OS-V: 0430 Cantilevered Thin Square Plate

Test No. FV16 A cantilevered thin square plate of 10m×10m dimension. OptiStruct is used to investigate the frequencies at different modes for different test cases.



Figure 1. FE Model with Boundary Conditions and Loadcases
Table 1. Test #2: Nodal Coordinates
Node No. Coordinates(m)
x y
1 4.0 4.0
2 2.25 2.25
3 4.75 2.5
4 7.25 2.75
5 7.5 4.75
6 7.75 7.25
7 5.25 7.25
8 2.25 7.25
9 2.5 4.75
Table 2. Test #4: Nodal Coordinates
Node No. Coordinates(m)
x y
1 4.0 4.0

Benchmark Model

Quad8 elements are used to model different test cases with specific grid point locations. The thickness of the plate is 0.05m. The x,y,z displacements and y rotations are zero along y-axis.

The material properties are:
Property
Value
Young's Modulus
200 x 109 N/m2
Poisson's Ratio
0.3
Density
8000 kg/m3

Modal Analysis Results

The frequency of each targeted mode is normalized with the NAFEMS closed form solution.
Frequencies (Hz) Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6
Reference Solution 0.421 1.029 2.582 3.306 3.753 6.555
Test 1 0.41 0.99 2.33 3.0 3.44 5.82
Normalized 1.026829 1.041498 1.109107 1.100899 1.090671 1.125708
Test 2 0.41 0.99 2.34 3 3.44 5.83
Normalized 1.026829 1.042553 1.103891 1.103103 1.091306 1.125129
Test 3 0.39 0.92 1.84 2.47 2.93 3.57
Normalized 1.085052 1.117264 1.403261 1.33792 1.280887 1.83871
Test 4 0.39 0.91 1.86 2.44 2.82 3.25
Normalized 1.087855 1.130769 1.391164 1.355474 1.333215 2.015063

Model Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this problem include:
  • FV16Test1.fem
  • FV16Test2.fem
  • FV16Test3.fem
  • FV16Test4.fem

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis