example_IV_4_01 - Example IV.4.1 Find the response of the...

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Example IV.4.1 Find the response of the building shown below for x 0 ( ) = ú x 0 ( ) = 0 and the forcing f t ( ) = f 0 g t ( ) acting on the fourth floor. Recall from our earlier work that the system has the following natural frequencies and (normalized) modal vectors are: ϖ = 0.4912 ; ϖ = 1.4142 ϖ = 2.1667 ; ϖ = 2.6579 f(t) m m m m m 2 3 4 5 1 f(t) f 0 a t g(t)
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first mode,  φ (129 σεχονδμοδε, φ (229 τηιρδμοδε, φ (329 φουρτημοδε, φ (429
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M [ ] ú ú x + K [ ] x = f t ( ) where: f t ( ) = 0 0 f t ( ) 0 ì í ï ï î ï ï ü ý ï ï þ ï ï The uncoupled EOM’s become: ú ú q j + w j 2 q j = ö f j t ( ) where x t ( ) = ÷ f j ( ) q j t ( ) j =1 4 å and the modal forcings are given by: ö f j t ( ) = ÷ f j ( ) T f t ( ) Explicitly we have: ö f 1 t ( ) = 0.5774 f 0 m g t ( ) ö f 2 t ( ) = 0 ö f 3 t ( ) = - 0.5774 f 0 m g t ( ) ö f 4 t ( ) = 0.5774 f 0 m g t ( ) Solving the modal EOM’s using the convolution integral gives:
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This document was uploaded on 12/23/2011.

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example_IV_4_01 - Example IV.4.1 Find the response of the...

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