VM67

VM67
Radial Vibrations of a Circular Ring

Overview

Reference:S. Timoshenko, D. H. Young, Vibration Problems in Engineering, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 425, article 68.
Analysis Type(s):Mode-frequency Analysis (ANTYPE = 2)
Element Type(s):Axisymmetric-Harmonic 4-Node Structural Solid Elements (PLANE25)
Input Listing:vm67.dat

Test Case

Determine the fundamental frequency fo of axisymmetric in-plane radial vibration and the second (extensional) harmonic frequency f2 of in-plane radial vibration of a circular ring. The cross-section of the ring is square with side length b, at a radius r to the centerline.

Figure 92: Ring Axisymmetric Problem Sketch

Ring Axisymmetric Problem Sketch

Material PropertiesGeometric Properties
E = 30 x 106 psi
ρ = 0.00073 lb-sec2/in4
υ = 0.0
r = 10 in
b = 0.05 in

Analysis Assumptions and Modeling Notes

MODE = 0 for the axisymmetric mode of vibration and MODE = 2 for the second harmonic frequency of vibration. Coupling is used to ensure mode symmetry. A local coordinate system is defined at (x, y) = (9.975,0) for convenience.

Results Comparison

TargetMechanical APDLRatio
fo, Hz3226.43226.3981.000
f2, Hz12.49612.4961.000