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DLL 02: Slender folded beam, one end fixed other free – eigen modes

Description

Material Modulus of elasticity E=210 000 N/mm^2
Density \rho=7800 kg/m^3
Poisson’s ratio \nu= 0.3
Geometry Cross-section Dimensions b = 50 mm
h = 5 mm
Boundary conditions In point A Fixed support
Mesh No. of divisions 12

Results

Handcalculation

    \[f_i=(2\cdot \begin{bmatrix}1 \\2 \\ 3 \\ 4 \end{bmatrix} -1 )^2\cdot \pi \cdot \frac{h}{8\cdot l^2}\cdot \sqrt{\frac{E}{12\cdot \rho }}=\begin{bmatrix}11.764 \\105.878 \\294.104 \\576.446 \end{bmatrix}Hz\]

Eigen mode Shape Independent reference Diamonds Difference
1 11,764Hz 11,757Hz 0,06%
2 105,878Hz 105.803Hz 0,07%
3 294,104Hz 293.930Hz 0,06%
4 576,445Hz 576.267Hz 0,03%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 02: poutre élancée encastrée-libre, replieée sur elle-même.
  • Tested in Diamonds 2023r01.

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