Verification › V.04 Dynamic analysis
V.04.3Cantilever Natural Frequencies
Within 0.011%Problem
Find the natural frequencies of a uniform cantilever.
Reference
- Euler-Bernoulli beam theory: fn = (βnL)² / (2π) · √(EI / (mL⁴)), with β1L = 1.8751 and β2L = 4.6941.
Model
- Cantilever 10 m long in 20 elements
- A 0.01 m², I 5 × 10⁻⁵ m⁴, E 200 GPa, density 7850 kg/m³
Comparison
| Mode | Theory | Sutranet | Difference |
|---|---|---|---|
| 1 (first bending) | 1.9973 | 1.9972 | 0.003% |
| 3 (second bending) | 12.5167 | 12.5152 | 0.011% |
- Mode 2 is mode 1 in the other plane (the section is the same about both axes).
Reproduce
This is a closed-form or table check with no project file; it runs in the solver test modal.rs.
Automated test: modal.rs, run on every change.
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