3. Modeling A#
3.1. Characteristics of modeling A#
Models POU_D_E and DIS_TR
Number of knots: 19
Number of stitches: 19 i.e. 18 SEG2 and 1 POI1
Node group:
\(\mathrm{PALIER}\text{\_}A\)
\(\mathrm{PALIER}\text{\_}B\)
3.2. Tested sizes and results#
First modal calculation: it is of type GEP **.We solve it*via* the operator CALC_MODES + SOLVEUR_MODAL =_F (METHODE =” SORENSEN “) (concept MODES).
\(N°\) |
displayed in the .mess |
Tolerance |
2 |
124.231 |
10-6 |
3 |
124.231 |
10-6 |
4 |
498.302 |
10-6 |
5 |
498.302 |
10-6 |
6 |
1118.15 |
10-6 |
7 |
1118.15 |
10-6 |
8 |
1993.47 |
10-6 |
9 |
1993.47 |
10-6 |
10 |
2021.39 |
10-6 |
11 |
2850.72 |
10-6 |
We are also testing the INFO_MODE command. Since GEP is standard (real symmetric matrices) its eigenvalues belong only to the real axis. In this case, we can therefore compare the two counting methods (COMPTAGE/METHODE =” STURM “and” APM “) and check that they actually give the same results.
We thus determine the number of eigenvalues (NB_FREQ) contained strictly in a frequency band [FREQ_MIN, FREQ_MAX] (if Sturm) or in the disk with center FREQ_CENTRE and radius, in frequency, \(\frac{\sqrt{\text{RAYON\_CONTOUR}}}{2\pi }\) (if APM). We specify the counting method used (Sturm or APM).
Concept |
FREQ_MIN/ CENTRE_CONTOUR |
RAYON_CONTOUR |
|
Counting method |
NBMOD01 |
-1.0 |
120.0 |
1 We count \({\lambda }_{1}\). |
Sturm |
NBMOD02 |
-1.0 |
130.0 |
3 We count \({({\lambda }_{i})}_{\text{i=1,3}}\). |
Sturm |
NBMOD03 |
-1.0 |
1200.0 |
7 We count \({({\lambda }_{i})}_{\text{i=1,7}}\). |
Sturm |
NBMOD11 |
0.0+0.0j |
5.684 105 |
||
(= \({(\mathrm{120x2}\pi )}^{2}\)) » |
1 Same NBMOD01 |
|
||
NBMOD12 |
0.0+0.0j |
6.671 105 |
||
(= \({(\mathrm{130x2}\pi )}^{2}\)) » |
3 Same NBMOD02 |
|
||
NBMOD13 |
0.0+0.0j |
5.684 107 |
||
(= \({(\mathrm{1200x2}\pi )}^{2}\)) » |
7 Same NBMOD03 |
|
Second modal calculation: it is of type QEP *.**It is solved*via using the CALC_MODES + SOLVEUR_MODAL =_F (METHODE =”QZ”) operator (=”QZ”) (concept MODEQ).
\(N°\) [1] _ |
\(\mathrm{FREQ}(\mathrm{Hz})\) displayed in .mess (= \(\frac{\mathrm{\Im }({\lambda }_{i})}{2\pi }\)) |
\(\mathit{AMORTISSEMENT}\) displayed in .mess (= \(\frac{\mathrm{-}\mathrm{\Re }({\lambda }_{i})}{\mathrm{\mid }{\lambda }_{i}\mathrm{\mid }}\)) |
Eigenvalue module (= \(\mathrm{\mid }{\lambda }_{i}\mathrm{\mid }\)) |
Tolerance |
Not applicable |
Not included in Code_Aster because true eigenvalue |
Not applicable |
0 |
Not applicable |
Not applicable |
Not included in Code_Aster because true eigenvalue |
Not applicable |
0 |
Not applicable |
1 |
123.915 + the conjugate complex |
10-11 |
778.5 |
0.5 |
2 |
124.546 + the conjugate complex |
10-09 |
782.5 |
0.5 |
|
|
|
|
… |
10 |
2850.72 + the conjugate complex |
10-15 |
18849.5 |
0.5 |
11 |
3099.17 + the conjugate complex |
10-11 |
19472.6 |
0.5 |
|
|
|
|
… |
41 |
21273.2 + the conjugate complex |
10-12 |
133663.4 |
0.5 |
42 |
21380.2 + the conjugate complex |
10-12 |
134335.7 |
0.5 |
|
|
|
|
… |
We are also testing the INFO_MODE command. Since it is a QEP with real matrices, its eigenvalues are either real or complex conjugate. So we can only use the APM method here. It determines the number of eigenvalues (NB_FREQ) contained here strictly in the disk with center CENTRE_CONTOUR and radius RAYON_CONTOUR.
Concept |
CENTRE_CONTOUR |
|
|
Enumeration method |
|
NBMOD04 |
0.0+0.0j |
779.114 (= \(\mathrm{124x2}\pi\)) |
4 We count the 2 zero values + the \(({\lambda }_{\mathrm{1,}}\stackrel{ˉ}{{\lambda }_{1}})\) couple. |
|
|
NBMOD05 |
0.0+779.114j (= \(0.0+\mathrm{124x2}\pi j\)) |
7 |
2 We count the 2 values \({\lambda }_{1}\) and \({\lambda }_{2}\) without their conjugate. |
|
|
NBMOD06 |
0.0+0.0j |
1.884 104 |
|||
(= \(\mathrm{3000x2}\pi\)) » |
22 We count the 2 zero values + the \({({\lambda }_{i},\stackrel{ˉ}{{\lambda }_{i}})}_{\text{i=1,10}}\) couples. |
|
|||
NBMOD07 |
0.0+0.0j |
1.338 105 |
|||
(= \(\mathrm{21300x2}\pi\)) » |
84 We count the 2 zero values + the \({({\lambda }_{i},\stackrel{ˉ}{{\lambda }_{i}})}_{\text{i=1,41}}\) couples. |
|
|||
NBMOD08 |
779.114 (1.0+j) (= \(\mathrm{124x2}\pi (1.0+j)\)) |
701.203 (= \(\mathrm{0.9x}\mathrm{124x2}\pi\)) |
0 |
|