Vibrations of a Simply Supported Thin Square Plate

Determine the frequencies of a simply supported thin square plate. The plate is 10.0 m x 10.0 m and its thickness is 0.05 m. All dimensions are in m.

File Name

Open drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\NAFEMS_Freq_Test13.SLDPRT.

Study Type

Frequency

Mesh Type

Shell mesh. Shell thickness is 0.05 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

  • Ux = Uy = Rz = 0 at all nodes
  • Uz = 0 along edges
  • Rx = 0 along edges x = 0 and x = 10 m
  • Ry = 0 along edges y = 0 and y = 10 m

Results

Frequency Theory (Hz) SOLIDWORKS Simulation (Hz) Mode Shape
1 2.377 2.377
2 and 3 5.942 5.941
4 9.507 9.504
5 11.884 11.881
6 11.884 11.881
7 and 8 15.449 15.443

Reference

NAFEMS, Publication R0015, The International Association for the Engineering Analysis Community, "Selected Benchmarks for Natural Frequency Analysis," Issue 2, Test 13, 1987.