2. Benchmark solution

2.1. Calculation method used for the reference solution

For both problems, the reference solution is that obtained by a direct calculation of the natural modes. It is thus considered that the natural modes calculated by Code_Aster with a direct calculation are subject to validation by test case SDLL01 and correspond to the analytical solution. The effective masses and participation factors from this modal base are also used as a reference for validation.

Both problems are modelled with Euler’s right beam elements: POU_D_E

Problem 1:

Cutting:	beam \(\mathit{AC}\): 20 meshes SEG2
Boundary conditions: In all the knots in \(A\): in \(C\):	DDL_IMPO =( TOUT =” OUI “, DZ=0.0, DRX =0.0, DRY =0.0,) (GROUP_NO =”A”, DX=0.0, DY=0.0) (GROUP_NO =”C”, DY=0.0,)

Problem 2 :

Cutting:	beam \(\mathit{AC}\): 20 meshes SEG2
Boundary conditions: in all nodes	DDL_IMPO =( TOUT =” OUI “, DZ=0.0, DRX =0.0, DRY =0.0,)

2.2. Benchmark results

Frequencies, effective masses and participation factors of the first 5 natural modes obtained with a direct calculation.

For both problems, it is verified that the reference quantities are indeed identical to those obtained on a modal basis of the mode_meca type resulting from a concept of the mode_gene type.

For problem 2, we also check that for the three rigid body modes:

• the sum of the effective masses corresponds to the mass of the beam,

• the sum of the effective unit masses is equal to 1.