2. Benchmark solutions

2.1. Calculation method used for reference solutions

These are natural frequencies: solutions to the homogeneous problem without damping.

It is partially given in [bib1]. The resolution method, of the finite element type, concerns a POU_D_TG model. However, a series of results are provided in the event that the effects of warping twist are overlooked, bringing the modeling back to a POU_D_T.

Mode number	1	2	2	3	4	5
Frequency (\(\mathrm{Hz}\))	3,797	7,788	7,788	11,74	15,68	19,62

Table 2.1- A: Benchmark results according to [bib1]

Some confidence can be placed in these results published in a peer-reviewed journal. However, uncertainties exist if one wants to reproduce these calculations: the torsional constants \({J}_{x}\) and the shear constants \({k}_{y}\) are not provided in the article. They had to be recalculated based on the geometry of the section.

2.2. Benchmark results

Natural frequencies of the girder without damping

2.3. Uncertainty about the solution

Comparison between codes (CAILLOU [bib2] and ASTER), and analytical solution.

2.4. Bibliographical references

• WU J.S. & CHEN K.Z.: Dynamic Analysis of a channel beam due to a moving load. J. of Sound and Vibration, vol. 188, no. 3, pp 337-345, 1995.

• Code CAILLOU version 4 of October 30, 1996, IAT

• Report no. 2314/A from the Aerotechnical Institute « Proposal and implementation of new test cases missing the validation of beams ASTER »