3. Modeling A#

3.1. Characteristics of modeling#

We use straight Timoshenko POU_D_T beams and DIS_T discrete elements.

_images/100018180000196D0000082AA82EEF68684B27DF.svg

Cutting:

\(\mathrm{AD}\): 5 stitches SEG2 \(\mathrm{DB}\): 15 stitches SEG2 \(\mathrm{CD}\): 1 mesh SEG2

Modeling:

POU_D_Tpour all the meshes of the \(\mathrm{AB}\) beam DIS_Tpour the \(\mathrm{CD}\) mesh and the \(C\) stitch For the whole structure \(\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0\)

Boundary conditions: In all the knots of Beam \(\mathrm{AB}\): At the knots extremities: in \(C\):

DDL_IMPO: (GROUP_NO: NPOUTRE DZ:0., DRX :0, DRY :0.) (GROUP_NO: A DX: 0., DY: 0.) (GROUP_NO: B DY: 0.) (GROUP_NO: CDX: 0., DZ: 0.)

Node names:

Point \(A=\mathrm{N1}\) Point \(B=\mathrm{N21}\)

Point \(C=\mathrm{N22}\) Point \(D=\mathrm{N6}\)

3.2. Characteristics of the mesh#

Number of knots:

22

Number of meshes and types:

21 meshes SEG2

1 mesh P0I1

3.3. Tested sizes and results#

Frequency ( \(\mathrm{Hz}\) )

\(\lambda\)

Clean Mode Order

Reference

\(0.\)

flexure 1 Flexion 2

1.5707 6.2831

\(0.001\)

1 bend 2. Flexion 3 flexure 2

1 » 1.5460

1.5958

6.2336 »

\(0.01\)

1 bend 2 flexure 3 flexure 2

1 » 1.4937

1.6506

6.2874 »

3.4. notes#

For \(\lambda =0\), we did:

CALC_MODES

OPTION = “PLUS_PETITE” CALC_FREQ =_F (NMAX_FREQ = 2) SOLVEUR_MODAL =_F (METHODE = “TRI_DIAG”)

For \(\lambda =0.001\), we did:

CALC_MODES

OPTION = “PROCHE” CALC_FREQ =_F (FREQ = (1.5, 1.6, 6.5))

For \(\lambda \mathrm{=}0.01\), we did:

CALC_MODES

OPTION = “AJUSTE” CALC_FREQ =_F (FREQ = (1., 7.))

Contents of the results file:

Case 1:2 first natural frequencies, eigenvectors and modal parameters.

Case 2:3 first natural frequencies and modal parameters.

Case 3: first 3 natural frequencies, eigenvectors and modal parameters.