E06: Mass Spring Model Eigenvalues✔

This is a system with two lumped masses and three springs. Determine the fundamental natural frequency.


The model has 4 joints, 3 spring elements and 2 joint masses. The dynamic degrees of freedom is selected in the Global X-direction so that it matches with the spring directions.

The joint locations in the X direction are arbitrarily selected since the length has no effect on the stiffness of a spring element. The translational degrees of freedom in X direction at joints 2 and 3 are the degrees of freedom of the model. All other degrees of freedom are eliminated from the model. The values for the lumped masses and spring constants are given as:


M1= 0.5 lb-sec2/in
M2 = 1.0 lb-sec2/in
K1 = 200 lb/in
K2 = 800 lb/in
K3 = 200 lb/in

Solution Comparison


ThomsonLARSAOpenBrIMPercent Difference
(LARSA vs Thomson)
Percent Difference
(OpenBrIM vs Thomson)
f1(Hz)2.58142.58142.58170%0.39%
f2(Hz)8.32638.32638.32730%0.012%


Sources

  • Thomson, W.T.,"Vibration Theory and Applications," Prentice- Hall, Inc., Englewood Cliffs, N.Y., 2nd Edition, 1965, P. 163.
  • LARSA 4D