3. Modeling A

3.1. Characteristics of modeling

We model problem 1 with Euler’s right beam elements: POU_D_E

Problem 1:

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,)

3.2. notes

The natural modes are calculated with a lock at point \(B\) along the Y direction. A static mode is also calculated with a displacement imposed at point \(B\) component \(\mathit{DY}\). The base of Ritz is composed of dynamic modes and static mode. 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.

3.3. Tested sizes and results

Frequencies ( \(\mathit{Hz}\) ):

Clean modes	Reference direct calculation	Aster	tolerance
1	5.6600453	5.6600471	0.1%
2	22.6403247	22.6403247	0.1%
3	50.9421205	50.9433790	0.1%
4	90.5703803	90.5703803	0.1%
5	141.5378176	141.5651110	0.1%

Effective masses and participation factors:

For the effective masses and participation factors, the tests are based on the sum of the values for the first 5 modes.

Parameter	Reference direct calculation	Aster	tolerance
Sum of the effective masses for the first 5 modes	342.9564379	342.9564379	0.1%
Effective mass of the first mode	297.9380528	297.9380553	0.1%
Sum of the effective unit masses for the first 5 modes	0.9330542	0.9330463	0.1%
Sum of the absolute values of the participation factors for the first 5 modes	26.4666220	26.4660056	0.1%
Absolute value of the first mode participation factor	17.2608821	17.2608822	0.1%