
68 630 -12'0" API 36I 36I Anchor
69 640 -12'0" API 36I 36I
70 650 -12'0" API 36I 36I XY restraint
71 660 -12'0" API 36I 36I
72 670 -10'0" API 36I 36I Y restraint
73 680 -13'0" API 36I 36I Y restraint
74 690 Bend -9'0" API 36I 36I
75 700 7'11" API 36I 36I Y restraint
76 710 12'0" API 36I 36I Anchor
77 100 From
78 720 Bend 10'9" API 36O 36O
79 730 7'0" API 36O 36O Y restraint
80 740 Bend 9'0" API 36O 36O
81 750 16'9" API 36O 36O
82 760 26'11" API 36O 36O
83 770 Bend 5'8" API 36O 36O
84 780 6'0" API 36O 36O Y restraint
85 790 12'0" API 36O 36O Anchor
-----------------------------------------------------------------------------------
Caepipe dynamic_model_original Page 43
Version 8.00 May 30,2018
-----------------------------------------------------------------------------------
Anchors
-----------------------------------------------------------------------------------
(lb/inch) (in-lb/deg) Releases Anchor
Node KX/kx KY/ky KZ/kz KXX/kxx KYY/kyy KZZ/kzz X Y Z XXYYZZ In Pipe
-----------------------------------------------------------------------------------
10 Rigid Rigid Rigid Rigid Rigid Rigid GCS
110 Rigid Rigid Rigid Rigid Rigid Rigid GCS
510 Rigid Rigid Rigid Rigid Rigid Rigid GCS
630 Rigid Rigid Rigid Rigid Rigid Rigid GCS
710 Rigid Rigid Rigid Rigid Rigid Rigid GCS
790 Rigid Rigid Rigid Rigid Rigid Rigid GCS
-----------------------------------------------------------------------------------
Bends
-----------------------------------------------------------------------------------
Bend Radius Thickness Bend Flex. Int. Angle Int. Angle
Node (inch) (inch) Matl Factor Node (deg) Node (deg)
-----------------------------------------------------------------------------------
20 81 L
40 81 L
140 54 L
150 54 L
180 54 L
230 48 U
560 48 U
690 48 U
720 54 L
740 54 L
770 54 L
-----------------------------------------------------------------------------------
Reducers
-----------------------------------------------------------------------------------
OD1 Thk1 OD2 Thk2 Cone Angle Knuc Delta
From To (inch) (inch) (inch) (inch) (deg) kles (inch)
-----------------------------------------------------------------------------------
120 130 54 0.375 36 0.375
-----------------------------------------------------------------------------------
Restraints
-----------------------------------------------------------------------------------
Node X Y Z
-----------------------------------------------------------------------------------
50 Yes
70 Yes
80 Yes
90 Yes
160 Yes
170 Yes
190 Yes
200 Yes
220 Yes
240 Yes
260 Yes
280 Yes Yes
300 Yes
320 Yes
330 Yes Yes
350 Yes
Caepipe dynamic_model_original Page 4
Version 8.00 May 30,2018
-----------------------------------------------------------------------------------
Restraints
-----------------------------------------------------------------------------------
Node X Y Z
-----------------------------------------------------------------------------------
370 Yes
390 Yes Yes
410 Yes
430 Yes
450 Yes Yes
470 Yes
490 Yes
530 Yes
550 Yes
570 Yes
590 Yes
610 Yes Yes
650 Yes Yes
670 Yes
680 Yes
700 Yes
730 Yes
780 Yes
-----------------------------------------------------------------------------------
Pipe material API: API 5L Grade B
-----------------------------------------------------------------------------------
Density = 0.283 (lb/in3), Nu = 0.300, Joint factor = 1.00, Type = CS
Yield strength = 35000 (psi)
Temp E Alpha Allowable
(F) (psi) (in/in/F) (psi)
-------------------------------------------
-325 31.4E+6 5.00E-6 20000
-200 30.8E+6 5.35E-6 20000
-100 30.2E+6 5.65E-6 20000
70 29.5E+6 6.07E-6 20000
200 28.8E+6 6.38E-6 20000
300 28.3E+6 6.60E-6 20000
400 27.7E+6 6.82E-6 19900
500 27.3E+6 7.02E-6 19000
600 26.7E+6 7.23E-6 17900
650 26.1E+6 7.33E-6 17300
700 25.5E+6 7.44E-6 16700
750 24.8E+6 7.54E-6 13900
800 24.2E+6 7.65E-6 11400
850 23.3E+6 7.75E-6 8700
900 22.4E+6 7.84E-6 5900
950 21.4E+6 7.91E-6 4000
1000 20.4E+6 7.97E-6 2500
1050 19.2E+6 8.05E-6 1600
1100 18.0E+6 8.12E-6 1000
-----------------------------------------------------------------------------------
Caepipe dynamic_model_original Page 5
Version 8.00 May 30,2018
-----------------------------------------------------------------------------------
Pipe Sections
-----------------------------------------------------------------------------------
Nominal O.D. Thk Cor.Al M.Tol Ins.Dens Ins.Th Lin.Dens Lin.Th
Name Dia. Sch (inch) (inch) (inch) (%) (lb/ft3) (inch) (lb/ft3) (inch)
-----------------------------------------------------------------------------------
36I 36" STD 36 0.375 0 0.0
36O 36" STD 36 0.375 0 0.0
54O Non Std 54 0.375 0 0.0
54I Non Std 54 0.375 0 0.0
-----------------------------------------------------------------------------------
Loads
-----------------------------------------------------------------------------------
Static seismic load: X = -0.20, Y = -0.20, Z = -0.20 (g's)
Acceleration load combination = Square Root of Sum of Squares
X spectrum: Malta, NY_b Factor = 1.0000
Y spectrum: Malta, NY_b Factor = 0.0430
Z spectrum: Malta, NY_b Factor = 1.0000
Mode sum = SRSS Direction sum = SRSS
-----------------------------------------------------------------------------------
Wind Load 1
-----------------------------------------------------------------------------------
Shape factor = 0.60
Wind direction: X comp = 0.000, Y comp = 0.000, Z comp = 1.000
Elevation Pressure
(feet) (psf)
0 15
15 15
30 15
45 15
60 15
-----------------------------------------------------------------------------------
Pipe Loads
-----------------------------------------------------------------------------------
Load T1 P1 T2 P2 T3 P3 Specific Add.Wgt Wind
Name (F) (psi) (F) (psi) (F) (psi) gravity (lb/ft) Load
-----------------------------------------------------------------------------------
36O 100 125 Y
36I 100 125
54O 100 125 Y
54I 100 125
-----------------------------------------------------------------------------------
From the Modal Analysis results shown below, it was noted that the CAEPIPE was able to extract 92 modes with highest frequency being 95.967 Hz.
Caepipe dynamic_model_original Page 1
Version 8.00 May 30,2018
-----------------------------------------------------------------------------------
Frequency Period Participation factors Modal mass / Total mass
Mode (Hz) (sec) X Y Z X Y Z
-----------------------------------------------------------------------------------
1 1.875 0.5335 -5.7615 -0.0004 0.5255 0.0979 0.0000 0.0008
2 3.288 0.3041 -6.7721 -0.0000 0.0003 0.1353 0.0000 0.0000
3 5.971 0.1675 -4.1919 0.0000 -0.0001 0.0518 0.0000 0.0000
4 6.147 0.1627 0.0909 -0.0000 -0.1021 0.0000 0.0000 0.0000
5 7.800 0.1282 -0.4240 -0.0000 4.5032 0.0005 0.0000 0.0598
6 8.102 0.1234 0.0029 0.0001 0.3321 0.0000 0.0000 0.0003
7 9.933 0.1007 0.0861 -0.0000 -4.2655 0.0000 0.0000 0.0537
8 10.146 0.0986 -0.6501 0.0002 1.6688 0.0012 0.0000 0.0082
9 10.241 0.0976 -2.1689 -0.0000 0.0048 0.0139 0.0000 0.0000
10 11.279 0.0887 3.2684 -0.0002 -7.9718 0.0315 0.0000 0.1874
11 11.628 0.0860 6.7199 -0.0002 5.8034 0.1332 0.0000 0.0993
12 13.116 0.0762 -0.0013 1.4576 -3.8221 0.0000 0.0063 0.0431
13 13.276 0.0753 2.6364 0.0000 -0.0001 0.0205 0.0000 0.0000
14 13.931 0.0718 3.3527 0.0030 -3.2879 0.0332 0.0000 0.0319
15 16.027 0.0624 -3.6866 0.0000 -0.3181 0.0401 0.0000 0.0003
16 16.038 0.0624 -2.9281 -0.0001 -0.7810 0.0253 0.0000 0.0018
17 17.802 0.0562 -1.8832 0.0179 2.3004 0.0105 0.0000 0.0156
18 21.780 0.0459 0.0000 2.7930 3.3879 0.0000 0.0230 0.0339
19 22.412 0.0446 -0.0006 -3.2159 -1.3274 0.0000 0.0305 0.0052
20 22.683 0.0441 -0.3117 -0.0005 0.0747 0.0003 0.0000 0.0000
21 24.003 0.0417 -0.5955 -0.0000 0.1696 0.0010 0.0000 0.0001
22 24.910 0.0401 2.7763 -0.0000 -0.0070 0.0227 0.0000 0.0000
23 26.421 0.0378 -0.2314 0.0001 0.1348 0.0002 0.0000 0.0001
24 27.698 0.0361 -1.3316 0.0000 -0.0002 0.0052 0.0000 0.0000
25 29.713 0.0337 -1.2585 -0.0000 -0.0049 0.0047 0.0000 0.0000
26 30.079 0.0332 -0.3437 0.0000 -0.1955 0.0003 0.0000 0.0001
27 30.146 0.0332 0.0215 -0.0001 0.3494 0.0000 0.0000 0.0004
28 31.946 0.0313 -0.6062 0.0012 -1.6290 0.0011 0.0000 0.0078
29 33.670 0.0297 0.9928 -0.0040 2.8297 0.0029 0.0000 0.0236
30 36.072 0.0277 0.0014 1.4997 -2.1277 0.0000 0.0066 0.0134
31 37.812 0.0264 -0.4989 -0.0074 2.1572 0.0007 0.0000 0.0137
32 39.097 0.0256 1.2371 -0.0000 -0.0086 0.0045 0.0000 0.0000
33 41.172 0.0243 -0.0001 1.2001 -6.2487 0.0000 0.0042 0.1152
34 41.250 0.0242 -0.3414 -0.0000 1.6185 0.0003 0.0000 0.0077
35 42.488 0.0235 0.7544 -0.0001 -0.0047 0.0017 0.0000 0.0000
36 43.804 0.0228 -0.4830 0.0108 1.2389 0.0007 0.0000 0.0045
37 46.065 0.0217 -0.0011 0.0686 -0.0001 0.0000 0.0000 0.0000
38 46.766 0.0214 -0.0098 -0.5622 -0.0023 0.0000 0.0009 0.0000
39 47.504 0.0211 -0.2337 -0.0029 -0.2475 0.0002 0.0000 0.0002
40 49.063 0.0204 0.0015 0.3511 0.0007 0.0000 0.0004 0.0000
41 49.295 0.0203 -0.0000 -1.0018 -0.0000 0.0000 0.0030 0.0000
42 49.985 0.0200 1.3732 -0.0000 -1.3809 0.0056 0.0000 0.0056
43 50.052 0.0200 -0.1938 0.0000 -1.9635 0.0001 0.0000 0.0114
44 52.178 0.0192 -0.9811 -0.0281 -0.6345 0.0028 0.0000 0.0012
45 52.335 0.0191 0.0000 -0.8918 -0.0000 0.0000 0.0023 0.0000
46 53.313 0.0188 -0.0715 -1.0283 -0.1169 0.0000 0.0031 0.0000
47 53.496 0.0187 -1.0974 -0.0751 -1.8548 0.0036 0.0000 0.0101
48 54.481 0.0184 0.0407 -1.8917 0.0845 0.0000 0.0106 0.0000
49 56.408 0.0177 0.4159 -1.3502 0.0358 0.0005 0.0054 0.0000
50 56.457 0.0177 2.6140 0.2176 -0.1253 0.0202 0.0001 0.0000
51 56.920 0.0176 1.8036 0.0012 0.0177 0.0096 0.0000 0.0000
52 57.929 0.0173 -0.2764 -0.0033 -0.0311 0.0002 0.0000 0.0000
53 58.372 0.0171 -1.1204 0.0366 0.3623 0.0037 0.0000 0.0004
Caepipe dynamic_model_original Page 2
Version 8.00 May 30,2018
-----------------------------------------------------------------------------------
Frequency Period Participation factors Modal mass / Total mass
Mode (Hz) (sec) X Y Z X Y Z
-----------------------------------------------------------------------------------
54 58.736 0.0170 0.0013 -0.4068 0.0005 0.0000 0.0005 0.0000
55 62.338 0.0160 -0.0004 1.7473 2.3502 0.0000 0.0090 0.0163
56 63.166 0.0158 1.4680 0.0042 1.3132 0.0064 0.0000 0.0051
57 63.180 0.0158 1.1531 0.0001 -1.1840 0.0039 0.0000 0.0041
58 63.512 0.0157 0.0000 -0.1612 0.0000 0.0000 0.0001 0.0000
59 64.003 0.0156 -0.0020 -0.5988 0.0007 0.0000 0.0011 0.0000
60 64.339 0.0155 -0.0000 -1.1254 0.0000 0.0000 0.0037 0.0000
61 65.107 0.0154 -1.0551 -0.0210 1.1888 0.0033 0.0000 0.0042
62 65.192 0.0153 0.0016 0.3043 0.5961 0.0000 0.0003 0.0010
63 65.893 0.0152 -0.0078 -0.0572 0.0105 0.0000 0.0000 0.0000
64 69.245 0.0144 -0.0005 -0.9214 0.0006 0.0000 0.0025 0.0000
65 70.044 0.0143 -2.3140 -0.0000 -1.0324 0.0158 0.0000 0.0031
66 70.911 0.0141 -3.2315 -0.0000 -1.9392 0.0308 0.0000 0.0111
67 73.355 0.0136 -0.9182 0.2454 0.2391 0.0025 0.0002 0.0002
68 73.445 0.0136 -0.0085 1.5999 0.0018 0.0000 0.0075 0.0000
69 74.015 0.0135 0.0021 1.9142 0.0703 0.0000 0.0108 0.0000
70 74.156 0.0135 -0.0000 2.9214 -0.0000 0.0000 0.0252 0.0000
71 74.905 0.0134 0.0017 -3.8949 0.0017 0.0000 0.0447 0.0000
72 76.249 0.0131 -0.1108 0.0489 0.0287 0.0000 0.0000 0.0000
73 76.553 0.0131 0.0001 1.4453 0.0002 0.0000 0.0062 0.0000
74 76.599 0.0131 0.0000 3.2442 0.0000 0.0000 0.0310 0.0000
75 78.151 0.0128 -0.0001 -5.7802 -0.0001 0.0000 0.0985 0.0000
76 78.399 0.0128 0.1428 -1.8259 0.2005 0.0001 0.0098 0.0001
77 79.572 0.0126 -0.0000 -3.1388 -0.0000 0.0000 0.0291 0.0000
78 80.352 0.0124 -0.0611 -0.0303 0.0321 0.0000 0.0000 0.0000
79 80.590 0.0124 -0.4718 0.0055 -0.0030 0.0007 0.0000 0.0000
80 81.366 0.0123 0.0014 -1.7246 1.7171 0.0000 0.0088 0.0087
81 81.537 0.0123 -0.6787 0.0000 2.6001 0.0014 0.0000 0.0199
82 83.538 0.0120 2.6049 -0.0000 0.2580 0.0200 0.0000 0.0002
83 83.555 0.0120 0.0186 0.0064 -0.0224 0.0000 0.0000 0.0000
84 85.143 0.0117 -0.9456 0.0093 -0.0136 0.0026 0.0000 0.0000
85 86.260 0.0116 -0.0033 -0.7082 1.6260 0.0000 0.0015 0.0078
86 86.553 0.0116 0.1187 -0.0708 1.3196 0.0000 0.0000 0.0051
87 87.389 0.0114 -0.0038 -0.2207 -0.7108 0.0000 0.0001 0.0015
88 87.678 0.0114 1.8995 -0.0000 -1.1843 0.0106 0.0000 0.0041
89 90.219 0.0111 -0.3088 -0.2777 -0.2039 0.0003 0.0002 0.0001
90 93.121 0.0107 -0.5735 -0.1326 0.4279 0.0010 0.0001 0.0005
91 95.224 0.0105 0.0000 4.5908 0.5409 0.0000 0.0622 0.0009
92 95.967 0.0104 0.7252 -0.0000 -0.6981 0.0016 0.0000 0.0014
-------------------------------
Total 0.7887 0.4496 0.8526
----------------------------------------------------------------------------------
Now, the original model shown above was refined through the feature Layout window > Edit > Refine Nodal Mesh. The Mass modeling frequency was set to 110 Hz for refining the mesh for “Dynamic Analysis” as shown below.

The resulting refined model with additional mass points added by CAEPIPE is shown in the snap shots below.




Modal analysis was then performed using CAEPIPE for the refined model (with additional mass points automatically added) for mass modeling frequency 110 Hz and found that the CAEPIPE was able to extract all the modes below the cut-off frequency 110 Hz specified in the analysis options. Please see the modal analysis results obtained from CAEPIPE shown below.
Caepipe dynamic_model_refined Page 1
Version 8.00 May 30,2018
-----------------------------------------------------------------------------------
Frequency Period Participation factors Modal mass / Total mass
Mode (Hz) (sec) X Y Z X Y Z
-----------------------------------------------------------------------------------
1 1.755 0.5698 -5.7696 -0.0003 0.5155 0.0982 0.0000 0.0008
2 2.855 0.3502 6.7662 0.0000 -0.0002 0.1350 0.0000 0.0000
3 5.521 0.1811 -4.1344 0.0000 -0.0001 0.0504 0.0000 0.0000
4 6.151 0.1626 0.0878 -0.0000 -0.1088 0.0000 0.0000 0.0000
5 7.722 0.1295 0.4309 0.0000 -4.5502 0.0005 0.0000 0.0611
6 8.119 0.1232 0.0315 0.0001 0.3840 0.0000 0.0000 0.0004
7 9.824 0.1018 0.0839 -0.0000 -4.3165 0.0000 0.0000 0.0550
8 10.063 0.0994 2.3014 0.0000 0.0054 0.0156 0.0000 0.0000
9 10.134 0.0987 -0.6185 0.0003 2.3174 0.0011 0.0000 0.0158
10 11.111 0.0900 2.0288 0.0003 -8.3004 0.0121 0.0000 0.2032
11 11.613 0.0861 -7.1492 0.0006 -4.4135 0.1508 0.0000 0.0575
12 12.635 0.0791 -0.0006 1.5513 -3.8503 0.0000 0.0071 0.0437
13 13.233 0.0756 2.6877 0.0000 -0.0007 0.0213 0.0000 0.0000
14 13.640 0.0733 2.9690 0.0034 -4.0182 0.0260 0.0000 0.0476
15 15.725 0.0636 3.7891 -0.0000 0.3498 0.0423 0.0000 0.0004
16 15.805 0.0633 3.1354 0.0024 0.9356 0.0290 0.0000 0.0026
17 16.409 0.0609 2.2658 -0.0169 -2.5046 0.0151 0.0000 0.0185
18 17.349 0.0576 -0.0000 -2.7191 -3.1311 0.0000 0.0218 0.0289
19 20.661 0.0484 0.0007 3.2479 1.4079 0.0000 0.0311 0.0058
20 22.737 0.0440 0.2479 0.0001 -0.0877 0.0002 0.0000 0.0000
21 23.733 0.0421 0.7055 -0.0000 -0.0963 0.0015 0.0000 0.0000
22 23.782 0.0420 -2.9878 0.0000 0.0053 0.0263 0.0000 0.0000
23 26.507 0.0377 0.1027 0.0005 -0.1910 0.0000 0.0000 0.0001
24 27.187 0.0368 -0.6336 0.0000 -0.0045 0.0012 0.0000 0.0000
25 29.021 0.0345 -1.1191 0.0000 0.0002 0.0037 0.0000 0.0000
26 29.061 0.0344 0.3323 -0.0000 0.1679 0.0003 0.0000 0.0001
27 30.289 0.0330 -0.4261 0.0036 -1.0079 0.0005 0.0000 0.0030
28 31.215 0.0320 1.0457 -0.0087 2.3123 0.0032 0.0000 0.0158
29 33.583 0.0298 0.4478 -0.0064 1.5750 0.0006 0.0000 0.0073
30 36.362 0.0275 -1.1690 0.0000 -0.0052 0.0040 0.0000 0.0000
31 37.505 0.0267 -0.0033 1.4151 -2.1430 0.0000 0.0059 0.0135
32 37.885 0.0264 0.4183 0.0121 -2.4989 0.0005 0.0000 0.0184
33 40.194 0.0249 0.1951 -0.0000 -1.5005 0.0001 0.0000 0.0066
34 40.968 0.0244 0.0001 -1.1979 6.4128 0.0000 0.0042 0.1213
35 43.038 0.0232 0.3511 -0.0019 -1.2983 0.0004 0.0000 0.0050
36 43.372 0.0231 -0.4795 0.0000 -0.0105 0.0007 0.0000 0.0000
37 46.870 0.0213 0.0021 -0.0008 0.0010 0.0000 0.0000 0.0000
38 47.541 0.0210 -0.0144 -0.7462 -0.0080 0.0000 0.0016 0.0000
39 48.377 0.0207 -0.2963 -0.0021 -0.3487 0.0003 0.0000 0.0004
40 50.010 0.0200 -0.4830 0.0001 -1.8955 0.0007 0.0000 0.0106
41 50.132 0.0199 -0.0043 -0.3850 -0.0040 0.0000 0.0004 0.0000
42 50.285 0.0199 0.0000 1.2526 0.0000 0.0000 0.0046 0.0000
43 51.219 0.0195 1.2828 0.0000 -1.6462 0.0049 0.0000 0.0080
44 51.778 0.0193 1.4654 0.0565 1.8643 0.0063 0.0000 0.0103
45 53.561 0.0187 0.0000 -1.1367 -0.0000 0.0000 0.0038 0.0000
46 53.672 0.0186 -0.1396 0.0329 0.4238 0.0001 0.0000 0.0005
47 54.731 0.0183 0.0027 -1.2178 0.0180 0.0000 0.0044 0.0000
48 56.221 0.0178 -0.0024 -2.0037 0.0429 0.0000 0.0118 0.0000
49 57.051 0.0175 -1.6501 -0.0050 -0.0543 0.0080 0.0000 0.0000
50 57.365 0.0174 -0.2648 -0.0208 0.4221 0.0002 0.0000 0.0005
51 58.161 0.0172 -0.0620 -1.7053 0.0076 0.0000 0.0086 0.0000
52 58.480 0.0171 -2.8218 0.0672 0.2197 0.0235 0.0000 0.0001
53 59.590 0.0168 0.0011 -1.6797 -2.3900 0.0000 0.0083 0.0168
Caepipe dynamic_model_refined Page 2
Version 8.00 May 30,2018
-----------------------------------------------------------------------------------
Frequency Period Participation factors Modal mass / Total mass
Mode (Hz) (sec) X Y Z X Y Z
-----------------------------------------------------------------------------------
54 59.697 0.0168 1.3631 -0.0003 -0.0002 0.0055 0.0000 0.0000
55 60.969 0.0164 -0.0001 1.4746 0.5326 0.0000 0.0064 0.0008
56 61.166 0.0163 -0.0003 0.3240 -0.0009 0.0000 0.0003 0.0000
57 63.791 0.0157 1.1014 -0.0167 1.6815 0.0036 0.0000 0.0083
58 65.476 0.0153 0.0000 -0.0239 -0.0000 0.0000 0.0000 0.0000
59 66.097 0.0151 -2.0302 -0.0513 0.5933 0.0122 0.0000 0.0010
60 66.996 0.0149 0.6629 0.0000 -1.1896 0.0013 0.0000 0.0042
61 67.413 0.0148 0.0051 -0.4949 -0.0031 0.0000 0.0007 0.0000
62 67.702 0.0148 0.0000 -1.4164 -0.0000 0.0000 0.0059 0.0000
63 69.973 0.0143 -0.0065 -0.2969 0.0052 0.0000 0.0003 0.0000
64 70.117 0.0143 0.0002 -2.2385 0.7487 0.0000 0.0148 0.0017
65 70.175 0.0143 -2.4152 -0.0000 -0.9261 0.0172 0.0000 0.0025
66 74.234 0.0135 3.4185 0.0003 1.5639 0.0345 0.0000 0.0072
67 74.560 0.0134 0.0042 1.0701 -0.0017 0.0000 0.0034 0.0000
68 74.843 0.0134 -1.3329 0.8236 0.1534 0.0052 0.0020 0.0001
69 76.927 0.0130 -0.4107 -1.5744 0.2386 0.0005 0.0073 0.0002
70 78.576 0.0127 -0.1023 0.0017 -0.0013 0.0000 0.0000 0.0000
71 80.082 0.0125 0.0006 -0.5746 1.6438 0.0000 0.0010 0.0080
72 80.485 0.0124 0.0002 -2.1498 0.0002 0.0000 0.0136 0.0000
73 81.701 0.0122 -0.2466 -0.0537 0.0757 0.0002 0.0000 0.0000
74 81.749 0.0122 -0.0002 3.4973 0.0000 0.0000 0.0361 0.0000
75 82.787 0.0121 -0.0004 4.3124 -0.0023 0.0000 0.0549 0.0000
76 84.316 0.0119 1.6969 0.0000 -3.1197 0.0085 0.0000 0.0287
77 85.065 0.0118 -0.0026 -0.4712 0.8256 0.0000 0.0007 0.0020
78 85.440 0.0117 0.0000 3.7852 -0.0000 0.0000 0.0423 0.0000
79 85.507 0.0117 -0.0001 1.4996 0.0009 0.0000 0.0066 0.0000
80 87.100 0.0115 -0.0680 0.0853 -1.2077 0.0000 0.0000 0.0043
81 87.358 0.0114 -0.0000 3.5186 -0.0000 0.0000 0.0365 0.0000
82 87.548 0.0114 1.1884 -0.0035 -0.0409 0.0042 0.0000 0.0000
83 87.820 0.0114 0.1975 -0.0174 0.6688 0.0001 0.0000 0.0013
84 88.217 0.0113 -0.0001 6.8293 -0.0003 0.0000 0.1376 0.0000
85 88.587 0.0113 0.0003 -0.6062 -1.1192 0.0000 0.0011 0.0037
86 89.553 0.0112 2.9233 -0.0000 0.1706 0.0252 0.0000 0.0001
87 91.995 0.0109 -0.2639 -0.2144 -0.3238 0.0002 0.0001 0.0003
88 92.948 0.0108 0.1126 0.0508 0.0909 0.0000 0.0000 0.0000
89 93.055 0.0107 1.1698 -0.0041 0.6341 0.0040 0.0000 0.0012
90 102.283 0.0098 0.0000 -0.0302 -0.0000 0.0000 0.0000 0.0000
91 103.208 0.0097 0.0131 5.0475 0.3381 0.0000 0.0751 0.0003
92 103.322 0.0097 -0.6291 -0.0242 0.3139 0.0012 0.0000 0.0003
93 109.288 0.0092 -0.7946 -0.1550 0.6055 0.0019 0.0001 0.0011
94 110.299 0.0091 1.2405 -0.0000 0.3050 0.0045 0.0000 0.0003
-------------------------------
Total 0.8148 0.5606 0.8574