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Unformatted text preview: 1 Example IV.4.2 Say we reconsider the building problem. Here we will mount an eccentric shaker on the top floor of the building to simulate a modal test of the building. Find the response of the building as a function of the shaker frequency . How would the response change if the shaker were instead mounted on the second floor from the top? The natural frequencies and modal vectors are repeated here: 1 = 0.4912 k/m ; 2 = 1.4142 k/m 3 = 2.1667 k/m ; 4 = 2.6579 k/m P [ ] = (1) , (2) , (3) , (4 ) [ ] = 1 m 0.2280 0.5774 0.6565 0.4285 0.4285 0.5774 0.2280 0.6565 0.5774 0.5774 0.5774 0.6565 0.5774 0.4285 0.2280 1 2 3 4 f t ( ) = Me 2 sin t shaker 2 The EOMs for this model of the building are given by: M [ ] x + K [ ] x = f t ( ) where: f t ( ) = Me 2 1 sin t The uncoupled EOMs become: q j + j 2 q j = f j t ( ) where x t ( ) = j ( ) q j t ( ) j = 1 4 and the modal forcings are given by: f j t ( ) = j ( ) T f t ( ) Explicitly we have: f 1 t ( ) = 4 1 ( ) Me 2 sin t = f 01 sin t f 2 t ( ) = 4 2 ( ) Me 2 sin t = f 02 sin t f 3 t ( ) = 4 3 ( ) Me 2 sin t = f 03 sin t f 4 t ( ) = 4 4 ( ) Me 2 sin t = f 04...
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This document was uploaded on 12/23/2011.
 Fall '09

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