Problem 12: Linear Analysis to Find the Complex Eigen Solution of a System
Objective
The objective is to find the complex Eigen value solution for the system below.
Figure 1.
Entities Validated
- Rigid body
- Translational joint
- Force_Spring damper – translational
Type of Analysis
- Linear
Reference
Schaum’s Outline of, Theory and Problem of Mechanical Vibrations, First Edition by S Graham Kelly: 168 (ISBN 0-07-034041-2)
Model Files
- complex_eigen_analysis_2DOF.mdl - MotionView Model
- complex_eigen_analysis_2DOF.xml - MotionSolve Deck
Eigen File Results
Figure 2.
Result Comparison
| Output | Analytical | MotionSolve | % Error |
|---|---|---|---|
| Mode 1, Real (Hz) | 0.2391 | 0.2391 | 0 % |
| Mode 1, Imaginary (Hz) | 1.5775 | 1.5776 | 0.01 % |
| Mode 2, Real (Hz) | 0.5566 | 0.5566 | 0 % |
| Mode 2, Imaginary (Hz) | 2.6926 | 2.6927 | 0.004% |
Conclusion
MotionSolve results compare well with analytical results.