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  6. DLL 06: Cantilever beam with eccentric mass – eigen modes

DLL 06: Cantilever beam with eccentric mass – eigen modes

Description

Material For bar AB Modulus of elasticity E=210 000 N/mm^2
Density \rho=7800 kg/m^3
 For bar BC1 Modulus of elasticity E=999 999 N/mm^2
Density \rho=0.010 kg/m^3
Geometry Cross-section For all bars d_e = 0.35m
d_i = 0.32 m
Boundary conditions In point A Fixed support
Loads Case 1: Mass of 1000 kg in point B.
Bar BC is not present.
Case 2: Mass of 1000 kg in point C.
Bar BC is present.
Mesh No. of divisions 12

1. The eccentricity of the mass is created by adding bar BC to the model. The purpose is that bar BC is significantly stiffer than bar AB.

Results

Case 1

Eigen mode Shape Independent reference Diamonds Difference
1 1.65Hz 1.655Hz -0.30%
2 16.07Hz 16.07Hz 0.00%
3 50.02Hz 50.027Hz -0.01%
4 76.47Hz 76.45Hz 0.03%
5 80.47Hz 80.505Hz -0.04%
6 103.2Hz 103.235Hz -0.03%

Case 2

Eigen mode Shape Independent reference Diamonds Difference
1 1.636Hz 1.635Hz 0.06%
2 1.642Hz 1.641Hz 0.06%
3 13.46Hz 13.391Hz 0.52%
4 13.59Hz 13.562Hz 0.21%
5 28.9Hz 28.821Hz 0.27%
6 31.96Hz 30.872Hz 3.52%
7 61.61Hz 61.618Hz -0.01%
8 63.93Hz 61.969Hz 3.16%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 15: poutre encastrée-libre avec masse ou inertie excentrée
  • Tested in Diamonds 2023r01.

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