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
| Thomson | LARSA | OpenBrIM | Percent Difference (LARSA vs Thomson) | Percent Difference (OpenBrIM vs Thomson) | |
|---|---|---|---|---|---|
| f1(Hz) | 2.5814 | 2.5814 | 2.5817 | 0% | 0.39% |
| f2(Hz) | 8.3263 | 8.3263 | 8.3273 | 0% | 0.012% |
Sources
- Thomson, W.T.,"Vibration Theory and Applications," Prentice- Hall, Inc., Englewood Cliffs, N.Y., 2nd Edition, 1965, P. 163.
- LARSA 4D