E06: Mass Spring Model Eigenvalues✔
- Gokhan Alkan (Unlicensed)
- Seda Ozdemir (Unlicensed)
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:
App
Object Link: https://openbrim.org/objidpkvhrjjk5igivlkkoiqdn.project
Library
Object Link: https://openbrim.org/objid2epddxyg10ib2vzk5ayv9w.libobj
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