1. Reference problem#

1.1. Geometry#

_images/100000000000015F000000AFD4E802432478F73C.jpg

Modeling:

Mass (\(\mathrm{kg}\))

\({I}_{\mathrm{xx}}\) (\({\mathrm{kg.m}}^{2}\))

\({I}_{\mathrm{yy}}={I}_{\mathrm{zz}}\) (\({\mathrm{kg.m}}^{2}\))

Disc \({D}_{1}\)

14.580130

0.1232021

0.6463858

Disk \({D}_{2}\)

45.945793

0.97634809

0.4977460

Disc \({D}_{3}\)

55.134951

1.1716177

0.6023493

Beam length:

\({L}_{1}=\mathrm{AB}=0.2m\)

\({L}_{2}=\mathrm{BC}=0.3m\)

\({L}_{3}=\mathrm{CD}=0.5m\)

\({L}_{4}=\mathrm{DE}=0.3m\)

Circular section:

Diameter: \(D=0.1m\)

1.2. Material properties#

\(E={2.10}^{11}\mathrm{Pa}\)

\(\nu =0.3\)

\(\rho =7800\mathrm{kg}/{m}^{3}\)

1.3. Boundary conditions and loads#

Elastic supports with viscous damping in \(A\) and \(E\)

\({K}_{\mathrm{yy}}={5.10}^{7}{\mathrm{N.m}}^{-1}\); \({K}_{\mathrm{zz}}={7.10}^{7}{\mathrm{N.m}}^{-1}\); \({K}_{\mathrm{yz}}={K}_{\mathrm{zy}}=\mathrm{0 }\)

\({C}_{\mathrm{yy}}={5.10}^{3}N/({\mathrm{m.s}}^{-1})\); \({C}_{\mathrm{zz}}={7.10}^{3}N/({\mathrm{m.s}}^{-1})\); \({C}_{\mathrm{yz}}={C}_{\mathrm{zy}}=0\)

Attention the amortizations have been multiplied by 10, compared to the harmonic calculation of test SHLL102 in order to obtain a faster attenuation of solid body modes in order to minimize the duration of the calculation. The other settings are the same.

Imbalance with value \(0.05\mathrm{m.kg}\), installed on node \(C\) (disk 2).