VM86

VM86
Harmonic Response of a Dynamic System

Overview

Reference:	W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 56, ex. 3.1-2.
Analysis Type(s):	Harmonic Analysis (ANTYPE = 3)
Element Type(s):	Combination Elements (COMBIN40)
Input Listing:	vm86.dat

Test Case

A machine of weight W is supported on springs of total stiffness k. If a harmonic disturbing force of magnitude F₁ and frequency f (equal to the natural frequency of the machine, f_n) acts on the machine, determine the displacement response in terms of the peak amplitude A_o and phase angle Φ. Assume a viscous damping coefficient c.

Figure 123: Dynamic System Problem Sketch

Material Properties

W = 193 lb

k = 200 lb/in

c = 6 lb-sec/in

g = 386 in/sec²

F₁ = 10 lb

Analysis Assumptions and Modeling Notes

The mass of the machine is m = W/g = 0.5 lb-sec²/in. Hence the frequency of the disturbing force (f) becomes f = f_n = sqrt(k/m)/2π = 3.1831 Hz. The node locations are arbitrarily selected.

Results Comparison

	Target	Mechanical APDL	Ratio
A_o, in	0.0833	0.0833	1.000
angle, deg	-90.0	-90.0	1.000