1. Home
  2. Diamonds
  3. Validation
  4. Dynamic analysis
  5. Bar structures
  6. DLX 04: Thin circle – fixed at two points – eigen frequencies

DLX 04: Thin circle – fixed at two points – eigen frequencies

Description


Material Modulus of elasticity E=7 200 000 N/mm^2
Density \rho=2700 kg/m^3
Geometry Cross-section b = 10 mm
h = 5 mm
Boundary conditions In points A at angle \alpha=120 ^{\circ} Fixed support
Along the entire edge R_z, M_x and M_y fixed to impose 2D behaviour
Mesh No. of divisions 8

Results

Handcalculation

    \[f_i=\frac{1}{2\cdot \pi}\cdot \lambda_i\cdot \frac{h}{R^2}\cdot \sqrt{\frac{E}{12\cdot \rho }}\]

    \[ f_i=\frac{1}{2\cdot \pi}\cdot \begin{bmatrix}1.9832 \\ 4.8497 \\ 9.3204 \\ 11.8490 \\ 14.7614 \\ 21.5545 \\ 23.6157 \end{bmatrix}\cdot \frac{h}{R^2}\cdot \sqrt{\frac{E}{12\cdot \rho }}= \begin{bmatrix}23.5 \\ 57.5 \\ 110.6 \\ 140.6 \\ 175.1 \\ 255.7 \\ 280.1 \end{bmatrix}Hz\]

Eigen mode Shape Independent reference Diamonds Difference
1 23.5Hz 23.6Hz -0.31%
2 57.5Hz 57.8Hz -0.47%
3 110.6Hz 111.1Hz -0.48%
4 140.6Hz 141.2Hz -0.45%
5 175.1Hz 175.9Hz -0.45%
6 255.7Hz 256.8Hz -0.43%
7 280.1Hz 281.6Hz -0.52%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SDLL 12: anneau circulaire mince encastré en deux points
    The dimensions of the Afnor example were too small for Diamonds. So the radius R and young’s modulus E have been adjusted, and the results are recalculated accordingly.
  • Tested in Diamonds 2024r01.

Article Attachments

Was this article helpful?

Related Articles

Need Support?
Can't find the answer you're looking for? Don't worry we're here to help!
CONTACT SUPPORT