In-Plane Vibrations of a Pin-Ended Cross Frame

Determine the natural frequencies of a simply supported cross 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 0.125 m. All dimensions are in m.

File Name

Open drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\NAFEMS_Freq_Test1.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) = 8,000 Kg/m3
  • Poisson's ratio (ν) = 0.3

Restraints

The four end joints are simply-supported and constrained from out-of-plane rotations. The center node is constrained in the normal direction and from out-of-plane rotations.

Results

All reported frequencies correspond to in-plane modes.
Frequency Theory (Hz) SOLIDWORKS Simulation (Hz) Mode Shape(a)
1 11.336 11.336
2 & 3 17.709 17.681
4 17.709 17.709
9 45.345 45.345
10 and 11 57.390 57.075
12 57.390 57.39
(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", Ref -R0015, Issue 2, Test 1, 1987.