Harmonic Response of a Spring-mass System


Reference:R. K. Vierck, Vibration Analysis, 2nd Edition, Harper & Row Publishers, New York, NY, 1979, sec. 4-2.
Analysis Type(s):
Mode-frequency Analysis (ANTYPE = 2)
Harmonic Mode-Superposition Analysis (ANTYPE = 3)
Element Type(s):Combination Elements (COMBIN40)
Input Listing:vm183.dat

Test Case

Determine the natural frequencies of the spring-mass system shown and the displacement response when excited by a harmonic load of variable frequency from 0.1 to 1.0 Hz, with an amplitude of Fo.

Figure 183.1:  Spring-mass System Problem Sketch

Spring-mass System Problem Sketch

Material PropertiesLoading
k1 = 6 N/m
k2 = 16 N/m
m1 = m2 = 2 kg
Fo = 50 N

Analysis Assumptions and Modeling Notes

COMBIN40 combination elements are used to represent the springs and masses. Node locations are arbitrary.

Results Comparison

TargetMechanical APDLRatio
Y1 , m (@ .226 Hz)-1371.7-1371.731.000
Y2 , m (@ .226 Hz)-458.08-458.081.000
Y1 , m (@ .910 Hz)-0.8539-0.85391.000
Y2 , m (@ .910 Hz)0.11810.11811.000

Figure 183.2:  Displacement vs. Frequency

Displacement vs. Frequency

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