VM202

VM202
Transverse Vibrations of a Shear Beam

Overview

Reference:R. D. Blevins, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Co., New York, NY, 1979, pp. 171-176.
Analysis Type(s):Mode-frequency Analysis (ANTYPE = 2)
Element Type(s):8-Node Structural Shell (SHELL281)
Input Listing:vm202.dat

Test Case

A short, thin-walled uniform shear beam clamped at the base vibrates freely. Determine the first two modes of vibrations neglecting all flexural deformations.

Figure 315: Shear Beam Problem Sketch

Shear Beam Problem Sketch

Material PropertiesGeometric Properties
E = 200 GPa
υ = 0.27
ρ = 7860 Kg/m3
L = 30 m
W = 10 m
t = 0.1 m

Analysis Assumptions and Modeling Notes

Flexural deformations were eliminated by requiring all nodes with the same Z coordinate value to be coupled in UX and UY. Since this is a square beam, the frequencies are repeated, one made in the X direction, the other in the Y direction.

Results Comparison

TargetMechanical APDLRatio
f1, Hz17.37518.1761.046
f2, Hz52.17654.8831.052

Figure 316: Mode Shape 1 (f = 18.176 Hz)

Mode Shape 1 (f = 18.176 Hz)

Figure 317: Mode Shape 2 (f = 54.883 Hz)

Mode Shape 2 (f = 54.883 Hz)