In-Plane Vibrations of a Cantilevered Square Membrane

Determine the in-plane modes of vibration of a cantilevered square membrane. The membrane is 10 m x 10 m and its thickness is 0.01 m. All dimensions are in m.

File Name

Open drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\NAFEMS_Freq_Test31.SLDPRT.

Study Type

Frequency

Mesh Type

Shell mesh. Shell thickness is 0.01 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 = 0 at all nodes
  • Ux = Uy = 0 along y-axis

Results

Frequency Theory (Hz) SOLIDWORKS Simulation (Hz) Mode Shape (a)
1 52.404 52.367
2 125.69 125.69
3 140.78 141.01
4 222.54 224.03
5 241.41 241.63
6 255.74 256.46
(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 31, 1987.