NAFEMS FV13
Modal analysisPASS · 3.95%Simply-supported thin square plate — out-of-plane bending modes with repeated eigenvalue pairs; the reference row is independently reproducible by the Navier closed-form solution.
- Tolerance:
- 5%
Problem statement
- Geometry
- Thin square plate 10 m x 10 m, thickness t = 0.05 m (same plate family as FV12/FV16).
- Material
- Steel: E = 200 GPa, nu = 0.3, rho = 8000 kg/m^3.
- Boundary conditions
- Simply supported per the source model: w = 0 along all four edges, plus theta_x = 0 on the x = const edges and theta_y = 0 on the y = const edges (rotation about the edge itself stays free); in-plane motion constrained at all nodes (out-of-plane bending model).
- Measured quantity
- First eight natural frequencies: 2.377, 5.942, 5.942, 9.507, 11.884, 11.884, 15.449, 15.449 Hz — the (1,2)/(2,1), (1,3)/(3,1) and (2,3)/(3,2) pairs are repeated eigenvalues and their multiplicity must be reproduced.
Results comparison
| Reference value | 2.3775.9425.9429.50711.88411.88415.44915.449 Hz (моды 1-8, TNSB-1990) |
| Our result | 2.38686.03456.03459.669712.353412.353415.967215.9672 Hz |
| Deviation | 3.95% |
| Tolerance | 5% |
| Status | PASS · 3.95% |
| Element family | Shell element |
| Mesh details | MITC4-оболочки 16×16, пластина 10×10×0.05 м, опирание w=0 по контуру, in-plane закреплены, сетка 8×8 даёт 2.418 / 6.332 / 6.332 / 10.193 Гц (сходится); эталон независимо сверен аналитикой Навье f_mn=(π/2)(m²+n²)/a²·√(D/ρt): f11=2.376 Гц |
Updated: 2026-08-10 · WebCAE solver