Modes of Vibration of a Square Cantilevered Beam

Determine the modes of vibration of a cantilevered square beam. The beam has a length of 10 m and a cross-section of 0.125 m x 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_Test71.SLDPRT.

Study Type

Frequency

Mesh Type

Beam mesh

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

Ux = Uy = Rz = 0 at fixed end

Results

Frequency Theory (Hz) SOLIDWORKS Simulation (Hz)
1 and 2 1.01 1.01
3 and 4 6.327 6.327
5 and 6 17.716 17.715
7 and 8 34.717 34.713
9 and 10 57.390 57.382
11 and 12 85.73 85.716

Reference

NAFEMS, Publication R0015, The International Association for the Engineering Analysis Community, "Selected Benchmarks for Natural Frequency Analysis," Issue 2, Test 71, 1987.