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Dynamic Response of MDOF Structures

Dynamic Response of MDOF Structures. Equilibrium of forces condition gives the equations of motions:. Example : 2-DOF, identical mass & stiffness Free vibration. How do we solve this set of coupled equations?. By observation, the solution should be harmonic.

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Dynamic Response of MDOF Structures

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  1. Dynamic Response of MDOF Structures

  2. Equilibrium of forces condition gives the equations of motions:

  3. Example: 2-DOF, identical mass & stiffness Free vibration How do we solve this set of coupled equations?

  4. By observation, the solution should be harmonic. Substituting into the equations of motion: Need to find non-trivial solution  coefficient matrix has to be singular

  5. Natural frequencies of the 2-DOF system.

  6. 1 2

  7. Example: 5-DOF, identical mass & stiffness Free vibration

  8. Method for Uncoupling the Equations of Motion

  9. Orthogonality Properties of Modeshapes

  10. Scaling the Modeshapes • Arbitrary Set one modeshape coefficient equal to unity (ex: coeff. at roof level = 1.0) Mass normalized

  11. Repeat the 2-DOF example

  12. Forced Vibration modal representation

  13. How to find the initial conditions in the modal space? Premultiply by

  14. Including damping

  15. MDOF Examples

  16. find modes

  17. rad/sec

  18. Mass-normalized modeshapes

  19. 71 72

  20. Example

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