OS-V: 0430 Cantilevered Thin Square Plate

Test No. FV16 A cantilevered thin square plate of 10 m × 10 m 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

Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

Benchmark Model

Quad8 elements are used to model different test cases with specific grid point locations. The thickness of the plate is 0.05 m. 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

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis