VM87

VM87
Equivalent Structural Damping

Overview

Reference:	W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 72, article 3.9 and pg. 56, ex. 3.1-2.
Analysis Type(s):	Harmonic Analysis (ANTYPE = 3)
Element Type(s):	Combination Elements (COMBIN40)
Input Listing:	vm87.dat

Test Case

Test case description is the same as that for VM86 except for the assumption on damping. Assume that all damping is in the form of equivalent structural damping and there is no element damping.

Figure 124: Structural Damping Problem Sketch

Analysis Assumptions and Modeling Notes

The structural damping factor is γ = 2 ξ ω/ω_n where ξ is the damping ratio and is equal to c/2m ω_n. Therefore, γ = c/(m ω_n) = 6/(0.5 x 20) = 0.6 since ω = ω_n. The frequency-dependent multiplier β is calculated as β = 2 ξ/ω_n = γ/ω = 0.6/20 = 0.03 seconds. The node locations are arbitrarily selected.

Results Comparison

	Target	Mechanical APDL	Ratio
Amp, in	0.083333	0.083333	1.000
angle, deg	-90.000	-90.000	1.000