Frequency of a Cantilever Beam with Lumped Mass

Description

A 10" long cantilever beam has a square cross-section of 0.25" X 0.25". A mass of 10 lbs is attached to the free end of the cantilever as shown in the figure. Determine the natural frequency of the system if the mass is displaced slightly and released.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Frequency_10.SLDASM and open the file.

Study Type

Frequency.

Mesh Type

Solid mesh.

Material Properties

Modulus of elasticity = 30,000,000 psi, Poisson's ratio = 0, Density = 0.282072 lb/in³.

Modeling Hints

A small block of artificially high density is used to model the mass.

Results

Two studies are used: study Nodensity does not consider the mass of the beam (density = 0). Study Density considers the mass of the beam.

	Frequency, Hz
Theory	5.355
SOLIDWORKS Simulation (Nodensity)	5.351
SOLIDWORKS Simulation (Density)	5.341

Reference

William, W. Seto, “Theory and Problems of Mechanical Vibrations,” Schaum’s Outline Series, McGraw-Hill Book Co., Inc., New York, 1964, p. 7.