VM88

VM88
Response of an Eccentric Weight Exciter

Overview

Reference:	W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 60, ex. 3.3-1.
Analysis Type(s):	Harmonic Analysis (ANTYPE = 3)
Element Type(s):	Combination Elements (COMBIN40)
Input Listing:	vm88.dat

Test Case

A counter-rotating eccentric weight exciter of mass m having a mass unbalance m_u on an eccentricity e is used to produce forced oscillation of a spring-supported mass. For a viscous damping factor c, determine the amplitude and phase angle Φ of the displacement response when the rotating frequency f is (1) the resonant frequency f_n, and (2) f >> f_n.

Figure 125: Eccentric Weight Exciter Problem Sketch

Material Properties

m = 0.02590673 lb-sec²/in

c = 0.11754533 lb-sec/in

m_u = 0.08 x m

k = 30 lb/in

Analysis Assumptions and Modeling Notes

The node locations are arbitrarily selected. When the rotating frequency f is equal to the resonant frequency f_n, the force F₁ = m_uω² = 2.4 lb where ω = ω_n = sqrt(k/m) = 34.0294 rad/sec is the resonant circular frequency. When f >> f_n, it is assumed that f = 100 f_n = 541.5947 Hz and the corresponding force F₁ = 24000 lb.

Results Comparison

		Target	Mechanical APDL	Ratio
f = f_n	Amp, in	0.60000	0.60000	1.000
f = f_n	angle, deg	-90.000	-90.000	1.000
f =100 f_n	Amp, in	0.080000[1]	0.080008	1.000
f =100 f_n	angle, deg	-180.00	-179.92	1.000

Based on f =