VM47

VM47
Torsional Frequency of a Suspended Disk

Overview

Reference:

W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 10, ex. 1.3-2

Analysis Type(s):

Mode-frequency Analysis (ANTYPE = 2)

Element Type(s):

Spring-Damper Elements (COMBIN14)

Structural Mass Elements (MASS21)

Input Listing:

vm47.dat

Test Case

A disk of mass m which has a polar moment of inertia J is suspended at the end of a slender wire. The torsional stiffness of the wire is k_θ. Determine the natural frequency f of the disk in torsion.

Figure 64: Suspended Disk Problem Sketch

Material Properties

Geometric Properties

m = 1 lb-sec²/in

k_θ = 4.8 in-lb/rad

J = .30312 lb-in-sec²

Analysis Assumptions and Modeling Notes

The length of the wire is arbitrarily selected. Modal analysis is performed using Block Lanczos eigensolver.

Results Comparison

	Target	Mechanical APDL	Ratio
f, Hz	0.63333	0.63333	1.00