Analysis of harmonically excited building via modal uncoupling

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Here we consider a harmonically-excited (point load on the top floor) four-DOF building model using modal uncoupling. From this procedure we are able to see that the response of the building is dominated by the jth mode when the frequency of excitation is tuned to near the jth natural frequency. Shown below are animations of the building response corresponding to excitation frequencies near the natural frequencies.

When excited near the 2nd natural frequency, you see below that the fourth floor does not move. Why is does this occur?

 

 

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Response near the first natural frequency

 

 

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Response near the second natural frequency

 

 

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Response near the third natural frequency

 

 

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Response near the fourth natural frequency

 

 

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