2. Reference modeling#

2.1. Characteristics of reference modeling#

3D solid elements

_images/1000000000000193000001FA5CF5D97A6F260EEF.png

Discretized geometry is shown above. The 3D elements are solid with 8 nodes of the HEXA8 type. The number of knots on the circumference is 600, on the thickness 9 and on the length 9.

2.2. Characteristics of the mesh#

Number of knots: 48600

Number of meshes and type: 38400 HEXA8

2.3. Reference values tested#

Frequencies of natural modes of ovalization, trifoliate and out-of-plane.

Mode

Natural Frequencies \((\mathrm{Hz})\)

ovalization

210.55 210.55

trifoliate

587.92 587.92

off plan

205.89 205.89 588.88 588.88

2.4. notes#

The axisymmetric problem has dual in-plane and out-of-plane modes.

Off-plane modes have the following deformations:

\(205.89\mathrm{Hz}\):

 _images/1000079C0000068C000018FF5B49767D09204555.svg

\(588.88\mathrm{Hz}\):

 _images/10000A5800000C0400001D93FE963813BA96FB92.svg

2.5. Uncertainties#

The uncertainty comes from the convergence analysis of the mesh where the natural frequencies with the reference mesh \(600\times 8\times 8\) are compared to those of the mesh \(500\times 7\times 9\).

Number of elements

Natural frequencies ( \(\mathrm{Hz}\) )

Circumference

Thickness

Length

Ovalization

Trifoliate

100 200 400 500 600

3 3 5 7 8

3 3 8 9 8

232.03 225.20 221.02 210.64 210.55

648.62 628.74 616.34 588.18 587.92

The uncertainty about the frequency is 0.05%.