In-Plane Vibrations of a Free Square Frame

Determine the natural frequencies of a free square frame with four beams. Consider modes in the XY plane only. The frame is 10 m x 10 m and each beam has a square section of side 0.25m.

File Name

Open drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\NAFEMS_Freq_Test3.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

Restraints

The four corner joints are constrained in the normal direction.

Results

The first three calculated frequencies correspond to rigid body modes.
Frequency No. Theory (Hz) SOLIDWORKS Simulation (Hz) Mode Shape (a)
4 3.261 3.261
5 5.668 5.665
6 and 7 11.136 11.142
8 12.849 12.849
13 24.570 24.597
14 and 15 28.695 28.667
(a) The mode shapes are superimposed on the undeformed shape of the frame.

Reference

NAFEMS, Publication R0015, The International Association for the Engineering Analysis Community, "Selected Benchmarks for Natural Frequency Analysis", Issue 2, Test 3, 1987.