3. Modeling A#
3.1. Characteristics of modeling#
Beam element POU_D_T (Timoshenko’s right beam)
Cutting: beam \(\mathrm{AB}\): 120 SEG2 meshes of variable cross section.
Node names: |
Point \(A\) |
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\(x=0.1\) |
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\(x=0.2\) |
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\(x=0.3\) |
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\(x=0.4\) |
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\(x=0.5\) |
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Point \(B\) |
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3.2. Characteristics of the mesh#
Number of nodes: |
121 |
Number of meshes and types: |
120 SEG2 |
3.3. Tested sizes and results#
Clean mode order |
Frequency Reference |
% tolerance |
1 |
143.303 |
1.6 |
2 |
396.821 |
0.45 |
3 |
779.425 |
0.3 |
4 |
1289.577 |
0.9 |
The natural modes of Aster have been normalized to 1. at the point of maximum translational amplitude as in the reference.
Clean Mode \({F}_{i}(x)\) Normed to 1 at the maximum amplitude point
\(i\) |
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Reference Aster % difference % tolerance |
1 |
0.2349 0.2363 0.583 0.6 |
0.6962 0.6970 0.119 0.15 |
0.98960 0.9895 0. 0.1 |
0.8505 0.8516 0.132 0.15 |
0.3507 0.3529 0.631 0.7 |
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Reference Aster % difference % tolerance |
2 |
—0.4653 —0.4670 0.37 0.4 |
—0.7558 —0.7555 —0.041 0.1 |
0. —2.910—4 —2.910—4 1.10—3 |
0.9232 0.9226 —0.063 0.1 |
0.6941 0.6971 0.435 0.45 |
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Reference Aster % difference % tolerance |
3 |
0.6278 0.6290 0.192 0.2 |
0.1969 0.1952 —0.89 0.9 |
—0.7783 —0.7782 —0.014 0.1 |
0.2406 0.2377 —1.226 1.23 |
0.9366 0.9387 0.228 0.25 |
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Reference Aster % difference % tolerance |
4 |
—0.666 —0.6656 —0.081 0.1 |
0.4832 0.4840 0.18 0.2 |
0. 4.610—4 4.610—4 1.10—3 |
—0.5901 —0.5919 0.31 0.35 |
0.9937 0.9928 —0.089 0.1 |
3.4. notes#
Calculations made by:
CALC_MODES
OPTION = “PLUS_PETITE” CALC_FREQ =_F (NMAX_FREQ = 4) SOLVEUR_MODAL =_F (METHODE = “TRI_DIAG”)
Contents of the results file:
4 first natural frequencies, eigenvectors.