2. Benchmark solution#
2.1. Calculation method used for the reference solution#
The modal analysis is carried out with the code SAMCEF. The spectral modal analysis is carried out with the code CASTEM 2000.
2.2. Benchmark results#
Natural frequencies and modes calculated with SAMCEF.
Axial, tangential, and normal displacements along the wall located in plane \(\mathrm{xOz}\) (\(x\) and \(z\) positive) for modal recombinations \(\mathrm{CQC}\) and \(\mathrm{SRSS}\). (Calculated taking into account 4 modes).
In order to improve the identification of modes, the spectrum is evaluated with a Fourier model. This modeling was carried out with the software SAMCEF. Since the spectrum is very dense (200 modes with a frequency lower than \(7\mathit{Hz}\)), the following table only shows frequencies lower than \(4\mathrm{Hz}\). In this range, the cumulative effective mass according to \(z\) is zero.
No. h harmonic |
Frequencies (\(\mathit{Hz}\)) |
4 |
1.14 |
5 |
1.17 |
3 |
1.24 |
4 |
1.35 |
6 |
1.45 |
5 |
1.50 |
2 |
1.53 |
6 |
1.62 |
7 |
1.70 |
3 |
1.73 |
5 |
1.93 |
8 |
1.96 |
7 |
2.03 |
6 |
2.09 |
9 |
2,26 |
7 |
2,28 |
6 |
2.42 |
8 |
2.45 |
4 |
2.47 |
7 |
2.55 |
10 |
2.60 |
8 |
2.67 |
1 |
2.80 |
9 |
2,82 |
11 |
2.98 |
5 |
3.01 |
8 |
3.04 |
8 |
3,10 |
7 |
3,10 |
2 |
3,20 |
10 |
3,21 |
9 |
3,29 |
9 |
3,37 |
12 |
3.40 |
6 |
3.56 |
11 |
3.65 |
9 |
3,70 |
10 |
3,80 |
3 |
3,81 |
8 |
3.83 |
13 |
3.86 |
9 |
3,91 |
2.3. Uncertainty about the solution#
Comparisons between codes.
2.4. Bibliographical references#
The test case is based on the following reference:
P.L. GOULD and S.H. ABU - SITTA. Dynamic response of structures to wind and earthquake loading. PENTECH PRESS, 1980.