Lateral Vibration of an Axially Loaded Bar

Description

Determine the first three natural frequencies of lateral vibration of a simply supported bar. The bar has a rectangular cross-section 2"X2" and its length is 80". An axial force of 40,000 lbs is applied at the roller support.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Frequency_12.SLDPRT and open the file.

Study Type

Frequency.

Mesh Type

Solid mesh.

Meshing Parameters

Use a Global Size of 2 in.

Material Properties

Modulus of elasticity = 3 X 10⁷ psi, Poisson's ratio = 0.3, Density = 0.2812683 lb/in³.

Modeling Hints

Use the Intel Direct Sparse solver.

Results

	f1 (Hz)	f2 (Hz)	f3 (Hz)
Theory	17.055	105.32	249.39
SOLIDWORKS Simulation	16.983	104.19	243.13

The study NoLoadEffect shows the fundamental frequency to be 28.684 Hz when the load is not considered. Compressive loads lower the natural frequencies.

Reference

Timoshenko, S., and Young, D. H., “Vibration Problems in Engineering,” 3rd Edition, D. Van Nostrand Co., Inc., New York, 1955, p. 374.