Harmonic response of cantilever beam (P2 Tet10)
Harmonic analysisPASS · 0.23%Frequency response and resonant tip amplitude of a prismatic cantilever beam under harmonic tip transverse load, verified against Euler-Bernoulli analytical modal frequency and single-degree-of-freedom resonance peak amplitude.
- Tolerance:
- 2%
- Reference:
- Closed-form theory
The target value is an exact analytical solution, computed from the formula stated below — not a number taken from another solver.
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Open & Solve in BrowserProblem statement
- Geometry
- Prismatic cantilever beam: L = 200 mm, b = 20 mm, h = 20 mm, quadratic tetrahedral mesh (TET10).
- Material
- Structural steel: E = 200 GPa, ν = 0.3, ρ = 7850 kg/m³.
- Boundary conditions
- Fixed at root face (x = 0); harmonic transverse tip force F_z = -1000 N at free face (x = 200 mm).
- Measured quantity
- Fundamental bending resonance frequency f₁ (analytical: 407.7 Hz) and tip peak vibration amplitude under 5% modal damping (analytical: 9.707 mm).
Results comparison
| Reference value | f₁ = 407.7 Hz, u_res = 9.707 mm |
| Our result | f₁ = 406.8 Hz, u_res = 9.627 mm |
| Deviation | 0.23% |
| Tolerance | 2% |
| Status | PASS · 0.23% |
| Element family | Solid element |
| Mesh details | P2 TET10 second-order mesh, 1485 elements, 2514 nodes |
Updated: 2026-08-30 · WebCAE solver