NAFEMS FV4
Modal analysisPASS · 1.06%Cantilever beam with off-centre tip point masses — bending-torsion coupling and closely spaced eigenvalues.
- Tolerance:
- 5%
Problem statement
- Geometry
- Cantilever modeled by five 2-node beam elements; two rigid elements connect off-centre point masses m1 = 10000 kg and m2 = 1000 kg at the free end.
- Material
- Steel: E = 200 GPa, ν = 0.3, ρ = 8000 kg/m³.
- Boundary conditions
- All 6 DOF fixed at end A (fully clamped); free vibration with off-centre tip masses attached via rigid elements.
- Measured quantity
- First six natural frequencies (modes 1-6): 1.723, 1.727, 7.413, 9.972, 18.155, 26.957 Hz. Mode ordering and handling of the closely spaced pair (modes 1-2) must be checked.
Results comparison
| Reference value | 1.7231.7277.4139.97218.15526.957 Hz (TNSB-1990) |
| Our result | N=20: 1.7221.7257.4109.94518.03626.671 HzN=5: 1.7221.7257.4109.94618.04526.696 Hz |
| Deviation | 1.06% |
| Tolerance | 5% |
| Status | PASS · 1.06% |
| Element family | Beam element |
| Mesh details | (Тимошенко) + 2× + 2× (точечные, без поворотной инерции), предписанная сетка N=5 даёт 1.722 / 1.725 / 7.410 / 9.946 / 18.045 / 26.696 Гц; основная сверка N=20 |
Updated: 2026-08-10 · WebCAE solver