Modal frequency 02: out-of-plane vibration of a simply supported thin square plate
A simply-supported thick square plate is 10.0 m x 10.0 m and its thickness is 1 meter.
Case Description
A simply-supported thick square plate is 10.0 m x 10.0 m and its thickness is 1 meter. Determine the 4th through 10th natural frequencies.
Geometry
- L = 10 m
- t = 1 m
Study Type
- Modal Frequencies
Mesh Parameters
- Element Type = Solid, Tetrahedral
- Element Order = Parabolic
- Mesh Size = 1.67 m absolute (six across length of plate)
- Adaptive Mesh Refinement: None
Material Properties
- Modulus of elasticity = 2.0 X 105 MPa
- Density = 8000 kg/m3
- Poisson's ratio (v) = 0.3
Constraints
- Z direction constrained at all bottom edges
Comparison of Results
The first three modes are rigid-body modes. The 4th through 10th frequencies corresponds to out-of-plane modes.
| Natural frequencies | F4 | F5 | F6 | F7 | F8 | F9 | F10 |
| NAFEMS | 45.897 Hz | 109.44 Hz | 109.44 Hz | 167.89 Hz | 193.59 Hz | 206.19 Hz | 206.19 Hz |
| Fusion Value | 44.61 Hz | 108.5 Hz | 108.8 Hz | 165.8 Hz | 193.7 Hz | 202.9 Hz | 207.0 Hz |
| % Difference | -2.80 % | -1.59 % | -0.86 % | -1.24 % | 0.057 % | -1.60 % | 0.39 % |
Reference
NAFEMS Publication Test No. FV52, The International Association for the Engineering Analysis Community, "NAFEMS Background To Benchmarks", G.A.O Davies, R.T. Fenner, R.W. Lewis, June, 1992.