F-03 (Cantilevered Tapered Membrane Vibration) |
  
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F-03 (Cantilevered Tapered Membrane Vibration) |
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Objective
To verify the behavior of membrane plate vibration
Problem Description
The cantilevered tapered membrane plate [Ref 1] shown below vibrates under its own weight.
Material properties: E = 2.0e11 Pa, ν = 0.30, ρ = 8000 Kg/m3
Plate thickness:, t = 0.05 m
Finite Element Model
128 shell elements
Model type: 2D Plane Stress
Results
The mode frequencies are given by [Ref 1].
Unit: mode frequency – Hz
Mode Frequency |
ENERCALC 3D |
[Ref 1] |
|
Compatible Membrane |
Incompatible Membrane |
||
Mode 1 |
44.7076 |
44.4487 |
44.623 |
Mode 2 |
130.3669 |
129.2843 |
130.03 |
Mode 3 |
162.4766 |
162.4449 |
162.70 |
Mode 4 |
246.2847 |
243.6222 |
246.05 |
Mode 5 |
378.4229 |
373.7379 |
379.90 |
Mode 6 |
389.4256 |
389.2006 |
391.44 |
Comments
The vibration frequencies given by ENERCALC 3D are very close to the referenced values.
Reference
[1]. Abbassian, Dawswell, Knowles “Selected Benchmarks for Natural Frequency Analysis”, Test No. 32, NAFEMS Finite Element Methods & Standards, Nov. 1987
