VM89

VM89
Natural Frequencies of a Two-mass-spring System

Overview

Reference:W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 163, ex. 6.2-2.
Analysis Type(s):Mode-frequency Analysis (ANTYPE = 2)
Element Type(s):
Spring-Damper Elements (COMBIN14)
Structural Mass Elements (MASS21)
Input Listing:vm89.dat

Test Case

Determine the normal modes and natural frequencies of the system shown below for the values of the masses and spring stiffnesses given.

Figure 126: Two-mass-spring System Problem Sketch

Two-mass-spring System Problem Sketch

Material Properties
m2 = 2m1 = 1.0 lb-sec2/in
k2 = k1 = 200 lb/in
kc = 4k1 = 800 lb/in

Analysis Assumptions and Modeling Notes

The spring lengths are arbitrarily selected and are used only to define the spring direction. Modal analysis is performed using Block-Lanczos eigensolver.

Results Comparison

Target[1]Mechanical APDLRatio
f1, Hz2.58142.58141.000
f2, Hz8.32638.32631.000
(A1/A2)1[2]0.92120.92121.000
(A1/A2)2[2]-2.1711-2.17121.000

  1. Solution Recalculated

  2. Normal Modes (UX of node 2 / UX of node 3)