VM68

VM68
PSD Response of a Two DOF Spring-mass System

Overview

Reference:

R. K. Vierck, Vibration Analysis, 2nd Edition, Harper & Row Publishers, New York, NY, 1979, sec. 7-2, 7-14.

Analysis Type(s):

Mode-frequency Analysis (ANTYPE = 2)

Spectrum Analysis (ANTYPE = 8)

Element Type(s):

Combination Elements (COMBIN40)

Input Listing:

vm68.dat

Test Case

Determine the first two natural frequencies, f₁ and f₂, and the response of a damped two degree of freedom system subject to a random acceleration with a spectral density function as shown in the figure below.

Figure 93: DOF Spring-mass System Problem Sketch

Material Properties

k₁ = 42832 lb/in

k₂ = 32416 lb/in

m₁ = 0.5 lb-sec²/in

m₂ = 1.0 lb-sec²/in

Analysis Assumptions and Modeling Notes

The load is applied at node 1 to simulate base excitation. A 2% constant modal damping is assumed. The acceleration results are converted from in/sec² to g in POST1.

Results Comparison

	Target	Mechanical APDL	Ratio
f₁ , Hz	20.57	20.572	1.000
f₂ , Hz	64.88	64.885	1.000
Mass 1 - 1 stress Std. dev.	9.059[1]	9.059	1.000
Mass 2 - 1 stress Std. dev.	10.63[1]	10.63	1.000

Numerical solution with a uniform frequency spacing equal to 0.001 Hz in the frequency range of 10 to 100 Hz