2. Benchmark solution#
2.1. Calculation method used for reference solutions#
The reference solution is a solution obtained with Python. Indeed, two calculation methods were used to determine the frequencies. Each of the methods uses the stiffness, mass, gyroscopic, and damping matrices calculated by*Code_Aster*. To find the frequencies of the quadratic modal problem, we use:
the numpy python mathematical library (search for eigenvalues)
the CALC_MODES command
Therefore, strictly speaking, it is not a non-regression. On the other hand, for the validation of
beam elements and in the absence of elements for comparison, it is indeed a question of non-regression.
2.2. Reference quantities#
\(\mathrm{FREQ}\) frequency
\(\mathrm{AMOR}\text{\_}\mathrm{REDUIT}\): reduced amortization
2.3. Benchmark result#
As an indication, the reference results for the right Euler beam are given below.
numpy |
|
\(N°\) |
\(\mathrm{FREQ}(\mathrm{Hz})\) |
\(1\) |
\(123.915\) |
\(2\) |
\(124.546\) |
\(3\) |
\(497.033\) |
\(4\) |
\(499.575\) |
CALC_MODES |
||
\(N°\) |
\(\mathrm{FREQ}(\mathrm{Hz})\) |
\(\mathrm{AMOR}\text{\_}\mathrm{REDUIT}\) |
\(1\) |
\(123.915\) |
\(0.0\) |
\(20\) |
\(7971.6\) |
\(0.0\) |
\(40\) |
\(21163.265\) |
\(0.0\) |
\(60\) |
\(37289.789\) |
\(0.0\) |
\(80\) |
\(74712.423\) |
\(0.0\) |
2.4. Uncertainty about the solution#
Digital solution