2. Benchmark solution#
2.1. Calculation method used for the reference solution#
The reference solution is numerical: it is obtained with the software for calculating structures by finite elements SAMCEF.
The method for calculating natural frequencies is the method known as SORENSEN (algorithm by default in the CALC_MODES operator).
2.2. Benchmark results#
Since the structure has six rigid modes, we are interested in the first 10 non-zero natural frequencies.
The following table shows the values of the frequencies obtained (in \(\mathrm{Hz}\)) according to the degree of the volume elements.
Mode |
Degree 1 |
Degree 2 |
1 |
2.54231 E3 |
2.47035 E3 |
2 |
2.54231 E3 |
2.47035 E3 |
3 |
2.60747 E3 |
2.47101 E3 |
4 |
2.60747 E3 |
2.47101 E3 |
5 |
2.60747 E3 |
2.47101 E3 |
6 |
2.74095 E3 |
2.61296 E3 |
7 |
2.74095 E3 |
2.61296 E3 |
8 |
2.74095 E3 |
2.61430 E3 |
9 |
2.76313 E3 |
2.61430 E3 |
10 |
2.76313 E3 |
2.61430 E3 |