In-Plane Vibrations of a Free Annular Membrane

Determine the in-plane modes of vibration of a ring-shaped membrane. The membrane has a thickness of 0.06 m and is simply-supported around its circumference. The membrane's inner radius is 1.8 m and its outer radius is 6.0 m. All dimensions are in m.

File Name

Open drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\NAFEMS_Freq_Test14.SLDPRT.

Study Type

Frequency

Mesh Type

Shell mesh. Shell thickness is 0.06 m. 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

Restraints

Uz = Rx = Ry = 0 at all nodes

Results

Study: Free_Membrane
The first three calculated frequencies correspond to rigid body modes.
Frequency Theory (Hz) SOLIDWORKS Simulation (Hz) Mode Shape (a)
4 and 5 129.24 125.9
6 226.17 224.32
7 and 8 234.74 232.78
9 and 10 264.66 262.97
11 and 12 336.61 335.1
13 and 14 376.79 375.35
(a) The mode shapes are superimposed on the undeformed shape of the membrane.

Reference

NAFEMS, Publication R0015, The International Association for the Engineering Analysis Community, "Selected Benchmarks for Natural Frequency Analysis", Issue 2, Test 33, 1987.