Analysis Type:

Prestress Modal

Model Type:

3D

Comparison:

ANSYS

Reference:

Timoshenko, S., and Young, D.H. Vibration Problems in Engineering, 3rd Edition. D. Van Nostrand Co., Inc., New York, 1955.

Description:

Determine the first three radially symmetric, out of plane, natural frequencies of a circular membrane. Use stiffness calculated from static analysis where membrane is loaded radially. Edges are simply supported.

Element Type:  plate  
Units:  IPS  
Dimensions:  radius: 15 thickness: 0.01  
Material Properties:  Mass Density: 0.00073 Cost Per Unit Mass: 0 Young's Modulus: 3e7  Poisson's Ratio: 0.3 Thermal Expansion: 0 Conductivity: 0 
Constraints:  edge simply supported  
Loads:  radial load of 100 lb/in 
Theory  ANSYS  % Difference  Structure  % Difference  
Mode 1  94.406  94.471  0.07%  94.442  0.03% 
Mode 6  216.77  217.38  0.28%  216.99  0.101% 
Mode 15  339.85  342.98  0.92%  341.11  0.37% 
Convergence %: 1 % on Frequency  Max P: 8  No. Equations: 994 
Results are only for radially symmetric modesâ€”modes 1, 6, and 15 of the solution. These are outofplane modes, in other words; they appear in the profile view. 