6. D modeling

6.1. Characteristics of modeling

Modeling: 18 Equidistributed POU_D_E beam elements

The elements have a variable circular cross section with the two radii \(\mathrm{R1}\) and \(\mathrm{R2}\) identical.

6.2. Characteristics of the mesh

The axis of the beam is oriented according to the vector \(x\).

Mesh:	Number of nodes: 19
	Number of meshes and types: 18 SEG2

Node names:	Point \(A\) = \(N1\)
	Point \(B\) = \(N19\)

3.3 Tested quantities and results

Rotor stopped (\(\Omega =0\)) (frequencies in \(\mathrm{Hz}\))

Identification	Reference type	Reference value	Tolerance
Mode 1	“ANALYTIQUE”	122.7475	0.1%
Mode 2	“ANALYTIQUE”	490.9899	0.1%
Mode 3	“ANALYTIQUE”	1104,7273	0.1%
Mode 4	“ANALYTIQUE”	1963,9596	0.1%

Calculation of natural frequencies using the Sorensen algorithm

Rotating rotor (\(\Omega ={10}^{4}{\mathrm{rd.s}}^{-1}\)), direct modes (frequencies in \(\mathrm{Hz}\))

Identification	Reference type	Reference value	Tolerance
Mode 2	“ANALYTIQUE”	125.8150	0.1%
Mode 4	“ANALYTIQUE”	503,2598	0.1%
Mode 6	“ANALYTIQUE”	1132,3346	0.1%
Fashion 9	“ANALYTIQUE”	2013.0393	0.1%

Rotating rotor (\(\Omega ={10}^{4}{\mathrm{rd.s}}^{-1}\)), retrograde modes (frequencies in \(\mathrm{Hz}\))

Identification	Reference type	Reference value	Tolerance
Mode 1	“ANALYTIQUE”	119.7548	0.1%
Mode 3	“ANALYTIQUE”	479.0191	0.1%
Mode 5	“ANALYTIQUE”	1077,7931	0.1%
Mode 7	“ANALYTIQUE”	1916.0765	0.1%