3. Modeling A#

3.1. Characteristics of modeling#

Beam element POU_D_T (Timoshenko’s right beam)

_images/100008580000182F00000BE388AE8EB2C0A43423.svg

Cutting: beam \(\mathrm{AB}\): 120 SEG2 meshes of variable cross section.

Node names:

Point \(A\)

\(x=0.\)

\(\mathrm{N1}\)

\(x=0.1\)

\(\mathrm{N21}\)

\(x=0.2\)

\(\mathrm{N41}\)

\(x=0.3\)

\(\mathrm{N61}\)

\(x=0.4\)

\(\mathrm{N81}\)

\(x=0.5\)

\(\mathrm{N101}\)

Point \(B\)

\(x=0.6\)

\(\mathrm{N121}\)

3.2. Characteristics of the mesh#

Number of nodes:

121

Number of meshes and types:

120 SEG2

3.3. Tested sizes and results#

Clean mode order

Frequency Reference

% tolerance

1

143.303

1.6

2

396.821

0.45

3

779.425

0.3

4

1289.577

0.9

The natural modes of Aster have been normalized to 1. at the point of maximum translational amplitude as in the reference.

Clean Mode \({F}_{i}(x)\) Normed to 1 at the maximum amplitude point

\(i\)

\(x=0.1\)

\(x=0.2\)

\(x=0.3\)

\(x=0.4\)

\(x=0.5\)

Reference Aster % difference % tolerance

1

0.2349 0.2363 0.583 0.6

0.6962 0.6970 0.119 0.15

0.98960 0.9895 0. 0.1

0.8505 0.8516 0.132 0.15

0.3507 0.3529 0.631 0.7

Reference Aster % difference % tolerance

2

—0.4653 —0.4670 0.37 0.4

—0.7558 —0.7555 —0.041 0.1

0. —2.910—4 —2.910—4 1.10—3

0.9232 0.9226 —0.063 0.1

0.6941 0.6971 0.435 0.45

Reference Aster % difference % tolerance

3

0.6278 0.6290 0.192 0.2

0.1969 0.1952 —0.89 0.9

—0.7783 —0.7782 —0.014 0.1

0.2406 0.2377 —1.226 1.23

0.9366 0.9387 0.228 0.25

Reference Aster % difference % tolerance

4

—0.666 —0.6656 —0.081 0.1

0.4832 0.4840 0.18 0.2

0. 4.610—4 4.610—4 1.10—3

—0.5901 —0.5919 0.31 0.35

0.9937 0.9928 —0.089 0.1

3.4. notes#

Calculations made by:

CALC_MODES

OPTION = “PLUS_PETITE” CALC_FREQ =_F (NMAX_FREQ = 4) SOLVEUR_MODAL =_F (METHODE = “TRI_DIAG”)

Contents of the results file:

4 first natural frequencies, eigenvectors.