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

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	$b = 50 mm$ $h = 5 mm$
Geometry	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	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 2024r01.

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