Frequency Analysis of a Cantilever Beam

Description

Find the first two natural frequencies of a cantilever beam in the X-Y plane. The cantilever is 6" long and has a rectangular cross section of 0.1" by 0.2".

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Frequency_7.SLDPRT and open the file.

Study Type

Frequency.

Mesh Type

Solid (Study 1) - Shell mesh (Study 2).

Material Properties

Modulus of elasticity = 1 X 107 psi, Poisson's ratio = 0.3, Density = 0.0946239 lb/in3.

Results

  1st Mode (Hz) 2nd Mode (Hz)
Theory 181.17 1136.29
SOLIDWORKS Simulation (Solid mesh) High 183.16 1141.86
Draft 194.62 1212.89
SOLIDWORKS Simulation (Shell mesh ) High 182.11 1135.39
Draft 184.77 1151.82

The following formulas were used to calculate the natural frequencies of the beam:

f1 = (1.875)2 (EI/ML3)1/2/2π

f2 = (4.694)2 (EI/ML3)1/2/2π

where:

  • E: Modulus of elasticity
  • I: Moment of inertia of the section of the beam
  • M: Mass of the beam
  • L: The length of the beam