In-Plane and Out-of-Plane Vibrations of a Circular Ring

Determine the natural frequencies of an unsupported circular ring. Consider in-plane and out-of-plane modes. The ring has a diameter of 1 m and a circular cross-section of diameter 0.1 m. All dimensions are in m.

File Name

Open drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\NAFEMS_Freq_Test6.SLDPRT.

Study Type

Frequency

Mesh Type

Beam mesh. Use the standard mesh size.

Material Properties

  • Modulus of elasticity (E) = 2 x 1011 N/m2
  • Mass density (ρ) = 8000 Kg/m3
  • Poisson's ratio (ν) = 0.3

Results

The first six calculated frequencies correspond to rigid body modes.
Frequency Theory (Hz) SOLIDWORKS Simulation (Hz) Mode Shape (a)
7 and 8

out-of-plane

 51.849 51.853
9 and 10

in-plane

 53.382 53.535
11 and 12

out-of-plane

 148.77 148.99
13 and 14

in-plane

 150.99 151.39
15 and 16

out-of-plane

 286.98 287.58
17

in-plane

 289.51 290.25
(a) The mode shapes are superimposed on the undeformed shape of the ring.

Reference

NAFEMS, Publication R0015, The International Association for the Engineering Analysis Community, "Selected Benchmarks for Natural Frequency Analysis", Issue 2, Test 6, 1987.