3. Modeling A

3.1. Characteristics of modeling

This modeling allows the validation of integration by modal recombination.

Discreet element of translational rigidity

Characteristics of the elements

DISCRETavec	nodal masses	M_T_D_N	M_T_N	M_T_N
	stiffness matrices	K_T_D_L	K_T_L
	damping matrices	A_T_D_L	A_T_L

Block degrees of freedom in \(Y\) and \(Z\) for all nodes

Boundary conditions at extreme knots

Node names:

Point \(A=\mathrm{N1}\)	\({P}_{1}=\mathrm{N2}\)
Point \(B=\mathrm{N10}\)	\({P}_{2}=\mathrm{N3}\)
	…
	\({P}_{8}=\mathrm{N9}\)

Modal recombination with all modes (i.e. 8),

EULER diagram, resumption of a first calculation at \(t=0.455s\)

time step used: \(\Delta t=1.E–3s\).

3.2. Characteristics of the mesh

Number of knots: 10

Number of meshes and types: 9 SEG2

3.3. Tested sizes and results

Time	Reference
0.09	4.02 E—5
0.18	4.22 E—6
0.27	3.89 E—5
0.37	5.98 E—6
0.46	3.73 E—5
0.54	7.14 E—6
0.63	3.64 E—5
0.72	8.07 E—6
0.81	3.58 E—5
0.9	8.76 E—6
0.99	3.52 E—5
1.08	—3.08 E—5
1.18	3.02 E—5
1.27	—2.88 E—5
1.36	2.80 E—5
1.45	—2.65 E—5

3.4. notes

The relative minima (\(t=0.18,0.54,\dots\)) do not have very good precision during the excitation phase with a \(\Delta t=0.001\) step.