Response to a forced 2 DOF system

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SUMMARY

The discussion centers on solving a forced 2 degree of freedom (DOF) system to find steady state responses using MATLAB. The user has established the equations of motion and identified the mass [m], stiffness [k], damping [c], and force {f} matrices. However, they encounter difficulties in uncoupling the equations through eigen analysis due to a non-symmetric stiffness matrix. An alternative method mentioned is the matrix inversion technique, which successfully resolves the issue.

PREREQUISITES
  • Understanding of forced 2 degree of freedom systems
  • Familiarity with equations of motion (EOMs)
  • Proficiency in MATLAB for numerical analysis
  • Knowledge of eigen analysis and matrix operations
NEXT STEPS
  • Explore MATLAB's matrix inversion techniques for system decoupling
  • Research methods for analyzing non-symmetric stiffness matrices
  • Learn about alternative numerical methods for solving coupled systems
  • Investigate the use of modal analysis in multi-DOF systems
USEFUL FOR

Mechanical engineers, control system analysts, and researchers working on dynamic systems and vibration analysis will benefit from this discussion.

castwerks
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I have a forced 2 degree of freedom system that I am trying to find the steady state responses to. I have determined the two equations of motions and found the [m], [k], [c], and {f} matrixes.

However when i try to use eigen analysis ( q=phi'*[m]*phi ) I am unable to uncouple the two equation of motion to allow me to solve the system as two independ. single degree of freedom systems.

I believe I have correctly set up the EOMs... what other methods can I use to solve for the x and y steady state responses.

PS i am using matlab.
 
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What is your system? Are you sure it is possible to decouple the two equations?

-Kerry
 
i guess it is impossible to uncouple the system (non symetric striffness matrix)... i think i figured it out by matrix inversion method
 

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