4. B modeling#

4.1. Characteristics of modeling#

We model problem 2 with Euler’s right beam elements: POU_D_E

Problem 2 :

Mesh:	beam \(\mathit{AC}\): 20 SEG2, 21 knots
Boundary conditions: In all the knots in \(A\): in \(B\): 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 =”B”, DY=0.0,) (GROUP_NO =”C”, DY=0.0,)

4.2. notes#

The natural modes are calculated with blocking in the directions X and Y for the point \(A\) and in the direction Y for the points \(B\) and \(C\). The four static modes corresponding to these blocks are added, with imposed movements. The Ritz base is composed of dynamic modes and static modes. It is orthogonalized with a generalized mode calculation and then returned to a mode_meca type concept.

The modal base is filtered to keep the first 5 modes, then to keep the 3 rigid body modes.

4.3. Tested sizes and results#

Frequency ( \(\mathit{Hz}\) )

Clean modes	Reference direct calculation	Aster	tolerance
4	12.8307098	12.8307326	0.1%
5	35.3688446	35.3693819	0.1%

Since the first three modes are rigid body modes, with a theoretically zero frequency, the calculated frequency is not tested.

Effective masses and participation factors for the first 5 modes:

Parameter	Reference direct calculation	Aster	tolerance
Sum of the effective masses for the first 5 modes	367.5663404	367.5663404	0.1%
Sum of the effective unit masses for the first 5 modes			0.1%


Effective masses and participation factors for the first 3 modes:

The first three modes being rigid body modes, it is verified that the sum of the effective unit masses is equal to 1, and that the sum of the effective masses is equal to the mass of the beam. However, it is not possible to compare the modes one by one.

Parameter	Analytical Reference	Aster	Tolerance
Sum of the effective masses for the first 3 modes	367.5663404	367.5663404	0.1%
Sum of the effective unit masses for the first 3 modes		0.999999999999	0.1%


Fparticipation actors:

Only the participation factors of the first three modes are non-zero and since they are rigid body modes, they cannot be compared with direct calculation.