Dynamic response of mdof structures
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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
Dynamic Response of MDOF Structures



Example 2 dof identical mass stiffness free vibration
Example motions:: 2-DOF, identical mass & stiffness Free vibration

How do we solve this set of coupled equations?


By observation, the solution should be harmonic. motions:

Substituting into the equations of motion:

Need to find non-trivial solution  coefficient matrix has to be singular


Natural frequencies motions:of the 2-DOF system.


1 motions:

2


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




Scaling the modeshapes
Scaling the Modeshapes motions:

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



Forced vibration
Forced Vibration motions:

modal representation




Mdof examples
MDOF Examples motions:


find modes motions:


rad/sec motions:



71 motions:

72


Example
Example motions:


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