TEST CASE 2.3 NATURAL FREQUENCIES OF A RECTANGULAR PLATE HINGED AROUND THE PERIMETER
Reference:
M.V. Barton, “Vibration of rectangular and skew cantilever plates”, Journal of Applied Mechanics, vol. 18, 1951, p. 129 – 134.
Problem description:
Determine the natural frequencies of a rectangular plate hinged around the perimeter.
Problem sketch:
Type of created problem:
Flat plate or grillage (Z, UX, UY).
Geometric characteristics:
a = 1.5 m; b = 1 m; t = 0.01 m.
Material properties:
Elastic modulus: E = 2.1·1011 Pa;
Poisson’s ratio: μ = 0.3;
Density: γ = 7800 kg/m3.
Boundary conditions:
On the perimeter: Z = 0.
Loads:
Dead load.
Model description:
The system is modeled using 100 finite elements of thin plate (FE type is 19) with additional nodes. To solve the problem, a modal analysis was performed.
Calculation results:
Form № |
Frequency, Hz |
Deviation, % |
|
Analytical solution |
LIRA 10 |
||
1 |
35.63 |
35.624 |
0.02 |
2 |
68.51 |
68.506 |
0.01 |
3 |
109.62 |
109.600 |
0.02 |
4 |
123.32 |
123.305 |
0.01 |
5 |
142.51 |
142.474 |
0.03 |
6 |
197.32 |
197.267 |
0.03 |