VM45

VM45
Natural Frequency of a Spring-Mass System

Overview

Reference:W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 6, ex. 1.2-2.
Analysis Type(s):Mode-frequency Analysis (ANTYPE = 2)
Element Type(s):
Spring-Damper Element (COMBIN14)
Structural Mass Element (MASS21)
Input Listing:vm45.dat

Test Case

An instrument of weight W is set on a rubber mount system having a stiffness k. Determine its natural frequency of vibration f.

Figure 62: Spring-mass System Problem Sketch

Spring-mass System Problem Sketch

Material PropertiesLoading
k = 48 lb/in
W = 2.5 lb
g = 386 in/sec2

Analysis Assumptions and Modeling Notes

The spring length is arbitrarily selected. The weight of the lumped mass element is divided by gravity in order to obtain the mass. Mass = W/g = 2.5/386 = .006477 lb-sec2/in.

Results Comparison

TargetMechanical APDLRatio
f, Hz13.70113.7011.000